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Concurrent Reinforcement Schedules for Problem Behavior and Appropriate Behavior: Experimental Applications of the Match...

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 Title Page
 Dedication
 Acknowledgement
 Table of Contents
 List of Tables
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 Abstract
 Introduction
 Experiment 1: Functional analysis...
 Experiment 2: Analysis of concurrent...
 General discussion
 References
 Biographical sketch
 

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CONCURRENT REINFORCEMENT SCHEDULES FOR PROBLEM BEHAVIOR AND APPROPRIATE BEHAVIOR: EXPERI MENTAL APPLICATIONS OF THE MATCHING LAW By CARRIE S. W. BORRERO A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2006

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Copyright 2006 by Carrie S. W. Borrero

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To my grandmothers, Grace Geraci Lipari and Dorothy Walsh Wright.

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iv ACKNOWLEDGMENTS I would like to thank those i ndividuals who helped make th is dissertation possible. First, I thank Dr. Timothy Vollmer, my s upervisory committee chair, for his support during the course of my gradua te training. He has provided invaluable advice on this and other projects. I also thank Dr. Maureen Conroy, Dr. Jesse Dallery, Dr. Brian Iwata and Dr. Christina McCrae for their assistance. Additional thanks are extended to my husband and daughter, John and Isabella Borrero; my parents, Donald and Santa Wright, and my brother, Christian Wright, for their love a nd support, without wh ich I could not have conducted this research. Finally, I would lik e to thank Jason Bourret, Monica Francisco, Andrew Samaha, and Kimberly Sloman, w ho assisted in vari ous aspects of the development, implementation, and data analysis for this project.

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v TABLE OF CONTENTS page ACKNOWLEDGMENTS.................................................................................................iv LIST OF TABLES.............................................................................................................vi LIST OF FIGURES..........................................................................................................vii ABSTRACT.....................................................................................................................viii CHAPTER 1 INTRODUCTION........................................................................................................1 Definition and Hist orical Overview..............................................................................2 2 EXPERIMENT 1: FUNCTIONAL ANAL YSIS OF PROBLEM BEHAVIOR........12 Method........................................................................................................................12 Participants..........................................................................................................12 Setting..................................................................................................................12 Procedure.............................................................................................................13 Results and Discussion...............................................................................................16 3 EXPERIMENT 2: ANALYSIS OF CONCURRENT SCHEDULES OF REINFORCEMENT AND TREATMEN T OF PROBLEM BEHAVIOR................22 Method........................................................................................................................22 Participants..........................................................................................................22 Setting..................................................................................................................22 Procedure.............................................................................................................23 Results and Discussion...............................................................................................28 4 GENERAL DISCUSSION.........................................................................................57 LIST OF REFERENCES...................................................................................................65 BIOGRAPHICAL SKETCH.............................................................................................70

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vi LIST OF TABLES Table page 4-1 Summary of correlation coefficients (r) for all participants using the Simple Matching Equation and the coefficients of determination using the (r2) Generalized Matching Equation...............................................................................64

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vii LIST OF FIGURES Figure page 2-1 Overall response rates for Greg and A lice during the functional analysis phase.....20 2-2 Within session response rates for Audrey during the functional analysis phase.....21 3-1 Overall response rates for problem and appropriate behavior for Greg...................46 3-2 Overall response rates for problem a nd appropriate behavior during the assessment phase for Audrey and Alice...................................................................47 3-3 Scatterplots of observed and predic ted response allocati on between problem behavior and appropriate behavior for Greg for each condition during the tangible assessment..................................................................................................48 3-4 Log response ratios plotted against log reinforcer ratios for Greg. The linear equation depicts slope and bias during all conditions of the tangible assessment...49 3-5 Scatterplots of observed and predic ted response allocati on between problem behavior and appropriate be havior for Greg for all conditions during the escape assessment................................................................................................................50 3-6 Log response ratios plotted against log reinforcer ratios for Greg. The linear equation depicts slope and bias during all conditions of the escape assessment.....51 3-7 Scatterplots of observed and predic ted response allocati on between problem behavior and appropriate be havior for Audrey during the tangible assessment......52 3-8 Log response ratios plotted against log reinforcer ratios for Audrey. The linear equation depicts slope and bias during all conditions of the tangible assessment...53 3-9 Scatterplots of observed and predic ted response allocati on between problem behavior and appropriate behavior for Alice during the escape assessment............54 3-10 Log response ratios plotted against log re inforcer ratios for Alice. The linear equation depicts slope and bias during all conditions of the escape assessment.....55 3-11 Scatterplots depicting ex amples of closer approximations to matching towards the end of the condition using the simple matching equation. Arrows show the first and last sessions within a condition..................................................................56

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viii Abstract of Dissertation Pres ented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy CONCURRENT REINFORCEMENT SCHEDULES FOR PROBLEM BEHAVIOR AND APPROPRIATE BEHAVIOR: EXPERI MENTAL APPLICATIONS OF THE MATCHING LAW By Carrie S. W. Borrero December 2006 Chair: Timothy R. Vollmer Major Department: Psychology The purpose of this study was to dete rmine if children who exhibit problem behavior would allocate res ponding in direct proportion to experimentally arranged reinforcement rates. Relative reinforcer rate s were manipulated to evaluate changes in relative response rate on concur rent variable-interval (VI) schedules, and results were interpreted using two iterations of the matc hing equation: the strict (simple) matching equation (Herrnstein, 1961) and the genera lized matching equation (Baum, 1974a). Three individuals diagnosed with developmen tal disabilities, who engaged in severe problem behavior, participated. In Experime nt 1, functional analyses were conducted to determine the reinforcers for problem behavior Results showed that problem behavior was sensitive to social positive reinforcement in the form of access to tangible items and social negative reinforcement in the form of escape from instructional demands for one participant, social positive reinforcement in the form of access to tangible items for

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ix another, and social positive reinforcement in the form of attenti on and social negative reinforcement in the form of escape from instructional demands for the third participant. In Experiment 2, concurrent schedules of re inforcement were in place for both problem and appropriate behavior. Results showed that the relative rates of responding approximated the relative rates of reinforcement. In addition, interventions for problem behavior were evaluated, and differential re inforcement of alternative behavior (DRA) and extinction (EXT) procedures were implem ented to increase the rate of appropriate behavior and decrease the rate of problem behavior.

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1 CHAPTER 1 INTRODUCTION Choice has been defined as the emission of one of two or more alternative and usually incompatible responses (Catania 1998). Typical laboratory arrangements implement concurrent-schedules with two or more alternatives, with each alternative correlated with a reinforcement schedule. Herrnstein (1961) provi ded a quantitative description of responding on concurrent sc hedules of reinforcement, known as the matching law. Generally, the matching law st ates that the relative rate of responding on one alternative will approximate the relative rate of reinforcement provided on that alternative. Baum (1974a) provided an alte rnative formulation of the matching law, known as the generalized matching law that accounted for deviations from strict matching by incorporating a bias parameter and a sensitivity parameter. The matching law has been evaluated in a number of investigations using both nonhumans (Baum; Baum, 1974b; Baum, 1979; Belke & Belliveau, 2001; Crowley & Donahoe, 2004; Herrnstein; Herrnstei n & Loveland, 1975; MacDonall, 1988, McSweeney, Farmer, Dougan, & Whipple, 1986) and humans (e.g., Borrero & Vollmer, 2002; Mace, Neef, Shade, & Mauro, 1994; Martens & Houk, 1989; McDowell, 1981; Neef, Mace, Shea, & Shade, 1992; Oliver, Hall, & Nixon, 1999; Symons, Hoch, Dahl, & McComas, 2003; Vollmer & Bourret, 2000). Previous research with humans has included both experimental and descrip tive analyses of re sponding however, the experimental evaluations of the matching law have evaluated academic responding (Mace

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2 et al.; Neef & Lutz, 2001; Neef, Mace & Shade, 1993; Neef, Shade & Miller, 1994), while the descriptive studies (Borrero & Vo llmer; Martens & Houk; McDowell; Oliver et al.; Symons et al.) have focused on severe problem behavior such as aggression, property destruction, and self-injurious behavior (SIB). The present study involved experimental analyses of responding on concurrent rein forcement schedules for individuals with developmental disabilities who engaged in se vere problem behavior. Results were then evaluated using both the simple (Herrnstein) and generalized (Baum) matching equations. Definition and Historical Overview Herrnstein (1961) evaluated the effects of relative reinforcement frequency on relative response frequency usi ng concurrent variable-interva l (VI) schedules. Initially, training was conducted with 3 pigeons in orde r to establish key-pecking and alternation of responding between two keys. Followi ng training, pigeons were exposed to a sequence of concurrent VI sc hedules for both keys: VI 3 min VI 3 min, VI 2.25 min VI 4.5 min, VI 1.8 min VI 9 min, and VI 1.5 min extinction (EXT). During most of the experiment, a change-over delay (COD) was implemented such that when pigeons switched keys, no reinforcer was possible for 1.5 s. Herrnstein plotted the percentage of responses across the percentage of reinfor cements provided for that alternative and demonstrated that the relative response rate increased as the relative reinforcement rate increased in a linear relationship. In addi tion, Herrnstein found that the COD had three effects on responding: (a) when the COD was in effect, switching between the two keys decreased, and (b) only when the COD was in effect did unequal reinforcement schedules on the two keys reduce switching, and (c) when the COD was not present, as compared to when the COD was present, matching was not obtained for two pigeons.

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3 Herrnstein (1961) described the relative rate of responding and the relative rate of reinforcement with the following Equation (1-1): R 1 R 1 R 2 r 1 r 1 r 2 where, R1 refers to the rate of res ponding on one alternative, and R2 refers to the rate of responding for a second alternative, while r1 is the rate of reinforcement for one alternative (R1) and r2 is the rate of reinforcement for the second alternative (R2). Results suggested that relative res ponse rate increased as a f unction of relative rate of reinforcement, although this result was only observed when the COD was in place. Baum (1974b) presented a variation of the matching equation now known as the Generalized Matching Equation. The Genera lized Matching Equation may be expressed as follows (Equation 1-2): log B1B2 a log R1R2 log b where B1 and B2 refer to the frequency of re sponding on the alternatives, and R1 and R2 represent the relative rates of reinforcemen t from each alternative. The generalized matching equation takes into account bias ( b ) and the slope ( a ) of the function, which provides information regarding sensitivity. These additional parameters provide information useful in determining if undermatch ing or bias occur. Undermatching refers to less than a one-unit increas e in log ratio of responding pr oduced by a one-unit increase in log ratio of reinforcement. When underm atching occurs, the slope is less than 1. Baum (1974b) suggested several factors that may lead to undermatching, including (a) poor discrimination (e.g., the organism does not discriminate between the two schedules), (b) absence of a COD, and (c ) states of deprivation.

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4 Bias refers to systematic deviations in re sponding that cannot be attributed to the relative reinforcement rates. When bias occurs, b differs from 1. If b is less than 1, this suggests that the organism favors the response in the denominator (B2). If b is greater than 1, this suggests that the organism favors the response in the numerator (B1). Baum (1974b) described factors that may lead to bias including (a) re sponse bias (e.g., one response may be more effortful than the other, color preferences, et c.), (b) a discrepancy between scheduled and obtained reinforcemen t, (c) qualitatively different reinforcers (e.g., hugs vs. reprimands, hemp vs. grain), a nd (d) qualitatively different schedules (e.g., VI vs. fixed-ratio [FR]). A number of applied studies have evaluated naturally occu rring situations using the matching law. McDowell (1981) applied the single alternative formulation of the matching law (Herrnstein, 1970) to evaluate data originally reported by Carr and McDowell (1980). The single alternative fo rmulation of the matching law may be expressed as follows (Equation 1-3): R k r r r e where R represents response rate, and r represents reinforcement rate for singlealternative environments. The parameter k is the y-asymptote and represents the total amount of behavior in which the organism can engage. Finally, re represents all other reinforcement not represented by r, and desc ribes how quickly the function reaches its asymptote. The larger the re, the more slowly the asymptot e is reached, and generally, a larger re value suggests a richer environment. McDowell (1981) evaluated self-injurious scratching displayed by an 11 year-old boy. In the initial investigation by Carr and McDowell (1980), the rates of self-

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5 scratching and verbal reprimands were record ed during naturalistic observations between the boy and his parents. Next, the research ers conducted an assessment and determined that verbal reprimands reinforced self-s cratching. Finally, they implemented an intervention including a time-out compone nt and a positive reinforcement component, which decreased self-scratching. McDowell evaluated the data from the naturalistic situation, and found that the boy s naturally occurring rates of self-scratching conformed to Equation 3 as a function of adult attention. The single al ternative formulation of the matching law accounted for 99.67% of the varian ce in the rate of scratching observed, and the results suggested Equation 3 provide d a comprehensive description for human behavior occurring in a non-la boratory environment (i.e., the natural environment). In a related study, Martens and Houk (1989) evaluated the single alternative formulation of the matching law to describe disruptive behavior and academic responding in a classroom setting, with an 18-year-o ld woman diagnosed with developmental disabilities and the staff in her classroo m. They evaluated matching based on time allocation between disruptive behavior (e.g., vocal outbursts, skin picking, off-task behavior, etc.) and on-task behavior (e.g., i ndependent work, compliance with requests, and instructional interactions). Attention de livered from the teacher or classroom aide was presumed to be a reinforcer by way of correlational analyses. Results showed that the matching equation was useful in descri bing response allocation between the two alternatives as a function of adult attention, and account ed for 83% of the variance observed in disruptive behavior. Oliver et al. (1999) evaluated time al location between problem behavior (i.e., aggression) and communicativ e behavior (e.g., sign language) with a 7-year-old boy

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6 diagnosed with Down syndrome. First, the researchers conducted a descriptive analysis in the classroom across various activities. Th ey then conducted an experimental analysis using procedures similar to those descri bed by Carr and Durand (1985) to identify reinforcers for aggression. Based on the resu lts from the descriptive and experimental analyses, Oliver et al. conc luded that the boys aggression was reinforced by escape from instructional demands. Finally, the researchers applied variat ions of the simple (1) and generalized matching equations (2) in whic h time allocation (and not response rate) was evaluated as a function of duration (and not rate) of reinforcement (e.g., Baum & Rachlin, 1969). There are two potential limitations to the investigations described above. First, Martens and Houk (1989) did not confirm that attention was in fact a reinforcer for problem behavior. Research on functiona l analysis methods (see Hanley, Iwata & McCord, 2003, for a recent review) demonstrates the utility of identifying events as reinforcers, and it is not necessary to assume an event is a reinforcer. Although Oliver et al. (1999) did conduct experiment al manipulations in an effo rt to identify reinforcers using methods described by Carr and Durand (1985), they did not experimentally manipulate consequences for problem behavior Second, functional an alysis research has demonstrated that problem behavior may be multiply controlled by several sources of reinforcement, including access to tangible items and escape from instructional activities. The studies by McDowell (1981) and Marten s and Houk did not take into account whether problem behavior was sensitive to additional sources of reinforcement. To address these potential limitations, Borrero and Vollmer (2002) conducted an investigation to evaluate the matching law by identifying reinforcers for problem

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7 behavior using the functional analysis method of behavioral assessm ent, and interpreting descriptive analysis data using identified reinforcers. The researchers conducted descriptive analyses in an inpatient hospital setting or classroom setting for 4 individuals diagnosed with developmental disabilities. All participants engage d in severe problem behavior (e.g., property destru ction, aggression, and SIB) as well as appropriate behavior (e.g., vocal requests, gestures, and complian ce with instructional demands). Next, Borrero and Vollmer conducted functional anal yses using procedures similar to those described by Iwata, Dorsey, Slifer, Baum an, and Richman (1982/ 1994) and identified reinforcers for problem behavior for all pa rticipants. Finally, they evaluated the descriptive data using both the simple a nd generalized matching equations (Equations 1 and 2). Results showed that the relative ra te of problem behavior approximately matched the relative rate of reinforcement for problem behavior for all partic ipants. In addition, they evaluated multiple sources of reinforcement based on the results from the functional analysis and found that responding was better described by the matching equation when several possible sources of reinforcemen t were included in the analysis. Additional research on the matching law w ith individuals who engage in problem behavior has also included analyses of be havior occurring during naturally occurring interactions (e.g., St. Peter et al., 2005) however no expe rimental analysis of the matching law has been conducted for such indivi duals. As noted previously, the majority of descriptive research eval uating the matching law has involved evaluations of problem behavior, while experimental research has largely focused on academic tasks (e.g., Mace et al., 1994; Neef et al., 1993; Neef et al., 1992; Neef et al., 1994).

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8 Neef et al. (1992) conducted an investigation to de monstrate that (a) human behavior is sensitive to concu rrent schedules of reinforcement when reinforcer quality is held constant, as suggested by the matching law and (b) the matching relation would not occur when reinforcer quality was not equa l, and that a bias for the higher quality reinforcer would occur. The participants were individuals diagnosed with emotional disturbances and learning difficulties. Prior to each session, the participant was asked if she preferred to work for nickels or tokens During each session, identical stacks of arithmetic problems were placed in front of th e participant, where each stack of cards was associated with a VI schedule of reinfor cement (e.g., VI 30-s, VI 120-s), and correct responses resulted in reinforcement (e.g., nick els or tokens) deliver ed according to the schedule in place for that alternative. Initially, sessions were conducted to identify the participants sensitivity to the VI schedules of reinforcement, and a timer was included to signal the amount of time remaining in the reinforcement interval. Neef et al. (1992) then evaluated two additional conditions: (a) equal-quality rein forcers, during which two stack s of cards were presented on concurrent VI schedules, and the reinfor cers delivered were the same (i.e., either nickels or tokens were delivered for bot h alternatives), a nd (b) unequal-quality reinforcers, during which two stacks of cards were presented on concurrent VI schedules, and high-quality reinforcers were delivered on the leaner schedule of reinforcement (i.e., VI 120-s) and low-quality reinforcers we re delivered on the richer schedule of reinforcement (i.e., VI 30-s). During the initial condition, respondi ng was not allocated as would be predicted by the concurrent VI schedules until the timer was included to signal the reinforcement intervals. For all participants, time-allocation matching occurred

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9 following the introduction of the timer. Duri ng the equal-quality reinforcers condition, matching was observed, with the time allocat ed to each response alternative closely approximating the obtained reinforcement from that alternative. During the unequalquality reinforcers condition, matching wa s not observed, and responding suggested a preference for one of the two alternatives (i.e ., nickels or tokens) fo r two participants, or responding that maximized the number of rein forcers for that alternative, for one participant. This study provided support for th e applicability of the matching relation to socially significant human behavior, a nd highlighted some potentially important considerations, includ ing the use of additional procedur al manipulations (e.g., timer to signal reinforcement intervals) to improve discrimination between concurrent VI schedules, and biased responding, which may occu r if the quality of available reinforcers is not equal. Using the same general procedures describe d in prior work (i.e., Neef et al., 1992), Neef and colleagues (Mace et al., 1994; Neef et al., 1993; N eef et al., 1994) extended the work reported by Neef et al. (1992) and showed that response allocation under concurrent VI schedules was also sensitive to additional reinforcement parameters including reinforcer delay. Because this series of experiments involved academic behavior of individuals with emotional a nd learning disabilities the gene rality of the matching law was extended to socially signifi cant (appropriate) behavior. Collectively, previous research suggests a need for an experimental analysis of severe problem behavior exhibited by indivi duals with developmenta l disabilities, under concurrent reinforcement schedules, usi ng the matching law (Baum, 1974a, Herrnstein, 1961) as a conceptual framework. Prior re search has supported the matching law as a

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10 description of behavior acro ss a number of settings, incl uding the nonhuman laboratory, natural environment, the human laboratory, a nd instructional situa tions. The purpose of this dissertation was to conduct experimental analyses of problem behavior with 3 individuals diagnosed with developmental di sabilities who engaged in severe problem behavior. In Experiment 1, functional analyses were conduc ted for all participants to identify reinforcers for problem behavior. Specifically, conditions were included to determine if problem behavior was sensitive to (a) social positive reinforcement, including adult attention or access to preferred tangible ite ms (e.g., toys, edible items, etc.), (b) social negative reinforcement, in cluding escape from inst ructional demands or aversive situations (e.g., hygien e tasks, daily livin g skills, etc.), or (c) automatic reinforcement, suggesting that the reinfor cer for problem behavior is not sociallymediated (e.g., sensory reinforcem ent, pain alleviation, etc.). In Experiment 2, concurrent schedules of reinforcement were introduced for problem behavior and appropria te behavior (using reinforc ers previously identified in Experiment 1). Appropriate behavior wa s identified during formal descriptive observations of each participant as well as during the functional analysis, and included requests for access to tangible items (e.g., usi ng picture cards, sign language, or vocal requests), compliance with in structions, and gestures toward tangible items (e.g., reaching for items, pointing to objects, etc.). For each participant, concurrent schedules of reinforcement were arranged for problem be havior and appropriate behavior, with one schedule being richer than the other (i.e., mo re reinforcement was available for either problem or appropriate behavior), or the schedules being equal (2 participants). Following changes in responding with expos ure to the schedule arrangement, the

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11 schedules for problem and appropriate behavior were switched. That is, if the initial phase included a VI 20-s schedule for probl em behavior and a VI 60-s schedule for appropriate behavior, the sche dules were switched during the second phase such that a VI 60-s schedule was in place for problem behavi or and a VI 20-s schedule was in place for appropriate behavior. Additional replications for all phases were conducted. Finally, for all participants, an intervention phase was included to decrease problem behavior, including a continuous reinforcement schedu le (CRF) for appropriate behavior, and extinction (EXT) for all problem behavior. That is, during the intervention phase, all instances of appropriate behavior resulted in access to the reinforcer, and all instances of problem behavior did not result in access to the reinforcer. The goa l of the intervention phase was to reduce problem behavior to clin ically significant levels and increase levels of appropriate behavior.

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12 CHAPTER 2 EXPERIMENT 1: FUNCTIONAL ANAL YSIS OF PROBLEM BEHAVIOR Method Participants Three individuals diagnosed with developm ental disabilities who engaged in severe problem behavior participated. Greg was an 8-year-old boy diagnosed with mild mental retardation and autism. His problem be havior included screaming, defined as vocalizations at a volume louder than convers ation level, and disrupt ive behavior, defined as throwing, hitting, or kicking objects. Audr ey was a 14-year-old female diagnosed with mental retardation. Her problem behavior incl uded SIB, defined as hitting her chin, nose and face with a closed fist, as well as se lf-choking (i.e., pushing her fingertips into her throat). Alice was a 13-year-old girl w ho was diagnosed with childhood disintegrative disorder. Her problem behavior included disruption, defined as throwing objects, and aggression, defined as hi tting and kicking others. Setting For Greg and Alice, functional analyses were conducted on an inpatient hospital unit for the assessment and treatment of problem behavior at the University of Florida. All sessions were conducted in a room with a table and chai rs. Audreys assessment was conducted at a local school, and sessions were conducted in an available classroom, furnished with desks and chairs.

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13 Procedure All sessions were conducted by trained gradua te students serving as experimenters. Observers were graduate and undergraduate students who received in-vivo training in behavioral observation and had previously demonstrated high interobserver agreement (IOA) scores (> 90%) with trained observers. Observers in the hospital setting were seated behind a one-way mirror or sat unobtru sively at a table in the room. In the classroom setting, observers were seated unobt rusively at a desk in the classroom. Observers collected data on personal digital as sistants (PDA) that provided real-time data and scored events as either frequency (e .g., aggression, disruption, SIB, and screaming), or duration (e.g., delivery of a ttention, escape from instructio ns, etc.). Sessions were conducted two to three times each day, four da ys per week, and were 10 min in duration (with the exception of one cont rol session for Audrey). Stimulus Preference Assessment Prior to the functiona l analyses, free-operant stimulus preference assessments were conduc ted using procedures described by Roane, Vollmer, Ringdahl, and Marcus (1998) to iden tify preferred items to be included in the conditions of the functional analysis, for each pa rticipant. An array of 6-8 leisure items (e.g., musical keyboard, drawing toys, music, et c.) was placed on the floor or a table. Before beginning the assessment, the particip ant was shown the item and allowed brief (i.e., 2-3 s) contact with the item. The particip ant was then told that he or she could play with any of the items, and the duration of tim e the participant interacted with each item was scored. Preferred items were considered to be the three items for which interaction was of the greatest duration. Functional analysis. Functional analyses were conducted using procedures similar to those described by Iwata et al (1982/1994). Four test conditions were

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14 compared: (a) attention, (b) tangible, (c) escape, and (d) no consequence (Audrey and Alice only), to a control condition (play) using a multielelement design for all participants. Consequences for problem beha vior were provided contingent on screaming or disruption (Greg), SIB (Audrey), and aggression or disruption (Alice). During the attention condition, the particip ant was provided with preferred tangible items, and no demands were presented, while th e therapist diverted her attention to a work task. Contingent on problem behavior brief attention was provided for 30 s and consisted of a reprimand (e.g., Dont do that) followed by the therapist conversing with the participant. This condition was include d to determine if problem behavior was reinforced by adult attention. During the tangible condition, the pa rticipant was provided with adult attention and no demands were presen t, while the therapist restricted access to preferred tangible items. Contingent on probl em behavior, access to preferred items was provided for 30 s. This condition was includ ed to determine if problem behavior was reinforced by access to tangible items. During the escape condition, the therapist provided instructional demands (e.g., brushing teeth, washing face, combing hair, folding towels) using a three-prom pt instructional sequence (Horner & Keilitz, 1975). Contingent on problem behavi or, a 30-s break from instruct ions was provided and the task materials were removed. This conditi on was included to determine if problem behavior was negatively reinforced by escap e from instructional demands. During the no consequence condition (Audrey and Alice onl y) all preferred ta ngible items were removed, and the participant received no atten tion from the therapist. There were no programmed consequences for problem beha vior. This condition was included to determine if problem behavior persisted in the absence of programmed social

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15 consequences. Finally, during the contro l condition, the participant had continuous access to preferred tangible items, no dema nds were present, and adult attention was provided at least every 30 s. There were no programmed consequences for problem behavior. This condition was included as a point of comparison to the test conditions. Interobserver agreement (IOA). Two independent observers collected data on aggression, disruption, scream ing, and SIB for a proportion of functional analyses sessions to assess interobserver agreement (IOA) In addition, observers collected data on the delivery of attention, access to tangi ble items, and escape from instructional demands, and IOA was assessed. Observations were divided into 10-s bins, and the number of observed responses was scored for each bin. The smaller number of observed responses within each bin was divided by th e larger number of observed responses and converted to agreement percentages for fr equency measures (Iwata, Pace, Kalsher, Cowdery, & Cataldo, 1990). Agreement on th e nonoccurrence of beha vior within any given bin was scored as 100% agreement. The bins were then averaged across the session. In a session, the smaller number of s was divided by the larger number of s for duration measures (and agreement on the nonoccu rrence of behavior within any bin was scored as 100% agreement). The bin data we re then averaged across the sessions. For Greg, IOA was scored for 53% of functional analysis sessions, and averaged 98.7% for disruption (range, 96% to 100%), and 94.4% for screaming (range, 84% to 100%). IOA averaged 100% for therapist attention, and 97% for access to tangible items (range, 91.1% to 100%), and 99.8% for escape from instructions (range, 99.4% to 100%). For Audrey, IOA was scored for 28% of functional analysis sessions, and averaged 94% for SIB (range, 76% to 100%). IOA aver aged 88% for therapist attention (range,

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16 11% to 100%), 98% for access to tangible items (range, 92% to 100%), and 97% for escape from instructions (range, 86% to 100%). For Alice, IOA was scored for 42% of f unctional analysis sessions, and averaged 98.5% for aggression (range, 93% to 100%) and 98% for disruption (range, 95% to 100%). IOA averaged 82.75% for therapist attention ( range, 26% to 100%), 87% for access to tangible items (range, 1% to 100%), and 94% for escape from instructions (range, 80% to 100%). Results and Discussion Figure 2-1 shows the results of the functiona l analyses for Greg and Alice. Panel A of Figure 2-1 shows responses per min (rpm) of screaming for Greg. The highest rates of screaming occurred in the tangible condition, with a mean response rate of 1.68 rpm, as compared to the attention ( M = .05 rpm), escape ( M = .34 rpm), and control ( M = 0 rpm) conditions. These results suggested that Gr egs screaming was reinforced by access to tangible items. In addition, for Greg, Panel B of Figure 2-1 shows the responses per min of disruption. The highest ra tes of disruption were observe d during the escape condition, with a mean response rate of .4 rpm, as comp ared to the attention, tangible, and control conditions, which all had 0 rpm of disrupti on. Although the rate was low even in the escape condition, the behavior was correla ted with demand presentation and never occurred in conditions other than escape. Th ese results suggested that Gregs disruption was reinforced by escape from instructional demands. In Gregs case, screaming and disruption served different operant functions. Panel C of Figure 2-1 shows th e results of Alices functi onal analysis. The highest rates of aggression and disruption were observed during the escape ( M = .7 rpm) and attention ( M = .6 rpm) conditions, when compared to the no consequence ( M = 0 rpm),

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17 tangible ( M = .05 rpm), and control ( M = .05 rpm) conditions. These results suggested that Alices aggression and di sruption were reinforced by adult attention, and escape from instructional demands. Data were colle cted for aggression and disruption separately and similar results were obtained, therefore both topographies were combined in this analysis. That is, there was no evidence to suggest that a ggression or disruption served distinct functions. For Audrey, SIB rates seemed to carry ove r from one session to the next. As a result, overall session mean rates looked similar across condi tions even though the therapists reported what seemed to be obvi ously different effects of the functional analysis conditions. Because extinction bursts and carryover effects may have influenced overall session mean rates, a within-session (min-by-min) analysis was used to identify the operant functions of her SIB (Vollmer Iwata, Zarcone, Smith, & Mazaleski, 1993 ) Figure 2-2 shows the within-session results from Audreys functional analysis. The very first session was a no consequence sessi on. However, prior to the session a therapist removed access to tangible items. She engaged in a burst of SIB and reaching for the items that persisted th rough the first session. A similar burst was seen in the second no consequence session (seventh overall session); however, by the end of the session SIB had extinguished. A third no consequence session conducted immediately thereafter produced very low rates. Thus, although high mean rates of SIB were observed in two no consequence sessions, the with in-session data suggest th at the behavior was not automatically reinforced. In all three tangibl e sessions, SIB occurred at very stable rates and occurred almost immediately upon removal of the tangible items. The SIB would characteristically stop when the tangible items were returned to her. This effect resulted

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18 in a SIB rate of approximately 2.0 per min (the same rate at which the establishing operation was put in place). Rates of SIB were high in the escape condition and were highly correlated with demands. By the sec ond escape session (twelfth overall session), she had become more efficient and engage d in minimal SIB, primarily when demands were presented. Rates of SIB were zero in a ttention sessions (possibl y a false negative if the reinforcing effects of attention were outweighed by continuous access to tangibles, but this possibility was not evaluated). Occasional bursts occurred at the beginning of control sessions but the rate almost always waned by the end of the session. Overall the functional analysis data sugge sted that Audreys SIB was reinforced by escape and access to tangibles. It is possible that SIB would have been influe nced by attention if preferred tangibles were not included in her sessions, but for the purposes of this study it was important to identify at least one source of reinforcement for SIB and a more detailed evaluation of attention was not pursued. In summary, results of Experiment 1 identi fied the socially-mediated reinforcers for the problem behavior exhibi ted by three individuals diagnosed with developmental disabilities. For all participants, problem behavior was multiply controlled; that is, problem behavior was reinforced by more th an one type of event. Two individuals engaged in problem behavior reinforced by access to tangibles, one engaged in problem behavior reinforced by adu lt attention, and all three e ngaged in problem behavior reinforced by escape from instructional demands. This experiment was a necessary prerequisite to Experiment 2. The results of Experiment 1 provided a basis for Experiment 2, during which concurrent reinforcement schedules were in place for both problem and appropriate

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19 behavior. Such analyses would not have been possible without identifying the function(s) of problem behavi or. In Experiment 2, we attempted to evaluate how responding would be allocated between concu rrent schedules of reinforcement. In addition, for all participants, we eventually conducted inte rventions to reduce problem behavior to low levels and incr ease appropriate behavior.

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20 0 1 2 3Responses per Min (Scream)5101520 0 1 2 3Response per Min (Disruption)5101520 0 0.2 0.4 0.6 0.8 1 Responses per Min (Aggression & Disruption)5101520 Sessions Tangible Escape Attention Greg Greg Alice A B C Figure 2-1. Overall response rates for Greg and Alice during the functional analysis phase. A) Responses per min of scream ing for Greg. B) Responses per min of disruption for Greg. C) Responses pe r min of disruption and aggression for Alice.

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21 0 5 10 15 20Responses (SIB) Minutes No Cons. Control Attention EscapeAudrey Control AttentionControl TangibleEscape ControlControl No Cons.No Cons. TangibleTangibleA Figure 2-2. Within session response rates fo r Audrey during the functional analysis phase. A) Responses per minute of se lf-injurious behavior for Audrey.

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22 CHAPTER 3 EXPERIMENT 2: ANALYSIS OF CONCURRENT SCHEDULES OF REINFORCEMENT AND TREATMEN T OF PROBLEM BEHAVIOR Method Participants Participants were the same three indivi duals who participated in Experiment 1. Problem behavior was defined for each partic ipant as in Experiment 1, and appropriate behavior was also assessed for each participan t. Gregs appropriate behavior was defined as vocal requests for preferred tangible items (e.g., Toys), and compliance with instructional demands (e.g., hygiene tasks). A udreys appropriate be havior was defined as requests for preferred tangible items (e.g., reaching for item). Alices appropriate behavior was defined as requests for a break from instructional demands through the use of a microswitch. When Alice touched the microswitch, a recorded message (e.g., Break, please) played. Due to clinical exigencies, Audreys escape behavior and Alices attention maintained behavior were addr essed outside the context of this research. Setting The setting was the same as in Experime nt 1. For two participants (Greg and Alice), analyses were conducted on an inpa tient hospital unit for the assessment and treatment of problem behavior. For one part icipant (Audrey), the analysis was conducted at a local school, in an available classr oom, furnished with desks and chairs.

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23 Procedure Trained graduate students serv ed as experimenters for all sessions. Observers were graduate and undergraduate students who r eceived in-vivo training in behavioral observation and who had previously demonstrat ed high interobserver agreement scores (> 90%) with trained observers. Observers in the hospital setting were seated behind a oneway mirror or sat unobtrusively at a table in the room. In th e classroom setting, observers were seated unobtrusively at a desk in the classroom. Ob servers collected data on PDA that provided real-time data and scored ev ents as either fre quency (e.g., aggression, disruption, SIB, and screaming), or duration (e.g., delivery of attention, escape from instructions). Sessions were conducted two to three times each day, four days per week, and lasted 10 min. All participants were exposed to an initial baseline condition, which was selected based on the results of Experiment 1. Each participant was exposed to four conditions using a reversal de sign in order to assess respons e allocation for both problem behavior and appropriate behavi or on concurrent schedules of reinforcement. The order of the conditions varied slightly for each participant, and was assigned randomly. Baseline. The baseline condition was identical to the condition(s) associated with problem behavior during the functional anal ysis. These conditions varied for each participant, and included the tangible condition for Greg, the tangible condition for Audrey, and the escape condition for Alice. During baseline, each instance of problem behavior resulted in delivery of the reinfor cer (i.e., access to tangible items for Greg and Audrey, or escape from instructions for Alic e). No programmed c onsequences were in place for appropriate behavior; that is, instances of appropriate behavi or did not result in access to the reinforcer.

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24 Matching Analysis. Concurrent schedules of reinforcement were in place for both problem and appropriate behavi or (e.g., VI 10-s VI 10-s, VI 20-s VI 60-s) during the analysis. The intervals were timed using a computer program that signaled (to observers) when each schedule had elapsed. When reinfo rcement was available for a response (i.e., the interval elapsed) an observer signaled the therapist by holding up a colored card to signal available reinforcement for a given re sponse (e.g., blue card for problem behavior, yellow card for appropriate behavior). An attempt was made to always keep the card display outside of the participants line of vision. The first instance of behavior following availability of a reinforcer resulted in delivery of the preferred tangible item for 30 s. After 30 s of reinforcer access, the it em was removed and the timer was reset for that response. Participants were exposed to a subset of conditions, including either the problem behavior (rich) or e qual concurrent schedules, and a ppropriate behavior (rich). Problem behavior (rich). The analysis conditions included concurrent VI schedules for both responses: problem be havior and appropria te behavior. The problem behavior (rich) condition (Greg only) was concurrent VI schedules (i.e ., VI 20-s VI 60s), in which, the higher rate of reinforcement (i.e., VI 20-s schedule) was associated with problem behavior while the lower rate of reinforcement (i.e., VI 60-s schedule) was associated with appropriate behavior. Equal concurrent schedules. The equal concurrent schedules condition (Audrey and Alice only) included concurre nt VI schedules (i.e., VI 10 -s VI 10-s, and VI 20-s VI 20-s) during which the schedules were equa l for problem and appropriate behavior. Appropriate behavior (rich). The appropriate behavior (rich) condition (all participants) included concurrent VI schedul es (e.g., VI 30-s VI 10s, VI 60-s VI 20-s,

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25 and VI 60-s VI 10-s), in which the higher reinforcement rate was associated with appropriate behavior while th e lower reinforcement rate was associated with problem behavior. Full treatment. Finally, the treatment c ondition was designed to eliminate problem behavior, and during this condi tion, differential reinforcemen t of alternative behavior (DRA) was implemented. During DRA, probl em behavior was placed on extinction (i.e., no reinforcers were delivered following problem behavior) and initiall y, each instance of appropriate behavior resulted in re inforcement (i.e., CRF schedule). Design. For Greg, the baseline condition, both the problem behavior (rich) and the appropriate behavior (rich) conditions, and full treatment were conducted for the tangible and escape functions of problem behavior. These conditions were evaluated in an ABCBCDAD reversal design for the ta ngible condition, and a BCBCDAD reversal design for the escape function, in which A repr esents the baseline condition, B represents the problem behavior (rich) condition, C represents the a ppropriate behavior (rich) condition, and D represents the full treatme nt condition. For Audrey, the baseline condition (A), the equal concurrent schedules condition (E) appropria te behavior (rich) condition (C), and full treatment (D) were conducted for the tangible function in a reversal (i.e., ADADECCEC) design. The probl em behavior (rich) condition (B) was not conducted for Audrey due to the severity of her SIB. For Alice, the baseline condition (A), the equal concurrent schedules conditi on (E), appropriate be havior (rich) (C) condition, and full treatment (D) were conducted for the escape function in a reversal (i.e., AECECD) design. The problem behavi or (rich) condition (B) was not conducted for Alice, because she was unexpectedly discharged from the hospital.

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26 Data Analysis. For all participants, results were evaluated from a matching perspective. In order to do so, rates of reinforcement for both problem and appropriate behavior were calculated a nd applied to Equation 1 and Equation 2 to determine if the relative rates of responding for problem and appropriate behavior approximated the relative rates of reinfo rcement. Given the complexities of response-stimulus relations, it is not clear what the definition of a reinfor ced response is, so in order to address this potential concern, three definitions of a re inforced response were included, and were evaluated using Equations 1 and 2. Last Response Method. One definition of a reinforced response was a response that occurred immediately prior to the deliver y of a reinforcer. If problem behavior and appropriate behavior are tem porally contiguous, and a reinfo rcer was delivered following one of the responses, it is possible that only the response that occurred immediately before the reinforcer delivery was reinfor ced (from the organisms perspective). For example, if problem behavior occurred 5 s before a reinforcer was delivered, and appropriate behavior occurred 1 s before a reinforcer was delivered, using this method, only appropriate behavior would be considered to be a reinforced response. This method of calculation will be called the Last Response Method Within 10 s Method. A second definition of a reinforced response was a response that occurred 10 s before a reinforcer was de livered. If problem and appropriate behavior are temporally contiguous, and a reinforcer was delivered immediately following one of the responses, it is possible that both respons es were reinforced (from the organisms perspective). For example, if problem beha vior occurred 5 s before a reinforcer was delivered, and appropriate behavior occurr ed immediately before a reinforcer was

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27 delivered, using this method, both responses would be define d as reinforced. Although 10 s is somewhat arbitrary, some time valu e had to be adopted. This method of calculation will be called the Within 10 s Method. Programmed Reinforcer Method. Finally, a third defini tion of a reinforced response was a response for which a rein forcer was delivered according to the programmed reinforcement schedule. In ot her words, whichever response actually produced the reinforcer was counted as the re inforced response. This method will be called the Programmed Reinforcer Method For all calculations, the rate of responding and reinfor cement were calculated for both problem and appropriate behavior for each participant. The rate of responding was calculated by taking the number of res ponses during a session and dividing by the duration of the session, in min. The rate of reinforcement was cal culated by taking the number of reinforced responses (according the each of the thr ee definitions provided above) and dividing by the durati on of the session, in min. The values obtained were then inserted into Equation 1 and Equation 2 to determine if the relative rates of responding approximated the relative rates of reinforcement for that response. Interobserver agreement (IOA). IOA was calculated as in Experiment 1, and two independent observers collected data on a ggression, disruption, screaming, and SIB, as well as appropriate responses including the use of picture cards, reaching, compliance with instructional demands, and requests for a tangible item. Sessions were divided into 10-s bins, and the number of observed responses was scored for each bin. The smaller number of observed responses within each bin was divided by the larger number of observed responses and converted to agreem ent percentages for frequency measures

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28 (Iwata et al., 1990). Agreement on the nonoccu rrence of behavior within any given bin was scored as 100% agreement. The bins we re then averaged acr oss the session. In a session, the smaller number of s was divided by the larger number of s for duration measures (and agreement on the nonoccurrence of behavior within any given bin was scored as 100%). The bin scores were then averaged across the sessions. For Greg, IOA was scored for 47% of assessment sessions during the tangible condition, and averaged 100% for disruption, 95% for screaming (ra nge, 80 to 100%), 94.4% for appropriate requests (range, 80.8 to 100%), and 91.7% for access to tangible items (range, 84.1 to 100%). IOA was scored for 44% of assessment sessions during the escape condition, and averaged 89.6% for disruption (range, 87.5-100%), 94.3% for compliance with instructional demands (range, 85.8 to 100%), and 88.7% for escape from instructions (range, 84.7 to 100%). For Audrey, IOA was scored for 36% of assessment sessions, and averaged 95.2% for SIB (range, 80 to 100%), and 95% for reaching for tangible items (range, 80 to 100%), and 83% for access to tangible items (range, 15% to 97%). For Alice, IOA was scored for 32% of assessment sessions, and averaged 98.5% for aggression (range, 94 to 100%), 93.17% for disruption (range, 82 to 100%), and 100% for a request for a break from instru ctional demands (range, 100 to 100%). IOA averaged 88% for escape from instructions (range 64 to 96%). Results and Discussion Panel A (top panel) of Figure 3-1 shows th e results of the analysis for Greg, during the tangible condition. Responses per min of problem and appropriate behavior are displayed for all phases. The initial baseline (A) for the tangible condition (top panel) shows the sessions conducted during the func tional analysis. Following the baseline,

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29 Gregs behavior was exposed to the problem behavior (rich) condition (B). During this condition Greg engaged in higher rates of problem behavior ( M = 2.21 rpm) than appropriate behavior ( M = .95 rpm). The schedules of re inforcement were then switched to VI 60-s for problem behavior and VI 20-s for appropriate behavior (i.e., appropriate behavior (rich) [C]). During this cond ition, similar rates of problem behavior ( M = 2.10 rpm) and appropriate behavior ( M = 2.1 rpm) were observed. During the reversal to the problem behavior (rich) condi tion (i.e., VI 20-s schedule fo r problem behavior and VI 60-s for appropriate behavior ) higher rates of problem behavior ( M = 1.50 rpm) than appropriate behavior ( M = 1.10 rpm) were observed. During this condition, it was observed that Gregs screaming occurred c ontiguous with appropr iate requests for tangible items, and a 2-s COD was included. During the second appropriate behavior (rich) condition (i.e., VI 60-s VI 20s) problem behavior occurred at a lower rate ( M = 3.30 rpm) relative to appropriate behavior ( M = 4.40 rpm). In order to produce a clinically acceptable treatment effect, problem behavior was placed on EXT and appropriate behavior was re inforced on a continuous re inforcement schedule (CRF) schedule (D) initially. In addition, because problem and appropriate behavior continued to occur together, the COD was increased to 5 s. Problem behavior decreased ( M = 2.79 rpm) and appropriate behavior continued to occur ( M = 3.30 rpm). For the final three sessions, the mean rate of problem behavior was .03 rpm. During a brief reversal to baseline levels of problem behavior increased ( M = 1.75 rpm), while appropriate behavior decreased relative to the previous condition ( M = .55 rpm). A final treatment phase was conducted and problem behavior decreased to low levels ( M = .82 rpm, 0 in the final two

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30 sessions) and appropriate behavior returned to levels observed in previous phases ( M = 2.02 rpm). Panel B (lower panel) of Fi gure 3-1 displays the results of the analysis for Greg during the escape condition. The problem behavior (rich) condition (B) was implemented first, and during this phase, pr oblem behavior occurre d at a higher rate ( M = 2.50 rpm) compared to a ppropriate behavior ( M = 1.1 rpm). The appropriate behavior (rich) condition (C) was conducted next, a nd, during this condition, problem behavior occurred at a lower rate ( M = 1.10 rpm) relative to appropriate behavior ( M = 2.10 rpm). During a reversal to the probl em behavior (rich) condition problem behavior occurred at a slightly higher rate ( M = 1.50 rpm) relative to appropriate behavior ( M = 1.12 rpm), with clear separation in respons e rates across the last five se ssions of the condition. The appropriate behavior (rich) c ondition was replicated, and initia lly higher rates of problem behavior ( M = 2.34 rpm) occurred relative to appropriate behavior ( M = .87 rpm). Problem behavior appeared to be decreasing, a nd at that time, Greg left the hospital for approximately two weeks (depicted on Figure 3-1 by the dashed vertical line). Following his return to the inpatient un it, the appropriate behavior (rich) condition continued, and eventually problem behavior decreased across the condition ( M = 2.87 rpm), while appropriate behavior continued to occur at stable levels ( M = .94 rpm). In order to reduce problem behavior to clinically signifi cant levels, a treatment condition (D) was conducted, and problem behavior was placed on extinction while appropriate behavior was reinforced on a CRF schedule. Problem be havior decreased to near zero levels ( M = .05 rpm) and appropriate behavior occurred at stable levels ( M = .39 rpm). During a brief reversal to the baseline c ondition problem behavior increased ( M = 1.70 rpm) as

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31 well as appropriate behavior ( M = 2.40 rpm), and a final trea tment condition resulted in a decrease in problem behavior ( M = .12 rpm) and stable levels of appropriate behavior ( M = .86 rpm). Panel A of Figure 3-2 shows th e results of the analysis for Audrey. Responses per min of problem and appropriate behavior are displayed for all phases. During the initial baseline (A) for Audrey, which included func tional analysis sessions (sessions 1-3) and additional baseline sessions (sessions 4-14), relatively high rates of SIB were observed ( M = 1.99 rpm) and relatively low levels of appropriate behavior (i.e., reaching) were observed ( M = .13 rpm). In order to decrease SI B to low levels, a treatment phase (D) was conducted, during which problem behavi or was placed on EXT, and appropriate behavior resulted in access to the reinforcer (i.e., tangible items) on a CRF schedule. SIB decreased ( M = .86 rpm) and appropriate behavior increased ( M = 1.44 rpm) during this phase. This effect was replicated during br ief reversals to the baseline and treatment conditions. During the reversal to th e baseline condition, SIB increased ( M = 1.70 rpm) and appropriate behavior decreased slightly ( M = 1.17 rpm). During the replication of the treatment condition, SIB decreased ( M = .30 rpm) and appropriate behavior increased ( M = 1.50 rpm). During the next phase, equal conc urrent schedules (i.e ., VI 10-s VI 10-s) (E) were implemented for both problem behavi or and appropriate behavior. The equal concurrent schedules cond ition yielded similar rates of problem behavior ( M = 1.17 rpm) and appropriate behavior ( M = 1.24 rpm). Following the eq ual concurrent schedules condition, the appropriate behavior (rich) c ondition (C) was implemented. During this condition, rates of problem behavior ( M = .97 rpm) and appropriate behavior ( M = 1.60 rpm) were similar, although towards the end of the phase, less problem behavior occurred

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32 relative to appropriate behavior Next, concurrent schedule s were arranged for problem behavior and appropriate behavi or in which the absolute values for both schedules were altered (VI 60-s VI 20-s), while continuing to favor appropriate behavior, and retaining the same proportional difference (1:3) in place in the prior appropriate behavior rich condition. Similar results were observed as in the previous appropria te behavior (rich) condition, and problem behavior occu rred at a slightly lower rate ( M = .23 rpm) relative to appropriate behavior ( M = 2.20 rpm). The equal concurrent schedules condition was then replicated and the ra tes of problem behavior ( M = 1.25 rpm) and appropriate behavior ( M = 1.31 rpm) were similar. A replicati on of the appropriate behavior (rich) condition was conducted, and initially, si milar rates of problem behavior ( M = 1.60 rpm) and appropriate behavior ( M = 1.86 rpm ) occurred at similar rate s, although towards the end of the phase, problem behavior occurred at a lower rate than a ppropriate behavior. Due to the severity of Audreys SIB, we implemented full treatment immediately following baseline. We conti nued to implement the full treat ment procedures for Audrey outside the context of this research. Panel B of Figure 3-2 shows the results of the escape analysis for Alice. The initial baseline condition (A) shows th e results from the functional analysis. The baseline yielded high rates of problem behavior a nd no appropriate behavior (compliance). During the equal concurrent schedules condi tion (E) problem behavior occurred at a lower rate ( M = .39 rpm) relative to appropriate behavior ( M = .90 rpm). Next, the appropriate behavior (rich) condition (VI 60-s VI 10-s) (C ) was implemented, and during this condition, problem behavior occurre d at an inexplicably higher rate ( M = 2.20 rpm) relative to appropriate behavior ( M = .90 rpm). Next, a replication of the equal

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33 concurrent schedules condition was implemen ted, and problem behavior occurred at a higher rate ( M = 1.05 rpm) relative to appropriate behavior ( M = .35 rpm). During the replication of the appropriate behavior (rich) condition, more problem behavior ( M = 1.20 rpm) occurred relative to appropriate behavior ( M = .27 rpm). Finally, a treatment phase (D) was conducted during which problem behavior was placed on extinction and appropriate behavior was rein forced on a CRF schedule. During this phase, problem behavior ( M = .60 rpm) occurred at relatively lo w rates (.20 rpm in final session), and appropriate behavior ( M = 2.94 rpm) occurred at relativel y high rates. Alices assessment was brief and additional repli cations were not conducted, due to her brief stay in the hospital. Figures 3-3 through 3-10 show the results from the matching analysis (i.e., simple matching and generalized matching) for all part icipants. For all scatter plots showing the results using the simple matching equation (i.e., Figures 3-3, 35, 3-7, and 3-9), the scatter plots show proportional response rate s as a function of proportional reinforcer rates. The dashed diagonal line represen ts perfect matching as described by Equation 1. Panel A (top left) shows the results using the last res ponse method of calculation and Panel B (top right) shows the means for each condition using the last response method of calculation depicted in panel A. In Panel A, each data point represents a session, and in Panel B, each data point represen ts the mean for the last five sessions in each condition of the assessment. Panel C (middle left) shows the results using the within 10-s method of calculation and Panel D (middle right) show s the means for each condition using the within 10-s method of calculation. In Panel C, each data point repres ents a session, and in Panel D, each data point represen ts the mean for the last five sessions in each condition.

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34 Finally, Panel E (bottom left) shows the resu lts using the programmed reinforcer method of calculation and Panel F (bottom right) s hows the means for each condition using the programmed reinforcer method of calculation. In Panel E, each data point represents a session, and in panel F, each data point repres ents the mean for the last five sessions in each condition. For the results using the generalized ma tching equation (i.e., Figures 3-4, 3-6, 3-8, and 3-10), the scatter plots show the log re sponse ratios plotted as a function of log reinforcer ratios. The linear equation depict s slope and bias. Th e dashed diagonal line represents perfect matching. The solid line is a best fit line. Panel A (top left) shows the results using the last response method of cal culation and Panel B (top right) shows the means for each condition using the last response method of calculation. In Panel A, each data point represents a session, and in Panel B, each data point repr esents the mean for the last five sessions in each condition. Panel C (middle left) shows the results using the within 10-s method of calcul ation and Panel D (middle ri ght) shows the means for each condition using the within 10-s method of cal culation. In Panel C, each data point represents a session, and in Panel D, each data point represents the mean for the last five sessions in each condition. Finally, Panel E (bottom left) shows the results using the programmed reinforcer method of calcula tion and Panel F (bottom right) shows the means for each condition using the programme d reinforcer method of calculation. Again, in Panel E, each data point represents a sessi on, and in Panel F, each data point represents the mean for the last five sessions in each condition. Figure 3-3 shows the results from the ma tching analysis of the tangible condition using Equation 1-1 for Greg. Due to a comput er virus that erased data on reinforcer

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35 presentations, calculations could not be c onducted for each session of each condition of Gregs analyses. However, a reasonably representative number of sessions were available. Generally, for the last response me thod of calculation (Panel A), the proportional rates of problem behavior were correlated with the proportional reinforcement rates for problem behavior (r = .80). During a number of sessions, more problem behavior was observed than w ould be predicted based on the rate of reinforcement for problem behavior. Th e means for each condition using the last response method of calculation (Panel B) also show that the relative rate of responding was correlated with the relative rate of reinforcement (r = .98). During the conditions with a higher rate of reinforcement for appr opriate behavior (VI 60-s VI 20-s) slightly more problem behavior was observed than would be predicted based on the proportional rate of reinforcement for problem behavior (denoted by data points above the dashed diagonal line). For the within 10-s method of data calcula tion (Panel C, the proportional rates of problem behavior were correlated with the proportional re inforcement rates for problem behavior (r = .80). During a numb er of sessions, less problem behavior was observed than would be predicted based on the proportional rate of reinforcement for problem behavior. The means for each c ondition using the within 10-s method of calculation (Panel D) also show that the rela tive rate of responding was correlated with the relative rate of reinforcement (r = .98) For the programmed reinforcer method of calculation (Panel E), the proporti onal rates of problem behavi or were correlated with the proportional reinforcement rates for problem behavior (r = .59), although during a number of sessions, less probl em behavior was observed than would be predicted based on the proportional rate of reinforcement for problem behavior. The means for each

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36 condition using the programmed reinforcer me thod of calculation (Panel F) also show that the relative rate of re sponding was correlated with the re lative rate of reinforcement (r = .99). During the condition with a higher ra te of reinforcement for problem behavior (VI 20-s VI 60-s) slightly less problem beha vior was observed than would be predicted based on the proportional rate of reinforcement for problem behavior. Figure 3-4 shows the results from Equa tion 1-2 for Greg during the tangible condition. Generally, for the last response me thod of calculation (Panel A), the proportional rates of problem behavior were correlated with the proportional reinforcement rates for problem behavior, howev er the best fit line does not indicate close adherence to the matching equation (r2 = .45). The means for each condition using the last response method of calculation (Panel B) also show that the relative rate of responding was correlated with the relative rate of reinforcement, and the best fit line indicated adherence to the matching equation (r2 = .92). The slope for both panels was less than 1.0, which suggests th at undermatching occurred. U ndermatching refers to the occurrence of less behavior th an would be predicted based on the relative rates of reinforcement. For the within 10-s method of calc ulation (Panel C), the proportional rates of problem behavior were correlated with the proportional re inforcement rates for problem behavior, however the best fit line does not indicate close adherence to the matching equation (r2 = .28) due to three sessions in particular during the second problem behavior rich condition. The means for each condition using the within 10-s method of calculation (Panel D) also show that the rela tive rate of responding was correlated with the relative rate of reinforcement, and the best fit line did not indicate strict adherence to the matching equation (r2 = .40). The slope for both panels was less than 1.0, which

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37 suggests that undermatching occurred. Fo r the programmed reinforcer method of calculation (Panel E), the proporti onal rates of problem behavi or were correlated with the proportional reinforcement rates for problem be havior, and the best fit line approximated perfect matching (r2 = .60). The means for each condition using the programmed reinforcer method of calculation (Panel F) al so show that the rela tive rate of responding was correlated with the relative rate of re inforcement, and the best fit line indicated matching (r2 = .81). The slope for both panels was le ss than 1.0, which suggests that undermatching occurred. Figure 3-5 shows the results from the ma tching analysis of the escape condition using Equation 1-1 for Greg. Due to a computer virus, calculations could not be conducted for each session of each condition. Generally, for the last response method of calculation (Panel A), the proporti onal rates of problem behavi or were correlated with the proportional reinforcement rates for problem be havior (r = .49), however for a number of sessions, more problem behavior was observe d than would be predicted based on the proportional rate of reinforcement for that re sponse. For the most part, these sessions (with more problem behavior observed than w ould be predicted) were those during which more reinforcement was available for appropria te behavior relative to problem behavior (VI 60-s VI 20-s). The means for each condi tion using the last response method of calculation (Panel B) also show that the rela tive rate of responding was correlated with the relative rate of reinforcement (r = .97). During the conditions with a higher rate of reinforcement for appropriate behavior (VI 60-s VI 20-s) slightly more problem behavior was observed than would be predicted based on the proportional rate of reinforcement for problem behavior. For the within 10-s met hod of calculation (Panel C), the proportional

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38 rates of problem behavior were positively co rrelated with the proportional reinforcement rates for problem behavior (r = .92). The means for each condition using the within 10-s method of calculation (Panel D) also show that the relative rate of responding was correlated with the relative rate of rein forcement (r = .78), however, more problem behavior was observed than would be pr edicted based on the proportional rate of reinforcement for problem behavior for one condition (one VI 60-s VI 20-s condition), and less problem behavior was observed than w ould be predicted for the other conditions (VI 20-s VI 60-s, and one VI 60-s VI 20-s condition). Similar results were observed for the programmed reinforcer met hod of calculation (Panel E) as in the last response method of calculation, and the proportional rates of pr oblem behavior were correlated with the proportional reinforcement rates for problem behavior (r = .41), although during a number of sessions, more problem behavior was observed than would be predicted based on the proportional rate of reinforcement for problem behavior. For the most part, these sessions were those during which more rein forcement was available for appropriate behavior relative to problem behavior (VI 60-s VI 20-s). The means for each condition using the programmed reinforcer method of cal culation (Panel F) also show that the relative rate of responding was correlated with the relative rate of reinforcement (r = .95), however, more problem behavior was observe d than would be predicted based on the proportional rate of reinforcement for probl em behavior during conditions with more reinforcement available for appropriate behavi or (i.e., VI 60-s VI 20-s), and less problem behavior was observed than would be predic ted for the conditions during which more reinforcement was available for problem behavior (i.e., VI 20-s VI 60-s).

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39 Figure 3-6 shows the results from Equa tion 1-2 for Greg during the escape condition. Generally, for the last response me thod of calculation (Panel A), the proportional rates of problem behavior were correlated with the proportional reinforcement rates for problem behavior, howev er the best fit line does not indicate close adherence to matching (r2 = .30). The means for each condition using the last response method of calculation (Panel B) also show that the relative rate of responding was correlated with the relative rate of reinforcement, and the best fit line indicated adherence to the matching equation (r2 = .60). The slope for both panels was less than 1.0, which suggests that undermatching occurred. For the within 10-s method of calculation (Panel C), the proportional rates of problem beha vior were closely correlated with the proportional reinforcement rates for problem behavior, and the best fit line indicated matching (r2 = .85). The means for each conditio n using the within 10-s method of calculation (Panel D) also show that the relative rate of responding was positively correlated with the relative rate of reinforcem ent, and the best fit line indicated matching (r2 = .88). The slope for both panels was less than 1.0, which suggests that undermatching occurred. For the programmed reinforcer method of calculation (Panel E), the proportional rates of problem beha vior were correlated with the proportional reinforcement rates for problem behavior, how ever the best fit line did not approximate perfect matching (r2 = .22). The means for each condition using the programmed reinforcer method of calculation (Panel F) al so show that the rela tive rate of responding was correlated with the relative rate of reinfo rcement, and the best fit line indicated strict adherence to the matching equation (r2 = .69). The slope for both panels was less than 1.0, which suggests that undermatching occurred.

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40 Figure 3-7 shows the results from the ma tching analysis of the tangible condition using Equation 1-1 for Audrey. Generally, fo r the last response method of calculation (Panel A), the proportional rates of probl em behavior were correlated with the proportional reinforcement rates for problem be havior (r = .79), however for a number of sessions, more problem behavior was observe d than would be predicted based on the proportional rate of reinforcement for that response. The means for each condition using the last response method of cal culation (Panel B) also show that the relative rate of responding was positively correlated with the re lative rate of reinforcement (r = .98). During the conditions with a higher rate of reinforcement for appropriate behavior (VI 60-s VI 20-s) slightly more problem behavi or was observed than would be predicted based on the proportional rate of reinforcement for problem behavior. Generally, for the within 10-s method of calculation (Panel C) the proportional rates of problem behavior were closely correlated with the proportional reinforcement rates for problem behavior (r = .87), with the points falling close to the li ne indicating perfect matching. The means for each condition using the within 10-s met hod of calculation Panel D) also show that the relative rate of responding was correlated with the relative rate of reinforcement (r = .95). Similar results were observed for the pr ogrammed reinforcer method of calculation (Panel E) as in the previous methods of calculation, and the proportional rates of problem behavior were positively correlated with the proportional reinforcement rates for problem behavior (r = .72). The means for each c ondition using the programmed reinforcer method of calculation (Panel F) also show that the relative rate of responding was positively correlated with the relative rate of reinforcement (r = .96).

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41 Figure 3-8 shows the results from Equati on 1-2 for Audrey during the tangible condition. Generally, for th e last response method of calculation (Panel A), the proportional rates of problem behavior were correlated with the proportional reinforcement rates for problem behavior, however the best fit line does not indicate matching (r2 = .23). The means for each c ondition using the last response method of calculation (Panel B) also show that the rela tive rate of responding was correlated with the relative rate of reinforcement, and the be st fit line did not indi cate adherence to the matching equation (r2 = .28). The slope fo r both panels was less than 1.0, which suggests that undermatching occurred. For th e within 10-s method of calculation (Panel C), the proportional rates of problem beha vior were correlated with the proportional reinforcement rates for problem behavior, a nd the best fit line indicated matching (r2 = .84). The means for each condition using the wi thin 10-s method of calculation (Panel D) also show that the relative rate of res ponding was positively correlated with the relative rate of reinforcement, and the best fit line indicated almost perfect matching (r2 = .99). The slope for Panel C was less than 1.0, whic h suggests that undermatching occurred. Generally, for the programmer reinforcer method of calculation (Panel E) the proportional rates of problem behavior were positively correlated with the proportional reinforcement rates for problem behavior, how ever the best fit line did not approximate perfect matching (r2 = .44). The means for each condition using the programmed reinforcer method of calculation (Panel F) al so show that the rela tive rate of responding was correlated with the relative rate of rein forcement, and the best fit line matching (r2 = .86). The slope for both panels was less th an 1.0, which suggests that undermatching occurred.

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42 Figure 3-9 shows the results from the ma tching analysis of the escape condition using Equation 1-1 for Alice. Generally, fo r the last response method of calculation (Panel A) the proportional rates of problem behavior were correlated with the proportional reinforcement rates for problem be havior (r = .77), however for a number of sessions, more problem behavior was observe d than would be predicted based on the proportional rate of reinforcement for that response. The means for each condition using the last response method of cal culation (Panel B) also show that the relative rate of responding was correlated with the relative rate of reinforcement (r = .77). For the within 10-s method of calculation (Panel C), the pr oportional rates of problem behavior were correlated with the proportional reinforcem ent rates for problem behavior (r = .75), however, during some sessions more problem behavior was observed than would be predicted based on the proportional rate of reinforcement for problem behavior. The means for each condition using the within 10 -s method of calculation (Panel D) also show that the relative rate of responding wa s correlated with the relative rate of reinforcement (r = .84). For the programmed reinforcer method of calculation (Panel E), similar results were observed as in the previous methods of calculation, and the proportional rates of problem behavior were correlated with the proportional reinforcement rates for problem behavior (r = .71). The means for each condition using the programmed reinforcer met hod of calculation (Panel F) al so show that the relative rate of responding was correlated with the re lative rate of reinforcement (r = .84). Figure 3-10 shows the results from Equa tion 1-2 for Alice du ring the tangible condition. Generally, for th e last response method of calculation (Panel A), the proportional rates of problem behavior were correlated with the proportional

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43 reinforcement rates for problem behavior, however the best fit line does not indicate matching (r2 = .25). The means for each condition using the last response method of calculation (Panel B) also show that the rela tive rate of responding was correlated with the relative rate of reinforcement, and th e best fit line did not indicate matching (r2 = .23). The slope for both panels was less than 1.0, which suggests that undermatching occurred. For the within 10-s method of calculation (Pan el C), the proportional rates of problem behavior were correlated with the proportional reinforcemen t rates for problem behavior, and the best fit line did not indicate matching (r2 = .32). The means for each condition using the within 10-s method of calculation (Panel D) also show that the relative rate of responding was correlated with the relative rate of reinforcement, however, the best fit line did not indicate matching (r2 = .01). The slope for both panels was less than 1.0, which suggests that undermatching occurred. Generally, for the programmed reinforcer method of calculation (Panel E) the propor tional rates of problem behavior were correlated with the proportional reinforcemen t rates for problem behavior, however the best fit line did not approxi mate perfect matching (r2 = .45). The means for each condition using the programmed reinforcer me thod of calculation (Panel F) also show that the relative rate of re sponding was correlated with the re lative rate of reinforcement, and the best fit line did not indicate stri ct adherence to the matching equation (r2 = .41). The slope for both Panel F was less than 1.0, which suggests that undermatching occurred. Figure 3-11 provides examples from each participant depicting closer approximations to matching towards the e nd of a condition. Ea ch figure has been discussed above and shown with the results for each participant. Ho wever in Figure 3-11

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44 the first and last sessions of a condition are noted with an arrow for each participant. Panel A shows the results using the within 10 s method of calculation for Gregs tangible analysis during the second VI 20-s VI 60-s pha se. In the last sessi on of the condition, the proportional rate of responding more closel y approximates the proportional rate of reinforcement relative to the first session in that condition. Panel B shows the results using the last response method of calculation for Audreys tangible analysis during the second VI 10-s VI 10-s phase. Again, in the last session of the condition, the proportional rate of responding more closel y approximates the proportional rate of reinforcement relative to the first session in that condition. Panel C shows similar results using the within 10 s method of calculation fo r Gregs escape analysis during the second VI 20-s VI 60-s phase. Finally, Panel D show s similar results using the last response method of calculation for Alices escape anal ysis during the first VI 60-s VI 20-s phase. In summary, results of the matching analysis indicated that, for all participants the relative rates of both problem behavior and appropriate behavior were sensitive to the schedules of reinforcement available for each al ternative. In additi on, interventions were implemented and successfully decreased leve ls of problem behavior to clinically acceptable levels. Further, evaluation of the results from a matching perspective using both the simple matching equation (1-1) a nd the generalized matching equation (1-2) indicated that for all participants, relativ e rates of problem behavior were positively correlated with the relative rate of reinforcem ent for problem behavior Results of this investigation suggest that the matching la w can provide an explanation for problem behavior exhibited by individua ls with developmental disabilities. While perfect matching was not obtained, matching is a st eady state phenomenon a nd all participants

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45 were exposed to the various conditions onl y briefly, and positive correlations were observed. One possible explanation may be th at the early sessions in each condition represent a transition period, dur ing which the participant begi ns to discriminate between the concurrent schedules of reinforcement, and that stable responding occurs towards the end of each condition. A comparison of the se ssion-by-session scatte r plots and the mean scatter plots suggests that closer approximations to matching were observed by calculating the mean of the last five sessions of each condition than calculating all sessions in each condition. This eff ect was observed for all participants. For Alice, we were not able to comp lete a thorough assessment given the time constraints of her hospitalization. However, while additional sessi ons and replications would have provided further s upport for our findings, we di d observe approximations to matching in a limited assessment. In addition, given the severity of Audreys problem behavior (i.e., SIB), we bega n her assessment with the treatment component, and were able to reduce problem behavior to clinically significant leve ls. We were then able to recommend a treatment package for use in the school and home settings while we continued to assess her problem behavior.

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46 0 2 4 6 8 10Responses per Min5101520253035404550 Sessions Problem Behavior (PB) Appropriate Behavior (AB) Baseline CRF (PB) EXT (AB) VI 20 (PB) VI 60 (AB) VI 60 (PB) VI 20 (AB) VI 20 (PB) VI 60 (AB) 2 s COD VI 60 (PB) VI 20 (AB) 2 s COD EXT (PB) CRF (AB) 5 s COD BL EXT (PB) CRF (AB) 5 s COD 0 2 4 6 8 10Responses per Min51015202530354045505560 Sessions BL EXT (PB) CRF (AB) EXT (PB) CRF (AB) VI 60 (PB) VI 20 (AB) VI 20 (PB) VI 60 (AB) VI 60 (PB) VI 20 (AB) VI 20 (PB) VI 60 (AB)Greg Tangible Greg Escape Problem Behavior (PB) Appropriate Behavior (AB) A B Figure 3-1. Overall response rates for problem and appropriate behavior for Greg. A) Responses per min of problem and a ppropriate behavior during tangible sessions. B) Responses per min of pr oblem and appropriate behavior during escape sessions.

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47 0 1 2 3 4 5 6 7 8Responses per Min5101520253035404550556065707580859095 Sessions Problem Behavior (PB) Appropriate Behavior (AB) Baseline CRF (PB) EXT (AB) VI 10 (PB) VI 10 (AB) VI 60 (PB) VI 20 (AB) VI 30 (PB) VI 10 (AB) VI 10 (PB) VI 10 (AB) BL EXT (PB) CRF (AB) 0 1 2 3 4 5Responses per Min510152025 Sessions VI 60 (PB) VI 10 (AB)Audrey Tangible Alice Escape Problem Behavior (PB) Appropriate Behavior (AB) Baseline CRF (PB) EXT (AB) VI 30 (PB) VI 10 (AB) VI 20 (PB) VI 20 (AB) VI 20 (PB) VI 20 (AB) VI 60 (PB) VI 10 (AB) EXT (PB) CRF (AB) A B Figure 3-2. Overall response rates for problem and appropriate behavior during the assessment phase for Audrey and Alice. A) Responses per min of problem and appropriate behavior for Audrey. B) Responses per min of problem and appropriate behavior for Alice.

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48 0 0.2 0.4 0.6 0.8 1Problem Behavior/ Total Behavior 00.20.40.60.81 Reinforced Problem Behavior/ Total Reinforcers 0 0.2 0.4 0.6 0.8 1Problem Behavior/ Total Behavior00.20.40.60.81 Reinforced Problem Behavior/ Total Reinforcers 0 0.2 0.4 0.6 0.8 1Problem Behavior/ Total Behavior 00.20.40.60.81 Reinforced Problem Behavior/ Total Reinforcers 0 0.2 0.4 0.6 0.8 1Problem Behavior/ Total Behavior00.20.40.60.81 Reinforced Problem Behavior/ Total Reinforcers 0 0.2 0.4 0.6 0.8 1Problem Behavior/ Total Behavior00.20.40.60.81 Reinforced Problem Behavior/ Total Reinforcers 0 0.2 0.4 0.6 0.8 1Problem Behavior/ Total Behavior00.20.40.60.81 Reinforced Problem Behavior/ Total Reinforcers Greg Tangible AB CD EF Figure 3-3. Scatterplots of observed and predicted respons e allocation between problem behavior and appropriate behavior for Greg for each condition during the tangible assessment. A) Last response method of calculation. B) Means using the last response method of calculati on. C) 10 s method of calculation. D) Means using the 10 s method of cal culation. E) Programmed method of calculation. F) Means using the programm ed reinforcer method of calculation.

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49 -1.5 -1 -0.5 0 0.5 1 1.5 Log Problem Behavior/ Log Appropriate Behavior-1.5-1-0.500.511.5 Log ReinforcedProblem Behavior/ Log Reinforced Appropriate Behavior y = -0.358x 0.019 -1.5 -1 -0.5 0 0.5 1 1.5 Log Problem Behavior/ Log Appropriate Behavior-1.5-1-0.500.511.5 Log ReinforcedProblem Behavior/ Log Reinforced Appropriate Behavior y = 0.249x + 0.063 -1.5 -1 -0.5 0 0.5 1 Log Problem Behavior/ Log Appropriate Behavior-1.5-1-0.500.511.5 Log ReinforcedProblem Behavior/ Log Reinforced Appropriate Behavior y = 0.411x + 0.067 -1.5 -1 -0.5 0 0.5 1 1.5 Log Problem Behavior/ Log Appropriate Behavior-1.5-1-0.500.511.5 Log ReinforcedProblem Behavior/ Log Reinforced Appropriate Behavior y = 0.322x + 0.093 -1.5 -1 -0.5 0 0.5 1 1.5 Log Problem Behavior/ Log Appropriate Behavior-1.5-1-0.500.511.5 Log ReinforcedProblem Behavior/ Log Reinforced Appropriate Behavior y = 0.886x 0.322 -1.5 -1 -0.5 0 0.5 1 1.5 Log Problem Behavior/ Log Appropriate Behavior -1.5-1-0.500.511.5 Log ReinforcedProblem Behavior/ Log Reinforced Appropriate Behavior y = 0.494x 0.163 Greg Tangible AB CD EF Figure 3-4. Log response ratios plotted against log reinforcer ratios for Greg. The linear equation depicts slope and bias duri ng all conditions of the tangible assessment. A) Last response method of calculation. B) Means using the last response method. C) 10 s method of calculation. D) Means using the 10 s method. E) Programmed reinforcer method of calculation. F) Means using the programmed reinforcer method.

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50 0 0.2 0.4 0.6 0.8 1Problem Behavior/ Total Behavior 00.20.40.60.81 Reinforced Problem Behavior/ Total Reinforcers 0 0.2 0.4 0.6 0.8 1Problem Behavior/ Total Behavior00.20.40.60.81 Reinforced Problem Behavior/ Total Reinforcers 0 0.2 0.4 0.6 0.8 1Problem Behavior/ Total Behavior 00.250.50.751 Reinforced Problem Behavior/ Total Reinforcers 0 0.2 0.4 0.6 0.8 1Problem Behavior/ Total Behavior00.20.40.60.81 Reinforced Problem Behavior/ Total Reinforcers 0 0.2 0.4 0.6 0.8 1Problem Behavior/ Total Behavior00.20.40.60.81 Reinforced Problem Behavior/ Total Reinforcers 0 0.2 0.4 0.6 0.8 1Problem Behavior/ Total Behavior00.20.40.60.81 Reinforced Problem Behavior/ Total Reinforcers Greg Escape AB CD EF Figure 3-5. Scatterplots of observed and predicted respons e allocation between problem behavior and appropriate behavior for Greg for all conditions during the escape assessment. A) Last response method of calculation. B) Means using the last response method of calculati on. C) 10 s method of calculation. D) Means using the 10 s method of cal culation. E) Programmed method of calculation. F) Means using the programm ed reinforcer method of calculation.

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51 -1.5 -1 -0.5 0 0.5 1 1.5 Log Problem Behavior/ Log Appropriate Behavior-1.5-1-0.500.511.5 Log ReinforcedProblem Behavior/ Log Reinforced Appropriate Behavior y = 0.801x + 0.094 -1.5 -1 -0.5 0 0.5 1 1.5 Log Problem Behavior/ Log Appropriate Behavior-1.5-1-0.500.511.5 Log ReinforcedProblem Behavior/ Log Reinforced Appropriate Behavior y = 0.598x + 0.026 -1.5 -1 -0.5 0 0.5 1 1.5 Log Problem Behavior/ Log Appropriate Behavior-1.5-1-0.500.511.5 Log ReinforcedProblem Behavior/ Log Reinforced Appropriate Behavior y = 0.478x + 0.329 -1.5 -1 -0.5 0 0.5 1 1.5 Log Problem Behavior/ Log Appropriate Behavior-1.5-1-0.500.511.5 Log ReinforcedProblem Behavior/ Log Reinforced Appropriate Behavior y = 0.439x + 0.197 -1.5 -1 -0.5 0 0.5 1 1.5 Log Problem Behavior/ Log Appropriate Behavior-1.5-1-0.500.511.5 Log ReinforcedProblem Behavior/ Log Reinforced Appropriate Behavior y = 0.610x + 0.468 -1.5 -1 -0.5 0 0.5 1 1.5 Log Problem Behavior/ Log Appropriate Behavior-1.5-1-0.500.511.5 Log ReinforcedProblem Behavior/ Log Reinforced Appropriate Behavior y = 0.814x + 0.454 Greg Escape AB CD EF Figure 3-6. Log response ratios plotted against log reinforcer ratios for Greg. The linear equation depicts slope and bias during all conditions of the escape assessment. A) Last response method of calculation. B) Means using the last response method. C) 10 s method of calculation. D) Means using the 10 s method. E) Programmed reinforcer method of calculation. F) Means using the programmed reinforcer method.

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52 0 0.2 0.4 0.6 0.8 1Problem Behavior/ Total Behavior 00.20.40.60.81 Reinforced Problem Behavior/ Total Reinforcers 0 0.2 0.4 0.6 0.8 1Problem Behavior/ Total Behavior00.20.40.60.81 Reinforced Problem Behavior/ Total Reinforcers 0 0.2 0.4 0.6 0.8 1Problem Behavior/ Total Behavior 00.20.40.60.81 Reinforced Problem Behavior/ Total Reinforcers 0 0.2 0.4 0.6 0.8 1Problem Behavior/ Total Behavior00.20.40.60.81 Reinforced Problem Behavior/ Total Reinforcers 0 0.2 0.4 0.6 0.8 1Problem Behavior/ Total Behavior00.20.40.60.81 Reinforced Problem Behavior/ Total Reinforcers 0 0.2 0.4 0.6 0.8 1Problem Behavior/ Total Behavior00.20.40.60.81 Reinforced Problem Behavior/ Total Reinforcers Audrey AB CD EF Figure 3-7. Scatterplots of observed and predicted respons e allocation between problem behavior and appropriate be havior for Audrey during the tangible assessment. A) Last response method of calculati on. B) Means using the last response method of calculation. C) 10 s method of calculation. D) Means using the 10 s method. E) Programmed method of calculation. F) Means using the programmed reinforcer method of calculation.

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53 -1.5 -1 -0.5 0 0.5 1 1.5 Log Problem Behavior/ Log Appropriate Behavior-1.5-1-0.500.511.5 Log ReinforcedProblem Behavior/ Log Reinforced Appropriate Behavior y = 0.996x + 0.039 -1.5 -1 -0.5 0 0.5 1 1.5 Log Problem Behavior/ Log Appropriate Behavior-1.5-1-0.500.511.5 Log ReinforcedProblem Behavior/ Log Reinforced Appropriate Behavior y = 1.129x + 0.048 -1.5 -1 -0.5 0 0.5 1 1.5 Log Problem Behavior/ Log Appropriate Behavior-1.5-1-0.500.511.5 Log ReinforcedProblem Behavior/ Log Reinforced Appropriate Behavior y = 0.501x 0.179 -1.5 -1 -0.5 0 0.5 1 1.5 Log Problem Behavior/ Log Appropriate Behavior-1.5-1-0.500.511.5 Log ReinforcedProblem Behavior/ Log Reinforced Appropriate Behavior y = 0.593x 0.351 -1.5 -1 -0.5 0 0.5 1 1.5 Log Problem Behavior/ Log Appropriate Behavior-1.5-1-0.500.511.5 Log ReinforcedProblem Behavior/ Log Reinforced Appropriate Behavior y = 0.741x 0.036 -1.5 -1 -0.5 0 0.5 1 1.5 Log Problem Behavior/ Log Appropriate Behavior-1.5-1-0.500.511.5 Log ReinforcedProblem Behavior/ Log Reinforced Appropriate Behavior y = 0.910x 0.010 Audrey AB CD EF Figure 3-8. Log response ratios plotted against log reinforc er ratios for Audrey. The linear equation depicts slope and bias during all cond itions of the tangible assessment. A) Last response method of calculation. B) Means using the last response method. C) 10 s method of calculation. D) Means using the 10 s method. E) Programmed reinforcer method of calculation. F) Means using the programmed reinforcer method.

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54 0 0.2 0.4 0.6 0.8 1Problem Behavior/ Total Behavior 00.20.40.60.81 Reinforced Problem Behavior/ Total Reinforcers 0 0.2 0.4 0.6 0.8 1Problem Behavior/ Total Behavior00.20.40.60.81 Reinforced Problem Behavior/ Total Reinforcers 0 0.2 0.4 0.6 0.8 1Problem Behavior/ Total Behavior 00.20.40.60.81 Reinforced Problem Behavior/ Total Reinforcers 0 0.2 0.4 0.6 0.8 1Problem Behavior/ Total Behavior00.20.40.60.81 Reinforced Problem Behavior/ Total Reinforcers 0 0.2 0.4 0.6 0.8 1Problem Behavior/ Total Behavior00.20.40.60.81 Reinforced Problem Behavior/ Total Reinforcers 0 0.2 0.4 0.6 0.8 1Problem Behavior/ Total Behavior00.20.40.60.81 Reinforced Problem Behavior/ Total Reinforcers Alice AB CD EF Figure 3-9. Scatterplots of observed and predicted respons e allocation between problem behavior and appropriate be havior for Alice during the escape assessment. A) Last response method. B) Means using the last response method. C) 10 s method. D) Means using the 10 s met hod. E) Programmed reinforcer method. F) Means using the programmed reinforcer method.

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55 -1 -0.5 0 0.5 1 Log Problem Behavior/ Log Appropriate Behavior-1-0.500.51 Log ReinforcedProblem Behavior/ Log Reinforced Appropriate Behavior y = 0.669x + 0.077 -1 -0.5 0 0.5 1 Log Problem Behavior/ Log Appropriate Behavior-1-0.500.51 Log ReinforcedProblem Behavior/ Log Reinforced Appropriate Behavior y = -0.586x + 0.352 -1 -0.5 0 0.5 1 Log Problem Behavior/ Log Appropriate Behavior-1-0.500.51 Log ReinforcedProblem Behavior/ Log Reinforced Appropriate Behavior y = 0.687x + 0.089 -1 -0.5 0 0.5 1 Log Problem Behavior/ Log Appropriate Behavior-1-0.500.51 Log ReinforcedProblem Behavior/ Log Reinforced Appropriate Behavior y = 0.172x + 0.276 -1 -0.5 0 0.5 1 Log Problem Behavior/ Log Appropriate Behavior-1-0.500.51 Log ReinforcedProblem Behavior/ Log Reinforced Appropriate Behavior y = 1.172x + 0.056 -1 -0.5 0 0.5 1 Log Problem Behavior/ Log Appropriate Behavior-1-0.500.51 Log ReinforcedProblem Behavior/ Log Reinforced Appropriate Behavior y = 0.820x + 0.200 Alice AB CD EF Figure 3-10. Log response ratios plotted agai nst log reinforcer ratios for Alice. The linear equation depicts slope and bias during all c onditions of the escape assessment. A) Last response method. B) Means using the last response method. C) 10 s method. D) Means us ing the 10 s method. E) Programmed reinforcer method. F) Means using the programmed reinforcer method.

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56 0 0.2 0.4 0.6 0.8 1Problem Behavior/ Total Behavior00.20.40.60.81 Reinforced Problem Behavior/ Total Reinforcers Greg Tangible 0 0.2 0.4 0.6 0.8 1Problem Behavior/ Total Behavior00.20.40.60.81 Reinforced Problem Behavior/ Total Reinforcers Last session First session Last session Greg Escape 0 0.2 0.4 0.6 0.8 1Problem Behavior/ Total Behavior 00.20.40.60.81 Reinforced Problem Behavior/ Total Reinforcers First session Last session First session 0 0.2 0.4 0.6 0.8 1Problem Behavior/ Total Behavior 00.20.40.60.81 Reinforced Problem Behavior/ Total Reinforcers Last session First session Alice Audrey AB CD Figure 3-11. Scatterplots depicting exampl es of closer approximations to matching towards the end of the condition using the simple matching equation. Arrows show the first and last sessions within a condition. A) Results of the within 10s method for Gregs tangible analys is during the second VI 20-s VI 60-s phase. B) Results of the last respons e method of calculation for Audreys tangible analysis during the second VI 10s VI 10-s phase. C) Results of the within 10 s method of calculation for Gregs escape analysis during the second VI 20-s VI 60-s phase. D) Re sults of the last response method of calculation for Alices escape analysis dur ing the first VI 60-s VI 20-s phase.

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57 CHAPTER 4 GENERAL DISCUSSION In Experiment 1, functional analyses were conducted for problem behavior exhibited by three individuals diagnosed with developmenta l disabilities to identify reinforcers. For Greg, results suggested that screaming was reinforced by access to tangible items, and disruptive behavior wa s reinforced by escape from instructional demands. For Audrey, results suggested that SIB was reinforced by access to tangible items. Finally, for Alice, results suggested th at aggression and disrupt ion were reinforced by escape from instructional demands. In Experiment 2, an analysis of concurrent reinforcement schedules was conducted with independent reinforcement schedules in place for both problem behavior and appropriate behavior in or der to evaluate behavior from a matching perspective. For all evaluations, the re lative rate of responding was infl uenced by the relative rate of reinforcement. Analyses for Greg during the tangible and escap e conditions, and the analysis for Audrey during the tangible c ondition, provided closer approximations to matching than the limited analysis for Alice. Finally, in Experiment 2, full treatment evaluations were conducted to reduce problem be havior to clinically significant levels. DRA was implemented with EXT to increase a ppropriate behavior for all participants. For all evaluations, DRA and EXT were suc cessful in reducing problem behavior and increasing appropriate behavior. The matching law has been shown to be a useful way of describing response allocation across a variety of subj ects (e.g., Baum, 1974a, 1974b; Beardsley &

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58 McDowell, 1992; Conger & Killeen, 1974; Crowley & Donahoe, 2004; Herrnstein, 1961, 1975; MacDonall, 1988 ) for an array of response topogr aphies (Borrero & Vollmer, 2002; Martens & Houk, 1989; McDowell, 1981; Symons et al., 2003), and across nonexperimental (Symons et al., 2003; Vollm er & Bourret, 2000) and experimental (Mace et al. 1994; Neef & Lutz, 2001; Neef, Mace & Shade, 1993; N eef, Shade & Miller, 1994) arrangements. In order to evaluate the matching relati on, the rates of responding for problem and appropriate behavior were calc ulated, as well as the rates of reinforcement for problem and appropriate behavior. One notable difficulty involves de fining a reinforced response. It is not always clear how responses are reinforc ed, even with a schedule of reinforcement in place. Therefore, three calculations were included to account for possible differences in results based on th e way in which a reinforced response was defined. One method of calculation was the last response method during which the response that occurred immediately prior to the delivery of a reinforcer was the only response considered to be reinfor ced. This calculation accounted for sequential relations between a response and a known reinforcer. A second calculation was the within 10-s method during which any response that occurred 10 s before a reinforcer was delivered was considered to be a reinforced response. This calculation accounted for temporal relations between a response and a known rein forcer. Finally, a third calculation was the programmed reinforcer method, during which a response for which a reinforcer was delivered according to the programmed schedule of reinforcement was considered to be a reinforced response. This calcul ation accounted for the delivery of programmed

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59 reinforcers according to the sc hedule in place. It is not clear which calculation is the most useful, although some differences be tween the calculations were observed. In order to evaluate the differences between calculation methods, correlation coefficients (r) and coefficients of determination (r2) were evaluated. Table 4.1 shows, for all participants, the results of the data analysis using the simple matching equation (Equation 1-1) and the generalized matching equation (Equation 1-2), for all calculation methods (i.e., last response method, with in 10-s method, and programmed reinforcer method). The results for all calculations are summarized in Table 4.1, for both the session-by-session and mean analyses, with the closest approximations to matching shown in bold. For each method of calculation, four values are shown for the correlation coefficients and the coefficients of determina tion, resulting in 8 possible values for each coefficient. For 4 of 8 calculations, the last response method provided the larger correlation coefficients, for 4 of 8 calcula tions, the within 10 s method provided the larger correlation coefficients (the last response and within 10 s methods were equal for one calculation), and for 2 of 8 calculations, the programmed reinforcer method provided the larger correlation coefficients. The larg est coefficients of determinations were obtained using the within 10-s method for 4 of 8 calculations, the programmed reinforcer method for 3 of 8 calculations, and the last response method for 1 of 8 calculations. These results suggested that all methods of calculation supported an interpretation of the data from a matching perspective, and resu lts may vary depending on the definition of a reinforced response. A second difficulty may be that, such an alyses are quite time-consuming, and may be difficult to conduct when working with i ndividuals who engage in severe problem

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60 behavior. It may not be possi ble to conduct such lengthy analys es due to the severity of problem behavior (e.g., severe SI B and aggression), particularly when such an analysis delays the implementation of an interven tion. Audreys assessment may provide an alternative strategy for conduc ting thorough analyses, by evaluating a treatment prior to conducting the matching analyses. It is po ssible that evaluating the full treatment component prior to the assessment of concu rrent schedules could reduce some of the difficulties associated with evaluating severe problem behavior from a matching perspective. Designing a treatment package prior to a more lengthy assessment may alleviate some of the clinical concerns (e.g., continued risk of injury due to SIB) raised by parents and careproviders. For example, fo llowing the development of an effective treatment, parent and careprovider training could be conducted, and the treatment could be implemented in a timely manner outside of the experimental context. The present experiments suggest areas for fu ture research. This analysis included various concurrent schedules of reinforcem ent for problem and appropriate behavior. Evaluating concurrent schedules of reinforcemen t may be useful, as it is likely that in the natural environment, reinforcers are availabl e for both problem and appropriate behavior at the same time but with varying probabiliti es. Future research may conduct similar analyses using concurrent schedule arrang ements based on naturalistic observations. For example, descriptive analyses (Bijou, Pete rson, & Ault, 1968) could be conducted with parents and careproviders and th e results could be analyzed us ing reinforcers identified in a functional analysis (Iwata et al. 1982/1994) wi th procedures similar to those described by Borrero and Vollmer (2002). For example, if descriptive analysis data showed that problem behavior was reinforced on a VI 20s schedule, and appropr iate behavior was

PAGE 70

61 reinforced on a VI 40-s schedule, experime ntal analyses could be designed to mimic naturally occurring reinforcement rates in an ex perimental context. Concurrent schedules of reinforcement could be based on the de rived schedules of reinforcement observed during naturally occurring s ituations, and a subsequent matching analysis could be conducted. The extent to which relative response allocation is similar under both descriptive and experimental arrangements may provide great er support for the generality of the matching relation. Matching analyses may also suggest critical values of reinforcement parameters that may increas e both the acceptability and integrity of treatment implementation by primary caregivers in the natural environm ent. It is often difficult and perhaps unrealistic to train pare nts not to provide reinforcement following problem behavior. Matching analyses ma y suggest the lower limit of caregiver reinforcement that may be provided while ma intaining clinically acceptable levels of appropriate behavior (Vollmer, Roane, Ringdahl, & Marcus, 1999). An additional area of future research may also include analyses of various parameters of reinforcement. Previous re search (Borrero, Vollmer, Borrero, & Bourret, 2005; Mace et al., 1994; see Stromer, McComas, & Rehfeldt, 2000 for a comprehensive review) has suggested that duration of rein forcement (Dixon et al., 1998; Fisher, Piazza, & Chiang, 1996; Peck et al., 1996) delay to rein forcement (Neef et al ., 2005; Neef et al., 1994; Vollmer, Borrero, Lalli, & Daniel, 1999), quality of reinforcement (Neef, Bicard, & Endo, 2001; Neef & Lutz, 2001; Mace et al., 1996) and magnitude of reinforcement (Hoch, McComas, Johnson, Faranda, & Guen ther, 2002; Lerman, Kelley, Vorndran, Kuhn, & LaRue, 2002; Volkert, Lerman, & Vo rndran, 2005) are important variables for evaluating response allocation, in addition to rate of reinforcem ent. Investigations similar

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62 to these just cited could be conducted with any of the additional parameters of reinforcement by holding constant rate of reinforcement. In addition, the implications for the treatment of severe problem behavior may be significant. Often, problem behavior is so severe (e.g., head-banging on hard surfaces severe aggression, etc.) that it is not possible to withhold reinforcement (i.e., extinct ion). That is, especially in the case of behavior reinforced by attention, it is not possible to ignore the behavior, and some attention (e.g., blocking the response) will likely be necessary to ensure the safety of the individuals in the situation. However, it may be possible to manipulate other reinforcement parameters such as duration or quality of reinforcement. One limitation of these experiments may be the small number of concurrent schedule values. For Greg and Alice, we onl y manipulated two values for the concurrent schedules. For Audrey, we manipulated th ree values however, we did not conduct a thorough analysis of the third va lue, nor did we conduct a revers al to that phase (i.e., VI 60-s VI 20-s was assessed for only three sessi ons). Future research may also include parametric schedule value evaluations. For exam ple, the schedules could initial start with a VI 20-s for problem behavior and VI 60-s fo r appropriate behavior, and then values in between (e.g., VI 25-s VI 55-s) until the schedul es are switched (i.e., VI 60-s VI 20-s). Such evaluations may be useful in qu antifying reinforcer value by identifying indifference points (i.e., values which di ffer quantitatively but produce indifferent response allocation). A second limitation of these experiments may be the brevity of th e conditions. In a basic preparation, it may be possible to conduct conditions until meeting a stability criterion (e.g., a difference of less than 5% between data points) however, in the applied

PAGE 72

63 setting, it was not always possible to bring each condition to stab ility before exposing behavior to another condition (i.e., Alice). Therefore, the matching analyses conducted in these experiments may not be based on st able responding, and this could account for some of the variability observed. This may be supported by the observation of closer approximations to matching towards the e nd of each condition. Ideally, for all participants, each set of conditions would have been conducted until meeting stability criteria. The present experiments focused on evalua ting the rate of reinforcement and the effects on problem and appropriate behavior. It was designed to determine if the simple matching equation (1) and the ge neralized matching equation (2) provided desc riptions of response allocation on concurrent schedules of reinforcement with th ree individuals with developmental disabilities who engaged in severe problem behavior.

PAGE 73

64 Table 4-1. Summary of correlation coefficients (r) for all participants using the Simple Matching Equation and the coefficients of determination using the (r2) Generalized Matching Equation. Method of Calculation Last Response Within 10 s Programmed Greg Tangible r (All sessions) .80 .80 .59 r (Means) .98 .98 .99 r2 (All sessions) .45 .28 .60 r2 (Means) .92 .40 .81 Greg Escape r (All sessions) .49 .92 .41 r (Means) .97 .78 .95 r2 (All sessions) .30 .85 .22 r2 (Means) .60 .88 .69 Audrey r (All sessions) .79 .87 .72 r (Means) .98 .95 .96 r2 (All sessions) .23 .84 .44 r2 (Means) .28 .99 .86 Alice r (All sessions) .77 .75 .71 r (Means) .77 .84 .84 r2 (All sessions) .25 .32 .45 r2 (Means) .23 .01 .41

PAGE 74

65 LIST OF REFERENCES Baum, W. M. (1974a). Choice in free-ranging wild pigeons. Science, 185 78. Baum, W. M. (1974b). On two types of de viation from the matching law: Bias and undermatching. Journal of the Experimental Analysis of Behavior, 22 231. Baum, W. M. (1979). Matching, undermatchi ng, and overmatching in studies on choice. Journal of the Experimental Analysis of Behavior, 32 269. Baum, W. M., & Rachlin, H. C. ( 1969). Choice as time allocation. Journal of the Experimental Analysis of Behavior, 12 861-874. Beardsley, S. D., & McDowell, J. J (1992). Application of Herrnst eins hyperbola to time allocation of naturalistic human beha vior maintained by naturalistic social reinforcement. Journal of the Experimental Analysis of Behavior, 57 177. Belke, T. W., & Belliveau, J. (2001). The generalized matching law described choice on concurrent variable-interval sche dules of wheel-running reinforcement Journal of the Experimental An alysis of Behavior, 75 299-310. Bijou, S. W., Peterson, R. F., & Ault, M. H. (1968). A method to integrate descriptive and experimental field studi es at the level of data and empirical concepts. Journal of Applied Behavior Analysis, 1 175-191. Borrero, C. S.W., Vollmer, T. R., Borrero, J. C., & Bourret, J. (2005). A method for evaluating dimensions of reinforcemen t in parent-child interactions. Research in Developmental Disabilities 26, 577-592. Borrero, J. C., & Vollmer, T. R. (2002). An application of the matching law to severe problem behavior. Journal of Applied Behavior Analysis, 35 13-27. Carr, E. G., & Durand, V. M. (1985). Re ducing behavior problems through functional communication training. Journal of Applied Behavior Analysis, 18 111-126. Carr, E. G., & McDowell, J. J (1980). Soci al control of self-inj urious behavior or organic etiology. Behavior Therapy, 11 402. Catania, A. C. (1998). Learning ( 4th ed.). Upper Saddle River, NJ: Prentice Hall.

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66 Conger, R., & Killeen, P. (1974). Use of c oncurrent operants in small group research. Pacific Sociological Review 17 399. Crowley, M. A., & Donahoe, J. W. (2004). Ma tching: Its acquisition and generalization. Journal of the Experiment al Analysis of Behavior 82 143-159. Dixon, M. R., Hayes, L. J., Binder, L. M., Manthey, S., Sigman, C., & Zdanowshi, D. M. (1998). Using a self-control training procedure to incr ease appropriate behavior. Journal of Applied Behavior Analysis, 31 203-210. Fisher, W. W., Piazza, C. C., & Chiang, C. L. (1996). Effects of equal and unequal reinforcer duration during functional analyses. Journal of Applied Behavior Analysis, 29 117-120. Hanley, G. P., Iwata, B. A., & McCord, B. E. (2003). Functional analysis of problem behavior: A review Journal of Applied Behavior Analysis, 36 147-185. Herrnstein, R. J. (1961). Relative and absolu te strength of response as a function of frequency of reinforcement. Journal of the Experimental Analysis of Behavior, 4 563. Herrnstein, R. J. (1970). On the law of effect. Journal of the Experime ntal Analysis of Behavior, 13, 243-266. Herrnstein, R. J., & Loveland, D. H. (1975) Maximizing and matching on concurrent ratio schedules. Journal of the Experimental Analysis of Behavior, 24 107-116. Hoch, H., McComas, J. J., Johnson, L., Faranda, N., & Guenther, S. L. (2002). The effects of magnitude and quality of reinforcement on choice responding during play activities. Journal of Applied Behavior Analysis, 35 171-181. Horner, R. D., & Keilitz, I. (1975). Training me ntally retarded adolescents to brush their teeth. Journal of Applied Behavior Analysis, 8 301. Iwata, B. A., Dorsey, M. F., Slifer, K. J., Bauman, K. E., & Richman, G. S. (1994). Toward a functional analysis of self-injury. Journal of Applied Behavior Analysis, 27 197. (Reprinted from Analysis and Intervention in Developmental Disabilities, 2 3, 1982) Iwata, B. A., Pace, G. M., Kalsher, M. J., Cowdery, G. E., & Cataldo, M. F. (1990). Experimental analysis and extinction of self-injurious escape behavior. Journal of Applied Behavior Analysis, 23 11-27. Lerman, D. C., Kelley, M. E., Vorndran, C. M., Kuhn, S. A. C., & LaRue, R. H., Jr.

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67 (2002). Reinforcement magnitude a nd responding during treatment with differential reinforcement. Journal of Applied Behavior Analysis, 35 29-48. MacDonall, J. S. (1988). Concurrent variab le-ratio schedules: Implications for the generalized matching law. Journal of the Experimental Analysis of Behavior, 50 55-64. Mace, F. C., Neef, N. A., Shade, D., & Ma uro, B. C. (1994). Limited matching on concurrent-schedule reinforcement of academic behavior. Journal of Applied Behavior Analysis, 24 719. Mace, F. C., Neef, N. A., Shade, D., & Mauro, B. C. (1996). Effects of problem difficulty and reinforcer quality on time allocated to conc urrent arithmetic problems. Journal of Applied Behavior Analysis, 29 11-24. Martens, B. K., & Houk, J. L. (1989). The a pplication of Herrnstein s law of effect to disruptive and on-task behavior of a retarded adolescent girl. Journal of the Experimental Analysis of Behavior, 51 17. McDowell, J. J (1981). On the validity of and utility of the Herrn steins hyperbola in applied behavior analysis. In C. M. Bradshaw, E. Szabadi, & C. F. Lowe (Eds.), Quantification of steady-state operant behaviour (pp. 311). Amsterdam: Elsevier/ North Holland. McSweeney, F. K., Farmer, V. A., Dougan, J. D., & Whipple, J. E. (1986). The generalized matching law as a description of multiple-schedule responding. Journal of the Experimental Analysis of Behavior, 45 83-101. Neef, N. A., Bicard, D. F., & Endo, S. ( 2001). Assessment of impulsivity and the development of self-control in students with attention deficit hyperactivity disorder. Journal of Applied Behavior Analysis, 34 397-408. Neef, N. A., & Lutz, M. N. (2001). A brie f computer-based assessment of reinforcer dimensions affecting choice. Journal of Applied Behavior Analysis, 24 57. Neef, N. A., Mace, F. C., & Shade, D. ( 1993). Impulsivity in students with serious emotional disturbance: The interactive effects of reinforcer rate, delay, and quality. Journal of Applied Behavior Analysis, 26 37. Neef, N. A., Mace, F. C., Shea, M. C., & Shad e, D. (1992). Effects of reinforcer rate and reinforcer quality on time allocati on: Extensions of matching theory to educational settings. Journal of Applied Behavior Analysis, 25 691-699.

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68 Neef, N. A., Marckel, J., Ferreri, S. J., Bi card, D. F., Endo, S., Aman, M. G., et al. (2005). Behavioral assessment of impulsi vity: A comparison of children with and without attention defic it hyperactivity disorder. Journal of Applied Behavior Analysis, 38 23-37. Neef, N. A., Shade, D., & Miller, M. S. (1994). Assessing influential dimensions of reinforcers on choice in students wi th serious emotional disturbance. Journal of Applied Behavior Analysis, 27 575-583. Oliver, C., Hall, S., & Nixon, J. (1999). A molecular to mo lar analysis of communicative and problem behavior. Research in Developmental Disabilities, 20 197. Peck, S. M., Wacker, D. P., Berg, W. K., Coope r, L. J., Brown, K. A., Richman, D., et al. (1996). Choice-making treatment of young ch ildrens severe behavior problems. Journal of Applied Behavior Analysis, 29 263-290. Roane, H. S., Vollmer, T. R., Ringdahl, J. E., & Marcus, B. A. (1998). Evaluation of a brief stimulus preference assessment. Journal of Applied Behavior Analysis, 31 605. St. Peter, C. C., Vollmer, T. R., Bourret, J. C., Borrero, C. S. W., Sloman, K. N., & Rapp, J. T. (2005). On the role of attention in naturally occurring matching relations. Journal of Applied Behavior Analysis, 38 429-443. Stromer, R., McComas, J. J., & Rehfeldt, R. A. (2000). Designing interventions that include delayed reinforcement: Implicat ions of recent laboratory research. Journal of Applied Behavior Analysis, 33 359-371. Symons, F. J., Hoch, J., Dahl, N. A., & McComa s, J. J. (2003). Sequential and matching analyses of self-injurious behavior: A case of overmatching in the natural environment. Journal of Applied Behavior Analysis, 36 267-270. Volkert, V. M., Lerman, D. C., & Vorndran, C. (2005). The effects of reinforcer magnitude on functional analysis outcomes. Journal of Applied Behavior Analysis, 38 147-162. Vollmer, T. R., Borrero, J. C., Lalli, J. S., & Daniel, D. (1999). Evaluating self-control and impulsivity in children with severe behavior disorders. Journal of Applied Behavior Analysis, 32, 451-466. Vollmer, T. R., & Bourret, J. (2000). An a pplication of the matching law to evaluate the allocation of twoand three-point sh ots by college basketball players. Journal of Applied Behavior Analysis, 33 137.

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69 Vollmer, T. R., Iwata, B. A., Zarcone, J. R ., Smith, R. G., & Mazaleski, J. L. (1993). Within-session patterns of se lf-injury as indicators of behavioral function. Research in Developmental Disabilities, 14 479-492. Vollmer, T. R., Roane, H. S., Ringdahl, J. E., & Marcus, B. A. (1999). Evaluating treatment challenges with differential reinforcement of alternative behavior. Journal of Applied Behavior Analysis, 32 9.

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70 BIOGRAPHICAL SKETCH Carrie S. W. Borrero was born in Easton, Pennsylvania, in 1973 to Donald and Santa Wright, and grew up in Bethlehem, Penns ylvania. Carrie attended the University of Pittsburgh, and in 1995 graduated with a Bachelor of Science degree in psychology. In 1997, she entered the graduate program in counseling and human services at Villanova University in Pennsylvania. Carrie was aw arded her Master of Sc ience degree in 1999. She then entered the graduate program in psychology (behavior analysis) at the University of Florida.


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Table of Contents
    Title Page
        Page i
        Page ii
    Dedication
        Page iii
    Acknowledgement
        Page iv
    Table of Contents
        Page v
    List of Tables
        Page vi
    List of Figures
        Page vii
    Abstract
        Page viii
        Page ix
    Introduction
        Page 1
        Page 2
        Page 3
        Page 4
        Page 5
        Page 6
        Page 7
        Page 8
        Page 9
        Page 10
        Page 11
    Experiment 1: Functional analysis of problem behavior
        Page 12
        Page 13
        Page 14
        Page 15
        Page 16
        Page 17
        Page 18
        Page 19
        Page 20
        Page 21
    Experiment 2: Analysis of concurrent schedules of reinforcement and treatment of problem behavior
        Page 22
        Page 23
        Page 24
        Page 25
        Page 26
        Page 27
        Page 28
        Page 29
        Page 30
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        Page 33
        Page 34
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        Page 45
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        Page 50
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        Page 53
        Page 54
        Page 55
        Page 56
    General discussion
        Page 57
        Page 58
        Page 59
        Page 60
        Page 61
        Page 62
        Page 63
        Page 64
    References
        Page 65
        Page 66
        Page 67
        Page 68
        Page 69
    Biographical sketch
        Page 70
Full Text











CONCURRENT REINFORCEMENT SCHEDULES FOR PROBLEM BEHAVIOR
AND APPROPRIATE BEHAVIOR: EXPERIMENTAL APPLICATIONS OF THE
MATCHING LAW
















By

CARRIE S. W. BORRERO


A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE
UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE
REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY

UNIVERSITY OF FLORIDA


2006

































Copyright 2006

by

Carrie S. W. Borrero

































To my grandmothers, Grace Geraci Lipari and Dorothy Walsh Wright.















ACKNOWLEDGMENTS

I would like to thank those individuals who helped make this dissertation possible.

First, I thank Dr. Timothy Vollmer, my supervisory committee chair, for his support

during the course of my graduate training. He has provided invaluable advice on this and

other projects. I also thank Dr. Maureen Conroy, Dr. Jesse Dallery, Dr. Brian Iwata and

Dr. Christina McCrae for their assistance. Additional thanks are extended to my husband

and daughter, John and Isabella Borrero; my parents, Donald and Santa Wright, and my

brother, Christian Wright, for their love and support, without which I could not have

conducted this research. Finally, I would like to thank Jason Bourret, Monica Francisco,

Andrew Samaha, and Kimberly Sloman, who assisted in various aspects of the

development, implementation, and data analysis for this project.















TABLE OF CONTENTS



A C K N O W L E D G M E N T S ................................................................................................. iv

LIST OF TABLES ............. ................... .. .......... .................................... vi

LIST OF FIGURES ............................. .. .......... .................................. vii

ABSTRACT ................................................... ................. viii

CHAPTER

1 IN TR O D U C T IO N ........ .. ......................................... ..........................................1.

D definition and H historical O verview ................................................... ..................... 2

2 EXPERIMENT 1: FUNCTIONAL ANALYSIS OF PROBLEM BEHAVIOR........ 12

M e th o d ........................................................................................................................ 1 2
P a rtic ip a n ts ..........................................................................................................1 2
Setting .................................................................................. ....................... 12
P ro c e d u re .............................................................................................................1 3
R results and D iscu ssion .......................................................................... ...............16

3 EXPERIMENT 2: ANALYSIS OF CONCURRENT SCHEDULES OF
REINFORCEMENT AND TREATMENT OF PROBLEM BEHAVIOR ................22

M e th o d ........................................................................................................................2 2
P a rtic ip a n ts ..........................................................................................................2 2
Setting .................................................................................. ....................... 22
P ro c e d u re .............................................................................................................2 3
R results and D iscu ssion .......................................................................... ...............2 8

4 GEN ERAL D ISCU SSION ...................................................................................... 57

LIST O F R EFEREN CE S ................................................................................................65

BIO GRAPH ICAL SK ETCH ..........................................................................................70















LIST OF TABLES


Table page

4-1 Summary of correlation coefficients (r) for all participants using the Simple
Matching Equation and the coefficients of determination using the (r2)
G eneralized M watching E quation .......................................................... ................ 64















LIST OF FIGURES


Figure page

2-1 Overall response rates for Greg and Alice during the functional analysis phase .....20

2-2 Within session response rates for Audrey during the functional analysis phase. ....21

3-1 Overall response rates for problem and appropriate behavior for Greg................46

3-2 Overall response rates for problem and appropriate behavior during the
assessm ent phase for A udrey and A lice.............................................. ................ 47

3-3 Scatterplots of observed and predicted response allocation between problem
behavior and appropriate behavior for Greg for each condition during the
tangible assess ent ............... ............... ............................................... 48

3-4 Log response ratios plotted against log reinforcer ratios for Greg. The linear
equation depicts slope and bias during all conditions of the tangible assessment ...49

3-5 Scatterplots of observed and predicted response allocation between problem
behavior and appropriate behavior for Greg for all conditions during the escape
a sse ssm en t ................................................................................................................ 5 0

3-6 Log response ratios plotted against log reinforcer ratios for Greg. The linear
equation depicts slope and bias during all conditions of the escape assessment. ....51

3-7 Scatterplots of observed and predicted response allocation between problem
behavior and appropriate behavior for Audrey during the tangible assessment ......52

3-8 Log response ratios plotted against log reinforcer ratios for Audrey. The linear
equation depicts slope and bias during all conditions of the tangible assessment. ..53

3-9 Scatterplots of observed and predicted response allocation between problem
behavior and appropriate behavior for Alice during the escape assessment............54

3-10 Log response ratios plotted against log reinforcer ratios for Alice. The linear
equation depicts slope and bias during all conditions of the escape assessment. ....55

3-11 Scatterplots depicting examples of closer approximations to matching towards
the end of the condition using the simple matching equation. Arrows show the
first and last sessions w within a condition............................................. ................ 56















Abstract of Dissertation Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy

CONCURRENT REINFORCEMENT SCHEDULES FOR PROBLEM BEHAVIOR
AND APPROPRIATE BEHAVIOR: EXPERIMENTAL APPLICATIONS OF THE
MATCHING LAW

By

Carrie S. W. Borrero

December 2006

Chair: Timothy R. Vollmer
Major Department: Psychology

The purpose of this study was to determine if children who exhibit problem

behavior would allocate responding in direct proportion to experimentally arranged

reinforcement rates. Relative reinforcer rates were manipulated to evaluate changes in

relative response rate on concurrent variable-interval (VI) schedules, and results were

interpreted using two iterations of the matching equation: the strict (simple) matching

equation (Hermstein, 1961) and the generalized matching equation (Baum, 1974a).

Three individuals diagnosed with developmental disabilities, who engaged in severe

problem behavior, participated. In Experiment 1, functional analyses were conducted to

determine the reinforcers for problem behavior. Results showed that problem behavior

was sensitive to social positive reinforcement in the form of access to tangible items and

social negative reinforcement in the form of escape from instructional demands for one

participant, social positive reinforcement in the form of access to tangible items for









another, and social positive reinforcement in the form of attention and social negative

reinforcement in the form of escape from instructional demands for the third participant.

In Experiment 2, concurrent schedules of reinforcement were in place for both problem

and appropriate behavior. Results showed that the relative rates of responding

approximated the relative rates of reinforcement. In addition, interventions for problem

behavior were evaluated, and differential reinforcement of alternative behavior (DRA)

and extinction (EXT) procedures were implemented to increase the rate of appropriate

behavior and decrease the rate of problem behavior.















CHAPTER 1
INTRODUCTION

Choice has been defined as the emission of one of two or more alternative and

usually incompatible responses (Catania, 1998). Typical laboratory arrangements

implement concurrent-schedules with two or more alternatives, with each alternative

correlated with a reinforcement schedule. Hermstein (1961) provided a quantitative

description of responding on concurrent schedules of reinforcement, known as the

matching law. Generally, the matching law states that the relative rate of responding on

one alternative will approximate the relative rate of reinforcement provided on that

alternative. Baum (1974a) provided an alternative formulation of the matching law,

known as the generalized matching law that accounted for deviations from strict

matching by incorporating a bias parameter and a sensitivity parameter.

The matching law has been evaluated in a number of investigations using both non-

humans (Baum; Baum, 1974b; Baum, 1979; Belke & Belliveau, 2001; Crowley &

Donahoe, 2004; Hermstein; Herrnstein & Loveland, 1975; MacDonall, 1988,

McSweeney, Farmer, Dougan, & Whipple, 1986) and humans (e.g., Borrero & Vollmer,

2002; Mace, Neef, Shade, & Mauro, 1994; Martens & Houk, 1989; McDowell, 1981;

Neef, Mace, Shea, & Shade, 1992; Oliver, Hall, & Nixon, 1999; Symons, Hoch, Dahl, &

McComas, 2003; Vollmer & Bourret, 2000). Previous research with humans has

included both experimental and descriptive analyses of responding however, the

experimental evaluations of the matching law have evaluated academic responding (Mace









et al.; Neef& Lutz, 2001; Neef, Mace & Shade, 1993; Neef, Shade & Miller, 1994),

while the descriptive studies (Borrero & Vollmer; Martens & Houk; McDowell; Oliver et

al.; Symons et al.) have focused on severe problem behavior such as aggression, property

destruction, and self-injurious behavior (SIB). The present study involved experimental

analyses of responding on concurrent reinforcement schedules for individuals with

developmental disabilities who engaged in severe problem behavior. Results were then

evaluated using both the simple (Herrnstein) and generalized (Baum) matching equations.

Definition and Historical Overview

Herrnstein (1961) evaluated the effects of relative reinforcement frequency on

relative response frequency using concurrent variable-interval (VI) schedules. Initially,

training was conducted with 3 pigeons in order to establish key-pecking and alternation

of responding between two keys. Following training, pigeons were exposed to a

sequence of concurrent VI schedules for both keys: VI 3 min VI 3 min, VI 2.25 min VI

4.5 min, VI 1.8 min VI 9 min, and VI 1.5 min extinction (EXT). During most of the

experiment, a change-over delay (COD) was implemented such that when pigeons

switched keys, no reinforcer was possible for 1.5 s. Herrnstein plotted the percentage of

responses across the percentage of reinforcements provided for that alternative and

demonstrated that the relative response rate increased as the relative reinforcement rate

increased in a linear relationship. In addition, Herrnstein found that the COD had three

effects on responding: (a) when the COD was in effect, switching between the two keys

decreased, and (b) only when the COD was in effect did unequal reinforcement schedules

on the two keys reduce switching, and (c) when the COD was not present, as compared to

when the COD was present, matching was not obtained for two pigeons.









Herrnstein (1961) described the relative rate of responding and the relative rate of

reinforcement with the following Equation (1-1):

Ri rl
Ri +R2 rl + r2

where, Ri refers to the rate of responding on one alternative, and R2 refers to the rate of

responding for a second alternative, while ri is the rate of reinforcement for one

alternative (Ri) and r2 is the rate of reinforcement for the second alternative (R2). Results

suggested that relative response rate increased as a function of relative rate of

reinforcement, although this result was only observed when the COD was in place.

Baum (1974b) presented a variation of the matching equation now known as the

Generalized Matching Equation. The Generalized Matching Equation may be expressed

as follows (Equation 1-2):

( gin (Ri) ,
log alongg +loggb


where B, and B2 refer to the frequency of responding on the alternatives, and Ri and R2

represent the relative rates of reinforcement from each alternative. The generalized

matching equation takes into account bias (b) and the slope (a) of the function, which

provides information regarding sensitivity. These additional parameters provide

information useful in determining if undermatching or bias occur. Undermatching refers

to less than a one-unit increase in log ratio of responding produced by a one-unit increase

in log ratio of reinforcement. When undermatching occurs, the slope is less than 1.

Baum (1974b) suggested several factors that may lead to undermatching, including (a)

poor discrimination (e.g., the organism does not discriminate between the two schedules),

(b) absence of a COD, and (c) states of deprivation.









Bias refers to systematic deviations in responding that cannot be attributed to the

relative reinforcement rates. When bias occurs, b differs from 1. If b is less than 1, this

suggests that the organism favors the response in the denominator (B2). If b is greater

than 1, this suggests that the organism favors the response in the numerator (B1). Baum

(1974b) described factors that may lead to bias including (a) response bias (e.g., one

response may be more effortful than the other, color preferences, etc.), (b) a discrepancy

between scheduled and obtained reinforcement, (c) qualitatively different reinforcers

(e.g., hugs vs. reprimands, hemp vs. grain), and (d) qualitatively different schedules (e.g.,

VI vs. fixed-ratio [FR]).

A number of applied studies have evaluated naturally occurring situations using the

matching law. McDowell (1981) applied the single alternative formulation of the

matching law (Herrnstein, 1970) to evaluate data originally reported by Carr and

McDowell (1980). The single alternative formulation of the matching law may be

expressed as follows (Equation 1-3):

R kr
R=J-
r +re

where R represents response rate, and r represents reinforcement rate for single-

alternative environments. The parameter k is the y-asymptote and represents the total

amount of behavior in which the organism can engage. Finally, re represents all other

reinforcement not represented by r, and describes how quickly the function reaches its

asymptote. The larger the re, the more slowly the asymptote is reached, and generally, a

larger re value suggests a "richer" environment.

McDowell (1981) evaluated self-injurious scratching displayed by an 11 year-old

boy. In the initial investigation by Carr and McDowell (1980), the rates of self-









scratching and verbal reprimands were recorded during naturalistic observations between

the boy and his parents. Next, the researchers conducted an assessment and determined

that verbal reprimands reinforced self-scratching. Finally, they implemented an

intervention including a time-out component and a positive reinforcement component,

which decreased self-scratching. McDowell evaluated the data from the naturalistic

situation, and found that the boy's naturally occurring rates of self-scratching conformed

to Equation 3 as a function of adult attention. The single alternative formulation of the

matching law accounted for 99.67% of the variance in the rate of scratching observed,

and the results suggested Equation 3 provided a comprehensive description for human

behavior occurring in a non-laboratory environment (i.e., the natural environment).

In a related study, Martens and Houk (1989) evaluated the single alternative

formulation of the matching law to describe disruptive behavior and academic responding

in a classroom setting, with an 18-year-old woman diagnosed with developmental

disabilities and the staff in her classroom. They evaluated matching based on time

allocation between disruptive behavior (e.g., vocal outbursts, skin picking, off-task

behavior, etc.) and on-task behavior (e.g., independent work, compliance with requests,

and instructional interactions). Attention delivered from the teacher or classroom aide

was presumed to be a reinforcer by way of correlational analyses. Results showed that

the matching equation was useful in describing response allocation between the two

alternatives as a function of adult attention, and accounted for 83% of the variance

observed in disruptive behavior.

Oliver et al. (1999) evaluated time allocation between problem behavior (i.e.,

aggression) and communicative behavior (e.g., sign language) with a 7-year-old boy









diagnosed with Down syndrome. First, the researchers conducted a descriptive analysis

in the classroom across various activities. They then conducted an experimental analysis

using procedures similar to those described by Carr and Durand (1985) to identify

reinforcers for aggression. Based on the results from the descriptive and experimental

analyses, Oliver et al. concluded that the boy's aggression was reinforced by escape from

instructional demands. Finally, the researchers applied variations of the simple (1) and

generalized matching equations (2) in which time allocation (and not response rate) was

evaluated as a function of duration (and not rate) of reinforcement (e.g., Baum & Rachlin,

1969).

There are two potential limitations to the investigations described above. First,

Martens and Houk (1989) did not confirm that attention was in fact a reinforcer for

problem behavior. Research on functional analysis methods (see Hanley, Iwata &

McCord, 2003, for a recent review) demonstrates the utility of identifying events as

reinforcers, and it is not necessary to assume an event is a reinforcer. Although Oliver et

al. (1999) did conduct experimental manipulations in an effort to identify reinforcers

using methods described by Carr and Durand (1985), they did not experimentally

manipulate consequences for problem behavior. Second, functional analysis research has

demonstrated that problem behavior may be multiply controlled by several sources of

reinforcement, including access to tangible items and escape from instructional activities.

The studies by McDowell (1981) and Martens and Houk did not take into account

whether problem behavior was sensitive to additional sources of reinforcement.

To address these potential limitations, Borrero and Vollmer (2002) conducted an

investigation to evaluate the matching law by identifying reinforcers for problem









behavior using the functional analysis method of behavioral assessment, and interpreting

descriptive analysis data using identified reinforcers. The researchers conducted

descriptive analyses in an inpatient hospital setting or classroom setting for 4 individuals

diagnosed with developmental disabilities. All participants engaged in severe problem

behavior (e.g., property destruction, aggression, and SIB) as well as appropriate behavior

(e.g., vocal requests, gestures, and compliance with instructional demands). Next,

Borrero and Vollmer conducted functional analyses using procedures similar to those

described by Iwata, Dorsey, Slifer, Bauman, and Richman (1982/1994) and identified

reinforcers for problem behavior for all participants. Finally, they evaluated the

descriptive data using both the simple and generalized matching equations (Equations 1

and 2). Results showed that the relative rate of problem behavior approximately matched

the relative rate of reinforcement for problem behavior for all participants. In addition,

they evaluated multiple sources of reinforcement based on the results from the functional

analysis and found that responding was better described by the matching equation when

several possible sources of reinforcement were included in the analysis.

Additional research on the matching law with individuals who engage in problem

behavior has also included analyses of behavior occurring during naturally occurring

interactions (e.g., St. Peter et al., 2005) however no experimental analysis of the

matching law has been conducted for such individuals. As noted previously, the majority

of descriptive research evaluating the matching law has involved evaluations of problem

behavior, while experimental research has largely focused on academic tasks (e.g., Mace

et al., 1994; Neef et al., 1993; Neef et al., 1992; Neef et al., 1994).









Neef et al. (1992) conducted an investigation to demonstrate that (a) human

behavior is sensitive to concurrent schedules of reinforcement when reinforcer quality is

held constant, as suggested by the matching law and (b) the matching relation would not

occur when reinforcer quality was not equal, and that a bias for the higher quality

reinforcer would occur. The participants were individuals diagnosed with emotional

disturbances and learning difficulties. Prior to each session, the participant was asked if

she preferred to work for nickels or tokens. During each session, identical stacks of

arithmetic problems were placed in front of the participant, where each stack of cards was

associated with a VI schedule of reinforcement (e.g., VI 30-s, VI 120-s), and correct

responses resulted in reinforcement (e.g., nickels or tokens) delivered according to the

schedule in place for that alternative.

Initially, sessions were conducted to identify the participants' sensitivity to the VI

schedules of reinforcement, and a timer was included to signal the amount of time

remaining in the reinforcement interval. Neef et al. (1992) then evaluated two additional

conditions: (a) equal-quality reinforcers, during which two stacks of cards were presented

on concurrent VI schedules, and the reinforcers delivered were the same (i.e., either

nickels or tokens were delivered for both alternatives), and (b) unequal-quality

reinforcers, during which two stacks of cards were presented on concurrent VI schedules,

and high-quality reinforcers were delivered on the leaner schedule of reinforcement (i.e.,

VI 120-s) and low-quality reinforcers were delivered on the richer schedule of

reinforcement (i.e., VI 30-s). During the initial condition, responding was not allocated

as would be predicted by the concurrent VI schedules until the timer was included to

signal the reinforcement intervals. For all participants, time-allocation matching occurred









following the introduction of the timer. During the equal-quality reinforcers condition,

matching was observed, with the time allocated to each response alternative closely

approximating the obtained reinforcement from that alternative. During the unequal-

quality reinforcers condition, matching was not observed, and responding suggested a

preference for one of the two alternatives (i.e., nickels or tokens) for two participants, or

responding that maximized the number of reinforcers for that alternative, for one

participant. This study provided support for the applicability of the matching relation to

socially significant human behavior, and highlighted some potentially important

considerations, including the use of additional procedural manipulations (e.g., timer to

signal reinforcement intervals) to improve discrimination between concurrent VI

schedules, and biased responding, which may occur if the quality of available reinforcers

is not equal.

Using the same general procedures described in prior work (i.e., Neef et al., 1992),

Neef and colleagues (Mace et al., 1994; Neef et al., 1993; Neef et al., 1994) extended the

work reported by Neef et al. (1992) and showed that response allocation under concurrent

VI schedules was also sensitive to additional reinforcement parameters including

reinforcer delay. Because this series of experiments involved academic behavior of

individuals with emotional and learning disabilities the generality of the matching law

was extended to socially significant (appropriate) behavior.

Collectively, previous research suggests a need for an experimental analysis of

severe problem behavior exhibited by individuals with developmental disabilities, under

concurrent reinforcement schedules, using the matching law (Baum, 1974a, Herrnstein,

1961) as a conceptual framework. Prior research has supported the matching law as a









description of behavior across a number of settings, including the nonhuman laboratory,

natural environment, the human laboratory, and instructional situations. The purpose of

this dissertation was to conduct experimental analyses of problem behavior with 3

individuals diagnosed with developmental disabilities who engaged in severe problem

behavior. In Experiment 1, functional analyses were conducted for all participants to

identify reinforcers for problem behavior. Specifically, conditions were included to

determine if problem behavior was sensitive to (a) social positive reinforcement,

including adult attention or access to preferred tangible items (e.g., toys, edible items,

etc.), (b) social negative reinforcement, including escape from instructional demands or

aversive situations (e.g., hygiene tasks, daily living skills, etc.), or (c) automatic

reinforcement, suggesting that the reinforcer for problem behavior is not socially-

mediated (e.g., sensory reinforcement, pain alleviation, etc.).

In Experiment 2, concurrent schedules of reinforcement were introduced for

problem behavior and appropriate behavior (using reinforcers previously identified in

Experiment 1). Appropriate behavior was identified during formal descriptive

observations of each participant as well as during the functional analysis, and included

requests for access to tangible items (e.g., using picture cards, sign language, or vocal

requests), compliance with instructions, and gestures toward tangible items (e.g.,

reaching for items, pointing to objects, etc.). For each participant, concurrent schedules

of reinforcement were arranged for problem behavior and appropriate behavior, with one

schedule being richer than the other (i.e., more reinforcement was available for either

problem or appropriate behavior), or the schedules being equal (2 participants).

Following changes in responding with exposure to the schedule arrangement, the









schedules for problem and appropriate behavior were switched. That is, if the initial

phase included a VI 20-s schedule for problem behavior and a VI 60-s schedule for

appropriate behavior, the schedules were switched during the second phase such that a VI

60-s schedule was in place for problem behavior and a VI 20-s schedule was in place for

appropriate behavior. Additional replications for all phases were conducted. Finally, for

all participants, an intervention phase was included to decrease problem behavior,

including a continuous reinforcement schedule (CRF) for appropriate behavior, and

extinction (EXT) for all problem behavior. That is, during the intervention phase, all

instances of appropriate behavior resulted in access to the reinforcer, and all instances of

problem behavior did not result in access to the reinforcer. The goal of the intervention

phase was to reduce problem behavior to clinically significant levels and increase levels

of appropriate behavior.















CHAPTER 2
EXPERIMENT 1: FUNCTIONAL ANALYSIS OF PROBLEM BEHAVIOR


Method

Participants

Three individuals diagnosed with developmental disabilities who engaged in severe

problem behavior participated. Greg was an 8-year-old boy diagnosed with mild mental

retardation and autism. His problem behavior included screaming, defined as

vocalizations at a volume louder than conversation level, and disruptive behavior, defined

as throwing, hitting, or kicking objects. Audrey was a 14-year-old female diagnosed with

mental retardation. Her problem behavior included SIB, defined as hitting her chin, nose

and face with a closed fist, as well as self-choking (i.e., pushing her fingertips into her

throat). Alice was a 13-year-old girl who was diagnosed with childhood disintegrative

disorder. Her problem behavior included disruption, defined as throwing objects, and

aggression, defined as hitting and kicking others.

Setting

For Greg and Alice, functional analyses were conducted on an inpatient hospital

unit for the assessment and treatment of problem behavior at the University of Florida.

All sessions were conducted in a room with a table and chairs. Audrey's assessment was

conducted at a local school, and sessions were conducted in an available classroom,

furnished with desks and chairs.









Procedure

All sessions were conducted by trained graduate students serving as experimenters.

Observers were graduate and undergraduate students who received in-vivo training in

behavioral observation and had previously demonstrated high interobserver agreement

(IOA) scores (> 90%) with trained observers. Observers in the hospital setting were

seated behind a one-way mirror or sat unobtrusively at a table in the room. In the

classroom setting, observers were seated unobtrusively at a desk in the classroom.

Observers collected data on personal digital assistants (PDA) that provided real-time data

and scored events as either frequency (e.g., aggression, disruption, SIB, and screaming),

or duration (e.g., delivery of attention, escape from instructions, etc.). Sessions were

conducted two to three times each day, four days per week, and were 10 min in duration

(with the exception of one control session for Audrey).

Stimulus Preference Assessment. Prior to the functional analyses, free-operant

stimulus preference assessments were conducted using procedures described by Roane,

Vollmer, Ringdahl, and Marcus (1998) to identify preferred items to be included in the

conditions of the functional analysis, for each participant. An array of 6-8 leisure items

(e.g., musical keyboard, drawing toys, music, etc.) was placed on the floor or a table.

Before beginning the assessment, the participant was shown the item and allowed brief

(i.e., 2-3 s) contact with the item. The participant was then told that he or she could play

with any of the items, and the duration of time the participant interacted with each item

was scored. Preferred items were considered to be the three items for which interaction

was of the greatest duration.

Functional analysis. Functional analyses were conducted using procedures

similar to those described by Iwata et al. (1982/1994). Four test conditions were









compared: (a) attention, (b) tangible, (c) escape, and (d) no consequence (Audrey and

Alice only), to a control condition (play) using a multielelement design for all

participants. Consequences for problem behavior were provided contingent on screaming

or disruption (Greg), SIB (Audrey), and aggression or disruption (Alice).

During the attention condition, the participant was provided with preferred tangible

items, and no demands were presented, while the therapist diverted her attention to a

work task. Contingent on problem behavior, brief attention was provided for 30 s and

consisted of a reprimand (e.g., "Don't do that") followed by the therapist conversing with

the participant. This condition was included to determine if problem behavior was

reinforced by adult attention. During the tangible condition, the participant was provided

with adult attention and no demands were present, while the therapist restricted access to

preferred tangible items. Contingent on problem behavior, access to preferred items was

provided for 30 s. This condition was included to determine if problem behavior was

reinforced by access to tangible items. During the escape condition, the therapist

provided instructional demands (e.g., brushing teeth, washing face, combing hair, folding

towels) using a three-prompt instructional sequence (Horner & Keilitz, 1975).

Contingent on problem behavior, a 30-s break from instructions was provided and the

task materials were removed. This condition was included to determine if problem

behavior was negatively reinforced by escape from instructional demands. During the no

consequence condition (Audrey and Alice only) all preferred tangible items were

removed, and the participant received no attention from the therapist. There were no

programmed consequences for problem behavior. This condition was included to

determine if problem behavior persisted in the absence of programmed social









consequences. Finally, during the control condition, the participant had continuous

access to preferred tangible items, no demands were present, and adult attention was

provided at least every 30 s. There were no programmed consequences for problem

behavior. This condition was included as a point of comparison to the test conditions.

Interobserver agreement (IOA). Two independent observers collected data on

aggression, disruption, screaming, and SIB for a proportion of functional analyses

sessions to assess interobserver agreement (IOA). In addition, observers collected data

on the delivery of attention, access to tangible items, and escape from instructional

demands, and IOA was assessed. Observations were divided into 10-s bins, and the

number of observed responses was scored for each bin. The smaller number of observed

responses within each bin was divided by the larger number of observed responses and

converted to agreement percentages for frequency measures (Iwata, Pace, Kalsher,

Cowdery, & Cataldo, 1990). Agreement on the nonoccurrence of behavior within any

given bin was scored as 100% agreement. The bins were then averaged across the

session. In a session, the smaller number of s was divided by the larger number of s for

duration measures (and agreement on the nonoccurrence of behavior within any bin was

scored as 100% agreement). The bin data were then averaged across the sessions. For

Greg, IOA was scored for 53% of functional analysis sessions, and averaged 98.7% for

disruption (range, 96% to 100%), and 94.4% for screaming (range, 84% to 100%). IOA

averaged 100% for therapist attention, and 97% for access to tangible items (range,

91.1% to 100%), and 99.8% for escape from instructions (range, 99.4% to 100%).

For Audrey, IOA was scored for 28% of functional analysis sessions, and averaged

94% for SIB (range, 76% to 100%). IOA averaged 88% for therapist attention (range,









11% to 100%), 98% for access to tangible items (range, 92% to 100%), and 97% for

escape from instructions (range, 86% to 100%).

For Alice, IOA was scored for 42% of functional analysis sessions, and averaged

98.5% for aggression (range, 93% to 100%) and 98% for disruption (range, 95% to

100%). IOA averaged 82.75% for therapist attention (range, 26% to 100%), 87% for

access to tangible items (range, 1% to 100%), and 94% for escape from instructions

(range, 80% to 100%).

Results and Discussion

Figure 2-1 shows the results of the functional analyses for Greg and Alice. Panel A

of Figure 2-1 shows responses per min (rpm) of screaming for Greg. The highest rates of

screaming occurred in the tangible condition, with a mean response rate of 1.68 rpm, as

compared to the attention (M= .05 rpm), escape (M= .34 rpm), and control (M= 0 rpm)

conditions. These results suggested that Greg's screaming was reinforced by access to

tangible items. In addition, for Greg, Panel B of Figure 2-1 shows the responses per min

of disruption. The highest rates of disruption were observed during the escape condition,

with a mean response rate of .4 rpm, as compared to the attention, tangible, and control

conditions, which all had 0 rpm of disruption. Although the rate was low even in the

escape condition, the behavior was correlated with demand presentation and never

occurred in conditions other than escape. These results suggested that Greg's disruption

was reinforced by escape from instructional demands. In Greg's case, screaming and

disruption served different operant functions.

Panel C of Figure 2-1 shows the results of Alice's functional analysis. The highest

rates of aggression and disruption were observed during the escape (M= .7 rpm) and

attention (M= .6 rpm) conditions, when compared to the no consequence (M= 0 rpm),









tangible (M= .05 rpm), and control (M= .05 rpm) conditions. These results suggested

that Alice's aggression and disruption were reinforced by adult attention, and escape

from instructional demands. Data were collected for aggression and disruption separately

and similar results were obtained, therefore both topographies were combined in this

analysis. That is, there was no evidence to suggest that aggression or disruption served

distinct functions.

For Audrey, SIB rates seemed to carry over from one session to the next. As a

result, overall session mean rates looked similar across conditions even though the

therapists reported what seemed to be obviously different effects of the functional

analysis conditions. Because extinction bursts and carryover effects may have influenced

overall session mean rates, a within-session (min-by-min) analysis was used to identify

the operant functions of her SIB (Vollmer, Iwata, Zarcone, Smith, & Mazaleski, 1993).

Figure 2-2 shows the within-session results from Audrey's functional analysis. The

very first session was a no consequence session. However, prior to the session a therapist

removed access to tangible items. She engaged in a burst of SIB and reaching for the

items that persisted through the first session. A similar burst was seen in the second no

consequence session (seventh overall session); however, by the end of the session SIB

had extinguished. A third no consequence session conducted immediately thereafter

produced very low rates. Thus, although high mean rates of SIB were observed in two no

consequence sessions, the within-session data suggest that the behavior was not

automatically reinforced. In all three tangible sessions, SIB occurred at very stable rates

and occurred almost immediately upon removal of the tangible items. The SIB would

characteristically stop when the tangible items were returned to her. This effect resulted









in a SIB rate of approximately 2.0 per min (the same rate at which the establishing

operation was put in place). Rates of SIB were high in the escape condition and were

highly correlated with demands. By the second escape session (twelfth overall session),

she had become more "efficient" and engaged in minimal SIB, primarily when demands

were presented. Rates of SIB were zero in attention sessions (possibly a false negative if

the reinforcing effects of attention were outweighed by continuous access to tangibles,

but this possibility was not evaluated). Occasional bursts occurred at the beginning of

control sessions but the rate almost always waned by the end of the session. Overall the

functional analysis data suggested that Audrey's SIB was reinforced by escape and access

to tangibles. It is possible that SIB would have been influenced by attention if preferred

tangibles were not included in her sessions, but for the purposes of this study it was

important to identify at least one source of reinforcement for SIB and a more detailed

evaluation of attention was not pursued.

In summary, results of Experiment 1 identified the socially-mediated reinforcers for

the problem behavior exhibited by three individuals diagnosed with developmental

disabilities. For all participants, problem behavior was multiply controlled; that is,

problem behavior was reinforced by more than one type of event. Two individuals

engaged in problem behavior reinforced by access to tangibles, one engaged in problem

behavior reinforced by adult attention, and all three engaged in problem behavior

reinforced by escape from instructional demands. This experiment was a necessary

prerequisite to Experiment 2.

The results of Experiment 1 provided a basis for Experiment 2, during which

concurrent reinforcement schedules were in place for both problem and appropriate






19


behavior. Such analyses would not have been possible without identifying the

functions) of problem behavior. In Experiment 2, we attempted to evaluate how

responding would be allocated between concurrent schedules of reinforcement. In

addition, for all participants, we eventually conducted interventions to reduce problem

behavior to low levels and increase appropriate behavior.















C) '~
00
o ~
0


-
? 2-



1-

0-















S0.2
0.8-
S0.4-



0 0-


Escape


.. M--WP M


5


15


Greg
--I
20









B





Greg
0-I
20


SAttention


Alice
20
20


Sessions


Figure 2-1. Overall response rates for Greg and Alice during the functional analysis
phase. A) Responses per min of screaming for Greg. B) Responses per min
of disruption for Greg. C) Responses per min of disruption and aggression for
Alice.













Escape No Cons. Attention Control
on Control No Cons. Tangible Escape


5-
0- "Audrey

Minutes


Figure 2-2. Within session response rates for Audrey during the functional analysis
phase. A) Responses per minute of self-injurious behavior for Audrey.
















CHAPTER 3
EXPERIMENT 2: ANALYSIS OF CONCURRENT SCHEDULES OF
REINFORCEMENT AND TREATMENT OF PROBLEM BEHAVIOR


Method

Participants

Participants were the same three individuals who participated in Experiment 1.

Problem behavior was defined for each participant as in Experiment 1, and appropriate

behavior was also assessed for each participant. Greg's appropriate behavior was defined

as vocal requests for preferred tangible items (e.g., "Toys"), and compliance with

instructional demands (e.g., hygiene tasks). Audrey's appropriate behavior was defined

as requests for preferred tangible items (e.g., reaching for item). Alice's appropriate

behavior was defined as requests for a break from instructional demands through the use

of a microswitch. When Alice touched the microswitch, a recorded message (e.g.,

"Break, please") played. Due to clinical exigencies, Audrey's escape behavior and

Alice's attention maintained behavior were addressed outside the context of this research.

Setting

The setting was the same as in Experiment 1. For two participants (Greg and

Alice), analyses were conducted on an inpatient hospital unit for the assessment and

treatment of problem behavior. For one participant (Audrey), the analysis was conducted

at a local school, in an available classroom, furnished with desks and chairs.









Procedure

Trained graduate students served as experimenters for all sessions. Observers were

graduate and undergraduate students who received in-vivo training in behavioral

observation and who had previously demonstrated high interobserver agreement scores (>

90%) with trained observers. Observers in the hospital setting were seated behind a one-

way mirror or sat unobtrusively at a table in the room. In the classroom setting, observers

were seated unobtrusively at a desk in the classroom. Observers collected data on PDA

that provided real-time data and scored events as either frequency (e.g., aggression,

disruption, SIB, and screaming), or duration (e.g., delivery of attention, escape from

instructions). Sessions were conducted two to three times each day, four days per week,

and lasted 10 min. All participants were exposed to an initial baseline condition, which

was selected based on the results of Experiment 1. Each participant was exposed to four

conditions using a reversal design in order to assess response allocation for both problem

behavior and appropriate behavior on concurrent schedules of reinforcement. The order

of the conditions varied slightly for each participant, and was assigned randomly.

Baseline. The baseline condition was identical to the conditions) associated with

problem behavior during the functional analysis. These conditions varied for each

participant, and included the tangible condition for Greg, the tangible condition for

Audrey, and the escape condition for Alice. During baseline, each instance of problem

behavior resulted in delivery of the reinforcer (i.e., access to tangible items for Greg and

Audrey, or escape from instructions for Alice). No programmed consequences were in

place for appropriate behavior; that is, instances of appropriate behavior did not result in

access to the reinforcer.









Matching Analysis. Concurrent schedules of reinforcement were in place for both

problem and appropriate behavior (e.g., VI 10-s VI 10-s, VI 20-s VI 60-s) during the

analysis. The intervals were timed using a computer program that signaled (to observers)

when each schedule had elapsed. When reinforcement was available for a response (i.e.,

the interval elapsed) an observer signaled the therapist by holding up a colored card to

signal available reinforcement for a given response (e.g., blue card for problem behavior,

yellow card for appropriate behavior). An attempt was made to always keep the card

display outside of the participants' line of vision. The first instance of behavior

following availability of a reinforcer resulted in delivery of the preferred tangible item for

30 s. After 30 s of reinforcer access, the item was removed and the timer was reset for

that response. Participants were exposed to a subset of conditions, including either the

problem behavior (rich) or equal concurrent schedules, and appropriate behavior (rich).

Problem behavior (rich). The analysis conditions included concurrent VI

schedules for both responses: problem behavior and appropriate behavior. The problem

behavior (rich) condition (Greg only) was concurrent VI schedules (i.e., VI 20-s VI 60-

s), in which, the higher rate of reinforcement (i.e., VI 20-s schedule) was associated with

problem behavior while the lower rate of reinforcement (i.e., VI 60-s schedule) was

associated with appropriate behavior.

Equal concurrent schedules. The equal concurrent schedules condition (Audrey

and Alice only) included concurrent VI schedules (i.e., VI 10-s VI 10-s, and VI 20-s VI

20-s) during which the schedules were equal for problem and appropriate behavior.

Appropriate behavior (rich). The appropriate behavior (rich) condition (all

participants) included concurrent VI schedules (e.g., VI 30-s VI 10-s, VI 60-s VI 20-s,









and VI 60-s VI 10-s), in which the higher reinforcement rate was associated with

appropriate behavior while the lower reinforcement rate was associated with problem

behavior.

Full treatment. Finally, the treatment condition was designed to eliminate problem

behavior, and during this condition, differential reinforcement of alternative behavior

(DRA) was implemented. During DRA, problem behavior was placed on extinction (i.e.,

no reinforcers were delivered following problem behavior) and initially, each instance of

appropriate behavior resulted in reinforcement (i.e., CRF schedule).

Design. For Greg, the baseline condition, both the problem behavior (rich) and the

appropriate behavior (rich) conditions, and full treatment were conducted for the tangible

and escape functions of problem behavior. These conditions were evaluated in an

ABCBCDAD reversal design for the tangible condition, and a BCBCDAD reversal

design for the escape function, in which A represents the baseline condition, B represents

the problem behavior (rich) condition, C represents the appropriate behavior (rich)

condition, and D represents the full treatment condition. For Audrey, the baseline

condition (A), the equal concurrent schedules condition (E) appropriate behavior (rich)

condition (C), and full treatment (D) were conducted for the tangible function in a

reversal (i.e., ADADECCEC) design. The problem behavior (rich) condition (B) was not

conducted for Audrey due to the severity of her SIB. For Alice, the baseline condition

(A), the equal concurrent schedules condition (E), appropriate behavior (rich) (C)

condition, and full treatment (D) were conducted for the escape function in a reversal

(i.e., AECECD) design. The problem behavior (rich) condition (B) was not conducted

for Alice, because she was unexpectedly discharged from the hospital.









Data Analysis. For all participants, results were evaluated from a matching

perspective. In order to do so, rates of reinforcement for both problem and appropriate

behavior were calculated and applied to Equation 1 and Equation 2 to determine if the

relative rates of responding for problem and appropriate behavior approximated the

relative rates of reinforcement. Given the complexities of response-stimulus relations, it

is not clear what the definition of a reinforced response is, so in order to address this

potential concern, three definitions of a reinforced response were included, and were

evaluated using Equations 1 and 2.

Last Response Method. One definition of a reinforced response was a response

that occurred immediately prior to the delivery of a reinforcer. If problem behavior and

appropriate behavior are temporally contiguous, and a reinforcer was delivered following

one of the responses, it is possible that only the response that occurred immediately

before the reinforcer delivery was "reinforced" (from the organism's perspective). For

example, if problem behavior occurred 5 s before a reinforcer was delivered, and

appropriate behavior occurred 1 s before a reinforcer was delivered, using this method,

only appropriate behavior would be considered to be a reinforced response. This method

of calculation will be called the Last Response Method.

Within 10 s Method. A second definition of a reinforced response was a response

that occurred 10 s before a reinforcer was delivered. If problem and appropriate behavior

are temporally contiguous, and a reinforcer was delivered immediately following one of

the responses, it is possible that both responses were reinforced (from the organism's

perspective). For example, if problem behavior occurred 5 s before a reinforcer was

delivered, and appropriate behavior occurred immediately before a reinforcer was









delivered, using this method, both responses would be defined as reinforced. Although

10 s is somewhat arbitrary, some time value had to be adopted. This method of

calculation will be called the Within 10 s Method.

Programmed Reinforcer Method. Finally, a third definition of a reinforced

response was a response for which a reinforcer was delivered according to the

programmed reinforcement schedule. In other words, whichever response actually

produced the reinforcer was counted as the reinforced response. This method will be

called the Programmed Reinforcer Method.

For all calculations, the rate of responding and reinforcement were calculated for

both problem and appropriate behavior for each participant. The rate of responding was

calculated by taking the number of responses during a session and dividing by the

duration of the session, in min. The rate of reinforcement was calculated by taking the

number of reinforced responses (according the each of the three definitions provided

above) and dividing by the duration of the session, in min. The values obtained were

then inserted into Equation 1 and Equation 2 to determine if the relative rates of

responding approximated the relative rates of reinforcement for that response.

Interobserver agreement (IOA). IOA was calculated as in Experiment 1, and two

independent observers collected data on aggression, disruption, screaming, and SIB, as

well as appropriate responses including the use of picture cards, reaching, compliance

with instructional demands, and requests for a tangible item. Sessions were divided into

10-s bins, and the number of observed responses was scored for each bin. The smaller

number of observed responses within each bin was divided by the larger number of

observed responses and converted to agreement percentages for frequency measures









(Iwata et al., 1990). Agreement on the nonoccurrence of behavior within any given bin

was scored as 100% agreement. The bins were then averaged across the session. In a

session, the smaller number of s was divided by the larger number of s for duration

measures (and agreement on the nonoccurrence of behavior within any given bin was

scored as 100%). The bin scores were then averaged across the sessions. For Greg, IOA

was scored for 47% of assessment sessions during the tangible condition, and averaged

100% for disruption, 95% for screaming (range, 80 to 100%), 94.4% for appropriate

requests (range, 80.8 to 100%), and 91.7% for access to tangible items (range, 84.1 to

100%). IOA was scored for 44% of assessment sessions during the escape condition,

and averaged 89.6% for disruption (range, 87.5-100%), 94.3% for compliance with

instructional demands (range, 85.8 to 100%), and 88.7% for escape from instructions

(range, 84.7 to 100%).

For Audrey, IOA was scored for 36% of assessment sessions, and averaged 95.2%

for SIB (range, 80 to 100%), and 95% for reaching for tangible items (range, 80 to

100%), and 83% for access to tangible items (range, 15% to 97%).

For Alice, IOA was scored for 32% of assessment sessions, and averaged 98.5%

for aggression (range, 94 to 100%), 93.17% for disruption (range, 82 to 100%), and

100% for a request for a break from instructional demands (range, 100 to 100%). IOA

averaged 88% for escape from instructions (range 64 to 96%).

Results and Discussion

Panel A (top panel) of Figure 3-1 shows the results of the analysis for Greg, during

the tangible condition. Responses per min of problem and appropriate behavior are

displayed for all phases. The initial baseline (A) for the tangible condition (top panel)

shows the sessions conducted during the functional analysis. Following the baseline,









Greg's behavior was exposed to the problem behavior (rich) condition (B). During this

condition Greg engaged in higher rates of problem behavior (M= 2.21 rpm) than

appropriate behavior (M= .95 rpm). The schedules of reinforcement were then switched

to VI 60-s for problem behavior and VI 20-s for appropriate behavior (i.e., appropriate

behavior (rich) [C]). During this condition, similar rates of problem behavior (M= 2.10

rpm) and appropriate behavior (M= 2.1 rpm) were observed. During the reversal to the

problem behavior (rich) condition (i.e., VI 20-s schedule for problem behavior and VI

60-s for appropriate behavior) higher rates of problem behavior (M= 1.50 rpm) than

appropriate behavior (M= 1.10 rpm) were observed. During this condition, it was

observed that Greg's screaming occurred contiguous with appropriate requests for

tangible items, and a 2-s COD was included. During the second appropriate behavior

(rich) condition (i.e., VI 60-s VI 20-s) problem behavior occurred at a lower rate

(M= 3.30 rpm) relative to appropriate behavior (M= 4.40 rpm). In order to produce a

clinically acceptable treatment effect, problem behavior was placed on EXT and

appropriate behavior was reinforced on a continuous reinforcement schedule (CRF)

schedule (D) initially. In addition, because problem and appropriate behavior continued

to occur together, the COD was increased to 5 s. Problem behavior decreased (M= 2.79

rpm) and appropriate behavior continued to occur (M= 3.30 rpm). For the final three

sessions, the mean rate of problem behavior was .03 rpm. During a brief reversal to

baseline levels of problem behavior increased (M= 1.75 rpm), while appropriate behavior

decreased relative to the previous condition (M= .55 rpm). A final treatment phase was

conducted and problem behavior decreased to low levels (M= .82 rpm, 0 in the final two









sessions) and appropriate behavior returned to levels observed in previous phases (M=

2.02 rpm).

Panel B (lower panel) of Figure 3-1 displays the results of the analysis for Greg

during the escape condition. The problem behavior (rich) condition (B) was

implemented first, and during this phase, problem behavior occurred at a higher rate (M=

2.50 rpm) compared to appropriate behavior (M= 1.1 rpm). The appropriate behavior

(rich) condition (C) was conducted next, and, during this condition, problem behavior

occurred at a lower rate (M= 1.10 rpm) relative to appropriate behavior (M= 2.10 rpm).

During a reversal to the problem behavior (rich) condition problem behavior occurred at

a slightly higher rate (M= 1.50 rpm) relative to appropriate behavior (M= 1.12 rpm),

with clear separation in response rates across the last five sessions of the condition. The

appropriate behavior (rich) condition was replicated, and initially higher rates of problem

behavior (M= 2.34 rpm) occurred relative to appropriate behavior (M= .87 rpm).

Problem behavior appeared to be decreasing, and at that time, Greg left the hospital for

approximately two weeks (depicted on Figure 3-1 by the dashed vertical line). Following

his return to the inpatient unit, the appropriate behavior (rich) condition continued, and

eventually problem behavior decreased across the condition (M= 2.87 rpm), while

appropriate behavior continued to occur at stable levels (M= .94 rpm). In order to reduce

problem behavior to clinically significant levels, a treatment condition (D) was

conducted, and problem behavior was placed on extinction while appropriate behavior

was reinforced on a CRF schedule. Problem behavior decreased to near zero levels (M=

.05 rpm) and appropriate behavior occurred at stable levels (M= .39 rpm). During a

brief reversal to the baseline condition problem behavior increased (M= 1.70 rpm) as









well as appropriate behavior (M= 2.40 rpm), and a final treatment condition resulted in a

decrease in problem behavior (M= .12 rpm) and stable levels of appropriate behavior (M

= .86 rpm).

Panel A of Figure 3-2 shows the results of the analysis for Audrey. Responses per

min of problem and appropriate behavior are displayed for all phases. During the initial

baseline (A) for Audrey, which included functional analysis sessions (sessions 1-3) and

additional baseline sessions (sessions 4-14), relatively high rates of SIB were observed

(M= 1.99 rpm) and relatively low levels of appropriate behavior (i.e., reaching) were

observed (M= .13 rpm). In order to decrease SIB to low levels, a treatment phase (D)

was conducted, during which problem behavior was placed on EXT, and appropriate

behavior resulted in access to the reinforcer (i.e., tangible items) on a CRF schedule. SIB

decreased (M= .86 rpm) and appropriate behavior increased (M= 1.44 rpm) during this

phase. This effect was replicated during brief reversals to the baseline and treatment

conditions. During the reversal to the baseline condition, SIB increased (M= 1.70 rpm)

and appropriate behavior decreased slightly (M= 1.17 rpm). During the replication of the

treatment condition, SIB decreased (M= .30 rpm) and appropriate behavior increased (M

= 1.50 rpm). During the next phase, equal concurrent schedules (i.e., VI 10-s VI 10-s)

(E) were implemented for both problem behavior and appropriate behavior. The equal

concurrent schedules condition yielded similar rates of problem behavior (M= 1.17 rpm)

and appropriate behavior (M= 1.24 rpm). Following the equal concurrent schedules

condition, the appropriate behavior (rich) condition (C) was implemented. During this

condition, rates of problem behavior (M= .97 rpm) and appropriate behavior (M= 1.60

rpm) were similar, although towards the end of the phase, less problem behavior occurred









relative to appropriate behavior. Next, concurrent schedules were arranged for problem

behavior and appropriate behavior in which the absolute values for both schedules were

altered (VI 60-s VI 20-s), while continuing to favor appropriate behavior, and retaining

the same proportional difference (1:3) in place in the prior appropriate behavior rich

condition. Similar results were observed as in the previous appropriate behavior (rich)

condition, and problem behavior occurred at a slightly lower rate (M= .23 rpm) relative

to appropriate behavior (M= 2.20 rpm). The equal concurrent schedules condition was

then replicated and the rates of problem behavior (M= 1.25 rpm) and appropriate

behavior (M= 1.31 rpm) were similar. A replication of the appropriate behavior (rich)

condition was conducted, and initially, similar rates of problem behavior (M= 1.60 rpm)

and appropriate behavior (M= 1.86 rpm) occurred at similar rates, although towards the

end of the phase, problem behavior occurred at a lower rate than appropriate behavior.

Due to the severity of Audrey's SIB, we implemented full treatment immediately

following baseline. We continued to implement the full treatment procedures for Audrey

outside the context of this research.

Panel B of Figure 3-2 shows the results of the escape analysis for Alice. The initial

baseline condition (A) shows the results from the functional analysis. The baseline

yielded high rates of problem behavior and no appropriate behavior (compliance).

During the equal concurrent schedules condition (E) problem behavior occurred at a

lower rate (M= .39 rpm) relative to appropriate behavior (M= .90 rpm). Next, the

appropriate behavior (rich) condition (VI 60-s VI 10-s) (C) was implemented, and during

this condition, problem behavior occurred at an inexplicably higher rate (M= 2.20 rpm)

relative to appropriate behavior (M= .90 rpm). Next, a replication of the equal









concurrent schedules condition was implemented, and problem behavior occurred at a

higher rate (M= 1.05 rpm) relative to appropriate behavior (M= .35 rpm). During the

replication of the appropriate behavior (rich) condition, more problem behavior (M= 1.20

rpm) occurred relative to appropriate behavior (M= .27 rpm). Finally, a treatment phase

(D) was conducted during which problem behavior was placed on extinction and

appropriate behavior was reinforced on a CRF schedule. During this phase, problem

behavior (M= .60 rpm) occurred at relatively low rates (.20 rpm in final session), and

appropriate behavior (M= 2.94 rpm) occurred at relatively high rates. Alice's assessment

was brief and additional replications were not conducted, due to her brief stay in the

hospital.

Figures 3-3 through 3-10 show the results from the matching analysis (i.e., simple

matching and generalized matching) for all participants. For all scatter plots showing the

results using the simple matching equation (i.e., Figures 3-3, 3-5, 3-7, and 3-9), the

scatter plots show proportional response rates as a function of proportional reinforcer

rates. The dashed diagonal line represents perfect matching as described by Equation 1.

Panel A (top left) shows the results using the last response method of calculation and

Panel B (top right) shows the means for each condition using the last response method of

calculation depicted in panel A. In Panel A, each data point represents a session, and in

Panel B, each data point represents the mean for the last five sessions in each condition of

the assessment. Panel C (middle left) shows the results using the within 10-s method of

calculation and Panel D (middle right) shows the means for each condition using the

within 10-s method of calculation. In Panel C, each data point represents a session, and in

Panel D, each data point represents the mean for the last five sessions in each condition.









Finally, Panel E (bottom left) shows the results using the programmed reinforcer method

of calculation and Panel F (bottom right) shows the means for each condition using the

programmed reinforcer method of calculation. In Panel E, each data point represents a

session, and in panel F, each data point represents the mean for the last five sessions in

each condition.

For the results using the generalized matching equation (i.e., Figures 3-4, 3-6, 3-8,

and 3-10), the scatter plots show the log response ratios plotted as a function of log

reinforcer ratios. The linear equation depicts slope and bias. The dashed diagonal line

represents perfect matching. The solid line is a best fit line. Panel A (top left) shows the

results using the last response method of calculation and Panel B (top right) shows the

means for each condition using the last response method of calculation. In Panel A, each

data point represents a session, and in Panel B, each data point represents the mean for

the last five sessions in each condition. Panel C (middle left) shows the results using the

within 10-s method of calculation and Panel D (middle right) shows the means for each

condition using the within 10-s method of calculation. In Panel C, each data point

represents a session, and in Panel D, each data point represents the mean for the last five

sessions in each condition. Finally, Panel E (bottom left) shows the results using the

programmed reinforcer method of calculation and Panel F (bottom right) shows the

means for each condition using the programmed reinforcer method of calculation. Again,

in Panel E, each data point represents a session, and in Panel F, each data point represents

the mean for the last five sessions in each condition.

Figure 3-3 shows the results from the matching analysis of the tangible condition

using Equation 1-1 for Greg. Due to a computer virus that erased data on reinforcer









presentations, calculations could not be conducted for each session of each condition of

Greg's analyses. However, a reasonably representative number of sessions were

available. Generally, for the last response method of calculation (Panel A), the

proportional rates of problem behavior were correlated with the proportional

reinforcement rates for problem behavior (r = .80). During a number of sessions, more

problem behavior was observed than would be predicted based on the rate of

reinforcement for problem behavior. The means for each condition using the last

response method of calculation (Panel B) also show that the relative rate of responding

was correlated with the relative rate of reinforcement (r = .98). During the conditions

with a higher rate of reinforcement for appropriate behavior (VI 60-s VI 20-s) slightly

more problem behavior was observed than would be predicted based on the proportional

rate of reinforcement for problem behavior (denoted by data points above the dashed

diagonal line). For the within 10-s method of data calculation (Panel C, the proportional

rates of problem behavior were correlated with the proportional reinforcement rates for

problem behavior (r = .80). During a number of sessions, less problem behavior was

observed than would be predicted based on the proportional rate of reinforcement for

problem behavior. The means for each condition using the within 10-s method of

calculation (Panel D) also show that the relative rate of responding was correlated with

the relative rate of reinforcement (r = .98). For the programmed reinforcer method of

calculation (Panel E), the proportional rates of problem behavior were correlated with the

proportional reinforcement rates for problem behavior (r = .59), although during a

number of sessions, less problem behavior was observed than would be predicted based

on the proportional rate of reinforcement for problem behavior. The means for each









condition using the programmed reinforcer method of calculation (Panel F) also show

that the relative rate of responding was correlated with the relative rate of reinforcement

(r = .99). During the condition with a higher rate of reinforcement for problem behavior

(VI 20-s VI 60-s) slightly less problem behavior was observed than would be predicted

based on the proportional rate of reinforcement for problem behavior.

Figure 3-4 shows the results from Equation 1-2 for Greg during the tangible

condition. Generally, for the last response method of calculation (Panel A), the

proportional rates of problem behavior were correlated with the proportional

reinforcement rates for problem behavior, however the best fit line does not indicate close

adherence to the matching equation (r2 = .45). The means for each condition using the

last response method of calculation (Panel B) also show that the relative rate of

responding was correlated with the relative rate of reinforcement, and the best fit line

indicated adherence to the matching equation (r2 = .92). The slope for both panels was

less than 1.0, which suggests that undermatching occurred. Undermatching refers to the

occurrence of less behavior than would be predicted based on the relative rates of

reinforcement. For the within 10-s method of calculation (Panel C), the proportional

rates of problem behavior were correlated with the proportional reinforcement rates for

problem behavior, however the best fit line does not indicate close adherence to the

matching equation (r2 = .28) due to three sessions in particular during the second problem

behavior rich condition. The means for each condition using the within 10-s method of

calculation (Panel D) also show that the relative rate of responding was correlated with

the relative rate of reinforcement, and the best fit line did not indicate strict adherence to

the matching equation (r2 = .40). The slope for both panels was less than 1.0, which









suggests that undermatching occurred. For the programmed reinforcer method of

calculation (Panel E), the proportional rates of problem behavior were correlated with the

proportional reinforcement rates for problem behavior, and the best fit line approximated

perfect matching (r2 = .60). The means for each condition using the programmed

reinforcer method of calculation (Panel F) also show that the relative rate of responding

was correlated with the relative rate of reinforcement, and the best fit line indicated

matching (r2 = .81). The slope for both panels was less than 1.0, which suggests that

undermatching occurred.

Figure 3-5 shows the results from the matching analysis of the escape condition

using Equation 1-1 for Greg. Due to a computer virus, calculations could not be

conducted for each session of each condition. Generally, for the last response method of

calculation (Panel A), the proportional rates of problem behavior were correlated with the

proportional reinforcement rates for problem behavior (r = .49), however for a number of

sessions, more problem behavior was observed than would be predicted based on the

proportional rate of reinforcement for that response. For the most part, these sessions

(with more problem behavior observed than would be predicted) were those during which

more reinforcement was available for appropriate behavior relative to problem behavior

(VI 60-s VI 20-s). The means for each condition using the last response method of

calculation (Panel B) also show that the relative rate of responding was correlated with

the relative rate of reinforcement (r = .97). During the conditions with a higher rate of

reinforcement for appropriate behavior (VI 60-s VI 20-s) slightly more problem behavior

was observed than would be predicted based on the proportional rate of reinforcement for

problem behavior. For the within 10-s method of calculation (Panel C), the proportional









rates of problem behavior were positively correlated with the proportional reinforcement

rates for problem behavior (r = .92). The means for each condition using the within 10-s

method of calculation (Panel D) also show that the relative rate of responding was

correlated with the relative rate of reinforcement (r = .78), however, more problem

behavior was observed than would be predicted based on the proportional rate of

reinforcement for problem behavior for one condition (one VI 60-s VI 20-s condition),

and less problem behavior was observed than would be predicted for the other conditions

(VI 20-s VI 60-s, and one VI 60-s VI 20-s condition). Similar results were observed for

the programmed reinforcer method of calculation (Panel E) as in the last response method

of calculation, and the proportional rates of problem behavior were correlated with the

proportional reinforcement rates for problem behavior (r = .41), although during a

number of sessions, more problem behavior was observed than would be predicted based

on the proportional rate of reinforcement for problem behavior. For the most part, these

sessions were those during which more reinforcement was available for appropriate

behavior relative to problem behavior (VI 60-s VI 20-s). The means for each condition

using the programmed reinforcer method of calculation (Panel F) also show that the

relative rate of responding was correlated with the relative rate of reinforcement (r = .95),

however, more problem behavior was observed than would be predicted based on the

proportional rate of reinforcement for problem behavior during conditions with more

reinforcement available for appropriate behavior (i.e., VI 60-s VI 20-s), and less problem

behavior was observed than would be predicted for the conditions during which more

reinforcement was available for problem behavior (i.e., VI 20-s VI 60-s).









Figure 3-6 shows the results from Equation 1-2 for Greg during the escape

condition. Generally, for the last response method of calculation (Panel A), the

proportional rates of problem behavior were correlated with the proportional

reinforcement rates for problem behavior, however the best fit line does not indicate close

adherence to matching (r2 = .30). The means for each condition using the last response

method of calculation (Panel B) also show that the relative rate of responding was

correlated with the relative rate of reinforcement, and the best fit line indicated adherence

to the matching equation (r2 = .60). The slope for both panels was less than 1.0, which

suggests that undermatching occurred. For the within 10-s method of calculation (Panel

C), the proportional rates of problem behavior were closely correlated with the

proportional reinforcement rates for problem behavior, and the best fit line indicated

matching (r2 = .85). The means for each condition using the within 10-s method of

calculation (Panel D) also show that the relative rate of responding was positively

correlated with the relative rate of reinforcement, and the best fit line indicated matching

(r2 = .88). The slope for both panels was less than 1.0, which suggests that

undermatching occurred. For the programmed reinforcer method of calculation (Panel

E), the proportional rates of problem behavior were correlated with the proportional

reinforcement rates for problem behavior, however the best fit line did not approximate

perfect matching (r2 = .22). The means for each condition using the programmed

reinforcer method of calculation (Panel F) also show that the relative rate of responding

was correlated with the relative rate of reinforcement, and the best fit line indicated strict

adherence to the matching equation (r2 = .69). The slope for both panels was less than

1.0, which suggests that undermatching occurred.









Figure 3-7 shows the results from the matching analysis of the tangible condition

using Equation 1-1 for Audrey. Generally, for the last response method of calculation

(Panel A), the proportional rates of problem behavior were correlated with the

proportional reinforcement rates for problem behavior (r = .79), however for a number of

sessions, more problem behavior was observed than would be predicted based on the

proportional rate of reinforcement for that response. The means for each condition using

the last response method of calculation (Panel B) also show that the relative rate of

responding was positively correlated with the relative rate of reinforcement (r = .98).

During the conditions with a higher rate of reinforcement for appropriate behavior (VI

60-s VI 20-s) slightly more problem behavior was observed than would be predicted

based on the proportional rate of reinforcement for problem behavior. Generally, for the

within 10-s method of calculation (Panel C), the proportional rates of problem behavior

were closely correlated with the proportional reinforcement rates for problem behavior (r

= .87), with the points falling close to the line indicating perfect matching. The means

for each condition using the within 10-s method of calculation Panel D) also show that

the relative rate of responding was correlated with the relative rate of reinforcement (r =

.95). Similar results were observed for the programmed reinforcer method of calculation

(Panel E) as in the previous methods of calculation, and the proportional rates of problem

behavior were positively correlated with the proportional reinforcement rates for problem

behavior (r = .72). The means for each condition using the programmed reinforcer

method of calculation (Panel F) also show that the relative rate of responding was

positively correlated with the relative rate of reinforcement (r = .96).









Figure 3-8 shows the results from Equation 1-2 for Audrey during the tangible

condition. Generally, for the last response method of calculation (Panel A), the

proportional rates of problem behavior were correlated with the proportional

reinforcement rates for problem behavior, however the best fit line does not indicate

matching (r2 = .23). The means for each condition using the last response method of

calculation (Panel B) also show that the relative rate of responding was correlated with

the relative rate of reinforcement, and the best fit line did not indicate adherence to the

matching equation (r2 = .28). The slope for both panels was less than 1.0, which

suggests that undermatching occurred. For the within 10-s method of calculation (Panel

C), the proportional rates of problem behavior were correlated with the proportional

reinforcement rates for problem behavior, and the best fit line indicated matching (r2 =

.84). The means for each condition using the within 10-s method of calculation (Panel D)

also show that the relative rate of responding was positively correlated with the relative

rate of reinforcement, and the best fit line indicated almost perfect matching (r2 = .99).

The slope for Panel C was less than 1.0, which suggests that undermatching occurred.

Generally, for the programmer reinforcer method of calculation (Panel E) the

proportional rates of problem behavior were positively correlated with the proportional

reinforcement rates for problem behavior, however the best fit line did not approximate

perfect matching (r2 = .44). The means for each condition using the programmed

reinforcer method of calculation (Panel F) also show that the relative rate of responding

was correlated with the relative rate of reinforcement, and the best fit line matching (r2 =

.86). The slope for both panels was less than 1.0, which suggests that undermatching

occurred.









Figure 3-9 shows the results from the matching analysis of the escape condition

using Equation 1-1 for Alice. Generally, for the last response method of calculation

(Panel A) the proportional rates of problem behavior were correlated with the

proportional reinforcement rates for problem behavior (r = .77), however for a number of

sessions, more problem behavior was observed than would be predicted based on the

proportional rate of reinforcement for that response. The means for each condition using

the last response method of calculation (Panel B) also show that the relative rate of

responding was correlated with the relative rate of reinforcement (r = .77). For the within

10-s method of calculation (Panel C), the proportional rates of problem behavior were

correlated with the proportional reinforcement rates for problem behavior (r = .75),

however, during some sessions more problem behavior was observed than would be

predicted based on the proportional rate of reinforcement for problem behavior. The

means for each condition using the within 10-s method of calculation (Panel D) also

show that the relative rate of responding was correlated with the relative rate of

reinforcement (r = .84). For the programmed reinforcer method of calculation (Panel E),

similar results were observed as in the previous methods of calculation, and the

proportional rates of problem behavior were correlated with the proportional

reinforcement rates for problem behavior (r = .71). The means for each condition using

the programmed reinforcer method of calculation (Panel F) also show that the relative

rate of responding was correlated with the relative rate of reinforcement (r = .84).

Figure 3-10 shows the results from Equation 1-2 for Alice during the tangible

condition. Generally, for the last response method of calculation (Panel A), the

proportional rates of problem behavior were correlated with the proportional









reinforcement rates for problem behavior, however the best fit line does not indicate

matching (r2 = .25). The means for each condition using the last response method of

calculation (Panel B) also show that the relative rate of responding was correlated with

the relative rate of reinforcement, and the best fit line did not indicate matching (r2 = .23).

The slope for both panels was less than 1.0, which suggests that undermatching occurred.

For the within 10-s method of calculation (Panel C), the proportional rates of problem

behavior were correlated with the proportional reinforcement rates for problem behavior,

and the best fit line did not indicate matching (r2 = .32). The means for each condition

using the within 10-s method of calculation (Panel D) also show that the relative rate of

responding was correlated with the relative rate of reinforcement, however, the best fit

line did not indicate matching (r2 = .01). The slope for both panels was less than 1.0,

which suggests that undermatching occurred. Generally, for the programmed reinforcer

method of calculation (Panel E) the proportional rates of problem behavior were

correlated with the proportional reinforcement rates for problem behavior, however the

best fit line did not approximate perfect matching (r2 = .45). The means for each

condition using the programmed reinforcer method of calculation (Panel F) also show

that the relative rate of responding was correlated with the relative rate of reinforcement,

and the best fit line did not indicate strict adherence to the matching equation (r2 = .41).

The slope for both Panel F was less than 1.0, which suggests that undermatching

occurred.

Figure 3-11 provides examples from each participant depicting closer

approximations to matching towards the end of a condition. Each figure has been

discussed above and shown with the results for each participant. However in Figure 3-11









the first and last sessions of a condition are noted with an arrow for each participant.

Panel A shows the results using the within 10 s method of calculation for Greg's tangible

analysis during the second VI 20-s VI 60-s phase. In the last session of the condition, the

proportional rate of responding more closely approximates the proportional rate of

reinforcement relative to the first session in that condition. Panel B shows the results

using the last response method of calculation for Audrey's tangible analysis during the

second VI 10-s VI 10-s phase. Again, in the last session of the condition, the

proportional rate of responding more closely approximates the proportional rate of

reinforcement relative to the first session in that condition. Panel C shows similar results

using the within 10 s method of calculation for Greg's escape analysis during the second

VI 20-s VI 60-s phase. Finally, Panel D shows similar results using the last response

method of calculation for Alice's escape analysis during the first VI 60-s VI 20-s phase.

In summary, results of the matching analysis indicated that, for all participants the

relative rates of both problem behavior and appropriate behavior were sensitive to the

schedules of reinforcement available for each alternative. In addition, interventions were

implemented and successfully decreased levels of problem behavior to clinically

acceptable levels. Further, evaluation of the results from a matching perspective using

both the simple matching equation (1-1) and the generalized matching equation (1-2)

indicated that for all participants, relative rates of problem behavior were positively

correlated with the relative rate of reinforcement for problem behavior. Results of this

investigation suggest that the matching law can provide an explanation for problem

behavior exhibited by individuals with developmental disabilities. While "perfect

matching" was not obtained, matching is a steady state phenomenon and all participants









were exposed to the various conditions only briefly, and positive correlations were

observed. One possible explanation may be that the early sessions in each condition

represent a transition period, during which the participant begins to discriminate between

the concurrent schedules of reinforcement, and that stable responding occurs towards the

end of each condition. A comparison of the session-by-session scatter plots and the mean

scatter plots suggests that closer approximations to matching were observed by

calculating the mean of the last five sessions of each condition than calculating all

sessions in each condition. This effect was observed for all participants.

For Alice, we were not able to complete a thorough assessment given the time

constraints of her hospitalization. However, while additional sessions and replications

would have provided further support for our findings, we did observe approximations to

matching in a limited assessment. In addition, given the severity of Audrey's problem

behavior (i.e., SIB), we began her assessment with the treatment component, and were

able to reduce problem behavior to clinically significant levels. We were then able to

recommend a treatment package for use in the school and home settings while we

continued to assess her problem behavior.







46


VI 20 (PB) VI 20 (PB)
VI 60 (AB) VI 60 (AB)
2 s COD
S VI60 (PB) VI 60
VI 20 (AB) VI 20
1 1 1 o C


EXT (PB)
CRF (AB)
5 s COD

I


EXT (PB)
CRF (AB)
5 s COD
L I


Greg
,Tangible


5 10 15 20 25 30 35 40 45 50
Sessions


Sessions


Figure 3-1. Overall response rates for problem and appropriate behavior for Greg. A)
Responses per min of problem and appropriate behavior during tangible
sessions. B) Responses per min of problem and appropriate behavior during
escape sessions.









EXT (PB)
CRF (AB)
BLi VI 10 (PB)
VI 10 (AB)
I I II


4Y


VI 30 (PB) VI 10 (PB)
VI 10 (AB) VI 10 (AB)
| VI 60 (PB) |
VI20 (AB)


Appropriate
Behavior
(AB)
!


Problem
Behavior
(PB)


5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 8i
Sessions


Baseline
CRF (PB)
EXT (AB)


VI 20 (PB)
VI 20 (AB)
VI 60 (PB) VI 60 (PB)
VI 10 (AB) VI 10 (AB)


%A


A-A -


EXT (PB)
CRF (AB)






B





Alice
Escape


Sessions


Figure 3-2. Overall response rates for problem and appropriate behavior during the
assessment phase for Audrey and Alice. A) Responses per min of problem
and appropriate behavior for Audrey. B) Responses per min of problem and
appropriate behavior for Alice.


VI 30 (PB)
VI 10 (AB)




A








0 85 90 95


Baseline
CRF (PB)
EXT (AB)


VI 20 (PB)
VI 20 (AB)
1



Appropriate
Behavior
(AB)


Problem
Behavior
(PB)


U-0-0


I


Mft4;


















0.4

0.2


..0



.- g S







) 0.2 0.4 0.6 0.8 1
Reinforced Problem Behavior/
Total Reinforcers




/*


Ms.* c


/'s


0 K I
0 0.2 0.4 0.6 0.8 1
Reinforced Problem Behavior/
Total Reinforcers

1 0

.8- 0..*
.6- '
E
.4-

.2- a


0 0.2 0.4 0.6 0.8 1
Reinforced Problem Behavior/
Total Reinforcers


S
S


0 0.2 0.4 0.6 0.8 1
Reinforced Problem Behavior/
Total Reinforcers


1 /


/0
/0


0 0.2 0.4 0.6 0.8 1
Reinforced Problem Behavior,
Total Reinforcers


/ F



Greg
Tangible

0 0.2 0.4 0.6 0.8 1
Reinforced Problem Behavior/
Total Reinforcers


Figure 3-3. Scatterplots of observed and predicted response allocation between problem
behavior and appropriate behavior for Greg for each condition during the
tangible assessment. A) Last response method of calculation. B) Means using
the last response method of calculation. C) 10 s method of calculation. D)
Means using the 10 s method of calculation. E) Programmed method of
calculation. F) Means using the programmed reinforcer method of calculation.













y =-0.411x +0.067 /
0.5- 0 a




-1 / o
0- *f '&






-1.5 "
-1.5 -1 -0.5 0 0.5 1 1.5
Log ReinforcedProblem Behavior/
Log Reinforced Appropriate
Behavior
1.5 -
y- -0.358x- 0.019 ,'


0.5 ;* 0)

0 c I

-0.5- ).


-1.5
-1.5 -1 -0.5 0 0.5 1 1.5
Log ReinforcedProblem Behavior/
Log Reinforced Appropriate
Behavior

1.5 -
y = 0.886x 0.322 /


0.5 -

0- c1


-1 / 0
-0.5-


-1.5
-1.5 -1 -0.5 0 0.5 1 1.5
Log ReinforcedProblem Behavior/
Log Reinforced Appropriate
Behavior


0.322x + 0.093


0.5



-0.5 .

-1

-1.5
-1.5 -1 -0.5 0 0.5 1 1.5
Log ReinforcedProblem Behavior/
Log Reinforced Appropriate
Behavior

1.5 -
y 0.249x+ 0.063







-1 -

-1.5
-1.5 -1 -0.5 0 0.5 1 1.5
Log ReinforcedProblem Behavior/
Log Reinforced Appropriate
Behavior

1.5-
y 0.494x- 0.163


0.5-

0- F

-0.5 -

-1- ,' Greg
/' Tangible
-1.5
-1.5 -1 -0.5 0 0.5 1 1.5
Log ReinforcedProblem Behavior/
Log Reinforced Appropriate
Behavior


Figure 3-4. Log response ratios plotted against log reinforcer ratios for Greg. The linear
equation depicts slope and bias during all conditions of the tangible
assessment. A) Last response method of calculation. B) Means using the last
response method. C) 10 s method of calculation. D) Means using the 10 s
method. E) Programmed reinforcer method of calculation. F) Means using the
programmed reinforcer method.














6- g I

4- A


2-


0 0.2 0.4 0.6 0.8 1
Reinforced Problem Behavior/
Total Reinforcers

1

.8-

.6- .

.4' C
.4 g /

.2- "

0'
0 0.2 0.4 0.6 0.8 1
Reinforced Problem Behavior/
Total Reinforcers


S pp

U 5

~ .:~

S
S


II


0.25 0.5 0.75 1
Reinforced Problem Behavior/
Total Reinforcers


S
S


0 0.2 0.4 0.6 0.8 1
Reinforced Problem Behavior/
Total Reinforcers

1

8 -

6 -..' *

4 D*

2 -

0 '
0 0.2 0.4 0.6 0.8 1
Reinforced Problem Behavior/
Total Reinforcers


1-

8-

6 7,
.'- F
4 -

2 Greg
;'1 Escape
0 I I I I
0 0.2 0.4 0.6 0.8 1
Reinforced Problem Behavior/
Total Reinforcers


Figure 3-5. Scatterplots of observed and predicted response allocation between problem
behavior and appropriate behavior for Greg for all conditions during the
escape assessment. A) Last response method of calculation. B) Means using
the last response method of calculation. C) 10 s method of calculation. D)
Means using the 10 s method of calculation. E) Programmed method of
calculation. F) Means using the programmed reinforcer method of calculation.


t-:''





















-1 1


y = 0.478x + 0.329



0-A

OS-' A l'
1^





o ao
DO


-1.5 1 1 1---I I-
-1.5 -1 -0.5 0 0.5 1 1.5
Log ReinforcedProblem Behavior/
Log Reinforced Appropriate
Behavior


1.5
.- 1

0.5

-0. 5
.


1.5 1` I I I I I 1
-1.5 -1 -0.5 0 0.5 1 1.5
Log ReinforcedProblem Behavior/
Log Reinforced Appropriate
Behavior


1.5 F" I I I I
-1.5 -1 -0.5 0 0.5 1 1.5
Log ReinforcedProblem Behavior/
Log Reinforced Appropriate
Behavior


0oL
aol
2


-1.5
-1.5 -1 -0.5 0 0.5 1 1.5
Log ReinforcedProblem Behavior/
Log Reinforced Appropriate
Behavior


-1_
-1.5 "
-1.5 -1 -0.5 0 0.5 1 1.5
Log ReinforcedProblem Behavior/
Log Reinforced Appropriate
Behavior


y = 0.814x + 0.454
i 1- 1

0.5 ,:"

0- F
-0.5-

o ao -1- ,...,"" Greg
S ..' Escape
-1.5 "
-1.5 -1 -0.5 0 0.5 1 1.5
Log ReinforcedProblem Behavior/
Log Reinforced Appropriate
Behavior


Figure 3-6. Log response ratios plotted against log reinforcer ratios for Greg. The linear
equation depicts slope and bias during all conditions of the escape assessment.
A) Last response method of calculation. B) Means using the last response
method. C) 10 s method of calculation. D) Means using the 10 s method. E)
Programmed reinforcer method of calculation. F) Means using the
programmed reinforcer method.


















G O


'S


1-

f 0.8-

-S | 0.6-
A
0.4-

^ 0.2-


II I
0 0.2 0.4 0.6 0.8 1
Reinforced Problem Behavior/
Total Reinforcers


/f


A*

4 I


0 0.2 0.4 0.6 0.8 1
Reinforced Problem Behavior/
Total Reinforcers


J. 0.6-
C M
S0.4-

0.2-


0 0.2 0.4 0.6 0.8 1
Reinforced Problem Behavior/
Total Reinforcers


1-

0.8-



E
It 0.6-

0.4-

S0.2-


0 0.2 0.4 0.6 0.8 1
Reinforced Problem Behavior/
Total Reinforcers


O.r


0 0.2 0.4 0.6 0.8 1
Reinforced Problem Behavior/
Total Reinforcers


5/
s-/
S /


-4


F



Audrey


0 0.2 0.4 0.6 0.8 1
Reinforced Problem Behavior/
Total Reinforcers


Figure 3-7. Scatterplots of observed and predicted response allocation between problem
behavior and appropriate behavior for Audrey during the tangible assessment.
A) Last response method of calculation. B) Means using the last response
method of calculation. C) 10 s method of calculation. D) Means using the 10 s
method. E) Programmed method of calculation. F) Means using the
programmed reinforcer method of calculation.


1 -

0.8-
06
S0.6-

0.4-
-H
S0.2-

In


0.8

S0.6

0.4

0.2


0





1

S0.8

c 0.6

-2 0.4
1 0.2


P














J..








Cz
CO z

- .3




on '
o on




0



^







So



o>













o *rF


0 C

-0.5- |

-1 -<

-1.5
-1.5 -1 -0.5 0 0.5 1 1.5
Log ReinforcedProblem Behavior/
Log Reinforced Appropriate
Behavior

1.5 -.
y =0.741x 0.036 7.'
1

0.5- ,

0- S E

-0.5-

-1- 0<

-1.5 :
-1.5 -1 -0.5 0 0.5 1 1.5
Log ReinforcedProblem Behavior/
Log Reinforced Appropriate
Behavior


-1.5 f I I
-1.5 -1 -0.5 0 0.5 1 1.5
Log ReinforcedProblem Behavior/
Log Reinforced Appropriate
Behavior


-1

-1.5
-1.5 -1 -0.5 0 0.5 1 1.5
Log ReinforcedProblem Behavior/
Log Reinforced Appropriate
Behavior

1.5 y= 0.910x 0.010


0.5-

0- F

-0.5-

-1-
:1 Audrey

-1.5 -1 -0.5 0 0.5 1 1.5
Log ReinforcedProblem Behavior/
Log Reinforced Appropriate
Behavior


Figure 3-8. Log response ratios plotted against log reinforcer ratios for Audrey. The
linear equation depicts slope and bias during all conditions of the tangible
assessment. A) Last response method of calculation. B) Means using the last
response method. C) 10 s method of calculation. D) Means using the 10 s
method. E) Programmed reinforcer method of calculation. F) Means using the
programmed reinforcer method.


1.5 -1 -0.5 0 0.5 1 1.5
Log ReinforcedProblem Behavior/
Log Reinforced Appropriate
Behavior











1 S .3

.8 -* *

.6 .,
A
.4 ,

.2 "

0*"
0 0.2 0.4 0.6 0.8 1
Reinforced Problem Behavior/
Total Reinforcers


. *6 e
.4.



*
is I~

"4. CI
S '


0 0.2 0.4 0.6 0.8 1
Reinforced Problem Behavior/
Total Reinforcers

1- e

8 *S

6-
0, E
4 -

2-
0 *' *

0 0.2 0.4 0.6 0.8 1
Reinforced Problem Behavior/
Total Reinforcers


1 -

m- 0.8-
.2

0.6-

S 0.4-

A 0.2-

0-


S-







2 /
2 -


0 0.2 0.4 0.6 0.8 1
Reinforced Problem Behavior/
Total Reinforcers


*
S/S


0 0.2 0.4 0.6 0.8 1
Reinforced Problem Behavior/
Total Reinforcers


." *

/' F



Alice

0 0.2 0.4 0.6 0.8 1
Reinforced Problem Behavior/
Total Reinforcers


Figure 3-9. Scatterplots of observed and predicted response allocation between problem
behavior and appropriate behavior for Alice during the escape assessment. A)
Last response method. B) Means using the last response method. C) 10 s
method. D) Means using the 10 s method. E) Programmed reinforcer method.
F) Means using the programmed reinforcer method.













S0
.ca

m s



o o1
&9-


-1 -0.5 0 0.5 1
Log ReinforcedProblem Behavior/
Log Reinforced Appropriate
Behavior


y = 0.687x + 0.089

0.5- *




0- C
-0.5 /



-1 -0.5 0 0.5 1
Log ReinforcedProblem Behavior/
Log Reinforced Appropriate
Behavior


-1 -0.5 0 0.5 1
Log ReinforcedProblem Behavior/
Log Reinforced Appropriate
Behavior


0
0


~



0 oL


0- :B


).5 0



-1 -0.5 0 0.5 1
Log ReinforcedProblem Behavior/
Log Reinforced Appropriate
Behavior

1-.
y =0.172x + 0.276

).5- :


0- D


).5 -


-1
-1 -0.5 0 0.5 1
Log ReinforcedProblem Behavior/
Log Reinforced Appropriate
Behavior


0.5 -


1 0- F


^ -0.5-

'/*" Alice
-1-
-1 -0.5 0 0.5 1
Log ReinforcedProblem Behavior/
Log Reinforced Appropriate
Behavior


Figure 3-10. Log response ratios plotted against log reinforcer ratios for Alice. The
linear equation depicts slope and bias during all conditions of the escape
assessment. A) Last response method. B) Means using the last response
method. C) 10 s method. D) Means using the 10 s method. E) Programmed
reinforcer method. F) Means using the programmed reinforcer method.




















S


0 I I I
0 0.2 0.4 0.6


First
session
Greg
Tangible

0.8 1


Reinforced Problem Behavior/
Total Reinforcers


1-

0.8-

0.6-

& 0.4-
1H


-' Last
session


S First
' session


udrev


U | I I I I I
0 0.2 0.4 0.6 0.8 1
Reinforced Problem Behavior/
Total Reinforcers


session Greg
Escape

0.2 0.4 0.6 0.8 1
Reinforced Problem Behavior/
Total Reinforcers


1 -

0.8 -

'I 0.6-

C
S0.4-

0 2


First S S
se sion





/ Last D
S...session

S..Alice
,,; I I


0 0.2 0.4 0.6 0.8 1
Reinforced Problem Behavior/
Total Reinforcers


Figure 3-11. Scatterplots depicting examples of closer approximations to matching
towards the end of the condition using the simple matching equation. Arrows
show the first and last sessions within a condition. A) Results of the within
10s method for Greg's tangible analysis during the second VI 20-s VI 60-s
phase. B) Results of the last response method of calculation for Audrey's
tangible analysis during the second VI 10-s VI 10-s phase. C) Results of the
within 10 s method of calculation for Greg's escape analysis during the
second VI 20-s VI 60-s phase. D) Results of the last response method of
calculation for Alice's escape analysis during the first VI 60-s VI 20-s phase.


0
2;



-H


Last /"' *
session'T *


A


0





-H


'L


-/.z, -














CHAPTER 4
GENERAL DISCUSSION

In Experiment 1, functional analyses were conducted for problem behavior

exhibited by three individuals diagnosed with developmental disabilities to identify

reinforcers. For Greg, results suggested that screaming was reinforced by access to

tangible items, and disruptive behavior was reinforced by escape from instructional

demands. For Audrey, results suggested that SIB was reinforced by access to tangible

items. Finally, for Alice, results suggested that aggression and disruption were reinforced

by escape from instructional demands.

In Experiment 2, an analysis of concurrent reinforcement schedules was

conducted with independent reinforcement schedules in place for both problem behavior

and appropriate behavior in order to evaluate behavior from a matching perspective. For

all evaluations, the relative rate of responding was influenced by the relative rate of

reinforcement. Analyses for Greg during the tangible and escape conditions, and the

analysis for Audrey during the tangible condition, provided closer approximations to

matching than the limited analysis for Alice. Finally, in Experiment 2, full treatment

evaluations were conducted to reduce problem behavior to clinically significant levels.

DRA was implemented with EXT to increase appropriate behavior for all participants.

For all evaluations, DRA and EXT were successful in reducing problem behavior and

increasing appropriate behavior.

The matching law has been shown to be a useful way of describing response

allocation across a variety of subjects (e.g., Baum, 1974a, 1974b; Beardsley &









McDowell, 1992; Conger & Killeen, 1974; Crowley & Donahoe, 2004; Hermstein, 1961,

1975; MacDonall, 1988) for an array of response topographies (Borrero & Vollmer,

2002; Martens & Houk, 1989; McDowell, 1981; Symons et al., 2003), and across

nonexperimental (Symons et al., 2003; Vollmer & Bourret, 2000) and experimental

(Mace et al. 1994; Neef& Lutz, 2001; Neef, Mace & Shade, 1993; Neef, Shade & Miller,

1994) arrangements.

In order to evaluate the matching relation, the rates of responding for problem and

appropriate behavior were calculated, as well as the rates of reinforcement for problem

and appropriate behavior. One notable difficulty involves defining a "reinforced

response." It is not always clear how responses are reinforced, even with a schedule of

reinforcement in place. Therefore, three calculations were included to account for

possible differences in results based on the way in which a reinforced response was

defined. One method of calculation was the last response method, during which the

response that occurred immediately prior to the delivery of a reinforcer was the only

response considered to be reinforced. This calculation accounted for sequential relations

between a response and a known reinforcer. A second calculation was the il i/hin 10-s

method, during which any response that occurred 10 s before a reinforcer was delivered

was considered to be a reinforced response. This calculation accounted for temporal

relations between a response and a known reinforcer. Finally, a third calculation was the

programmed reinforcer method, during which a response for which a reinforcer was

delivered according to the programmed schedule of reinforcement was considered to be a

reinforced response. This calculation accounted for the delivery of programmed









reinforcers according to the schedule in place. It is not clear which calculation is the

most useful, although some differences between the calculations were observed.

In order to evaluate the differences between calculation methods, correlation

coefficients (r) and coefficients of determination (r2) were evaluated. Table 4.1 shows, for

all participants, the results of the data analysis using the simple matching equation

(Equation 1-1) and the generalized matching equation (Equation 1-2), for all calculation

methods (i.e., last response method, within 10-s method, and programmed reinforcer

method). The results for all calculations are summarized in Table 4.1, for both the

session-by-session and mean analyses, with the closest approximations to matching

shown in bold. For each method of calculation, four values are shown for the correlation

coefficients and the coefficients of determination, resulting in 8 possible values for each

coefficient. For 4 of 8 calculations, the last response method provided the larger

correlation coefficients, for 4 of 8 calculations, the within 10 s method provided the

larger correlation coefficients (the last response and within 10 s methods were equal for

one calculation), and for 2 of 8 calculations, the programmed reinforcer method provided

the larger correlation coefficients. The largest coefficients of determinations were

obtained using the within 10-s method for 4 of 8 calculations, the programmed reinforcer

method for 3 of 8 calculations, and the last response method for 1 of 8 calculations.

These results suggested that all methods of calculation supported an interpretation of the

data from a matching perspective, and results may vary depending on the definition of a

reinforced response.

A second difficulty may be that, such analyses are quite time-consuming, and may

be difficult to conduct when working with individuals who engage in severe problem









behavior. It may not be possible to conduct such lengthy analyses due to the severity of

problem behavior (e.g., severe SIB and aggression), particularly when such an analysis

delays the implementation of an intervention. Audrey's assessment may provide an

alternative strategy for conducting thorough analyses, by evaluating a treatment prior to

conducting the matching analyses. It is possible that evaluating the full treatment

component prior to the assessment of concurrent schedules could reduce some of the

difficulties associated with evaluating severe problem behavior from a matching

perspective. Designing a treatment package prior to a more lengthy assessment may

alleviate some of the clinical concerns (e.g., continued risk of injury due to SIB) raised by

parents and careproviders. For example, following the development of an effective

treatment, parent and careprovider training could be conducted, and the treatment could

be implemented in a timely manner outside of the experimental context.

The present experiments suggest areas for future research. This analysis included

various concurrent schedules of reinforcement for problem and appropriate behavior.

Evaluating concurrent schedules of reinforcement may be useful, as it is likely that in the

natural environment, reinforcers are available for both problem and appropriate behavior

at the same time but with varying probabilities. Future research may conduct similar

analyses using concurrent schedule arrangements based on naturalistic observations. For

example, descriptive analyses (Bijou, Peterson, & Ault, 1968) could be conducted with

parents and careproviders and the results could be analyzed using reinforcers identified in

a functional analysis (Iwata et al. 1982/1994) with procedures similar to those described

by Borrero and Vollmer (2002). For example, if descriptive analysis data showed that

problem behavior was reinforced on a VI 20-s schedule, and appropriate behavior was









reinforced on a VI 40-s schedule, experimental analyses could be designed to mimic

naturally occurring reinforcement rates in an experimental context. Concurrent schedules

of reinforcement could be based on the derived schedules of reinforcement observed

during naturally occurring situations, and a subsequent matching analysis could be

conducted. The extent to which relative response allocation is similar under both

descriptive and experimental arrangements may provide greater support for the generality

of the matching relation. Matching analyses may also suggest critical values of

reinforcement parameters that may increase both the acceptability and integrity of

treatment implementation by primary caregivers in the natural environment. It is often

difficult and perhaps unrealistic to train parents not to provide reinforcement following

problem behavior. Matching analyses may suggest the lower limit of caregiver

reinforcement that may be provided while maintaining clinically acceptable levels of

appropriate behavior (Vollmer, Roane, Ringdahl, & Marcus, 1999).

An additional area of future research may also include analyses of various

parameters of reinforcement. Previous research (Borrero, Vollmer, Borrero, & Bourret,

2005; Mace et al., 1994; see Stromer, McComas, & Rehfeldt, 2000 for a comprehensive

review) has suggested that duration of reinforcement (Dixon et al., 1998; Fisher, Piazza,

& Chiang, 1996; Peck et al., 1996) delay to reinforcement (Neef et al., 2005; Neef et al.,

1994; Vollmer, Borrero, Lalli, & Daniel, 1999), quality of reinforcement (Neef, Bicard,

& Endo, 2001; Neef & Lutz, 2001; Mace et al., 1996) and magnitude of reinforcement

(Hoch, McComas, Johnson, Faranda, & Guenther, 2002; Lerman, Kelley, Vorndran,

Kuhn, & LaRue, 2002; Volkert, Lerman, & Vorndran, 2005) are important variables for

evaluating response allocation, in addition to rate of reinforcement. Investigations similar









to these just cited could be conducted with any of the additional parameters of

reinforcement by holding constant rate of reinforcement. In addition, the implications for

the treatment of severe problem behavior may be significant. Often, problem behavior is

so severe (e.g., head-banging on hard surfaces, severe aggression, etc.) that it is not

possible to withhold reinforcement (i.e., extinction). That is, especially in the case of

behavior reinforced by attention, it is not possible to ignore the behavior, and some

attention (e.g., blocking the response) will likely be necessary to ensure the safety of the

individuals in the situation. However, it may be possible to manipulate other

reinforcement parameters such as duration or quality of reinforcement.

One limitation of these experiments may be the small number of concurrent

schedule values. For Greg and Alice, we only manipulated two values for the concurrent

schedules. For Audrey, we manipulated three values however, we did not conduct a

thorough analysis of the third value, nor did we conduct a reversal to that phase (i.e., VI

60-s VI 20-s was assessed for only three sessions). Future research may also include

parametric schedule value evaluations. For example, the schedules could initial start with

a VI 20-s for problem behavior and VI 60-s for appropriate behavior, and then values in

between (e.g., VI 25-s VI 55-s) until the schedules are switched (i.e., VI 60-s VI 20-s).

Such evaluations may be useful in quantifying reinforcer value by identifying

indifference points (i.e., values which differ quantitatively but produce indifferent

response allocation).

A second limitation of these experiments may be the brevity of the conditions. In a

basic preparation, it may be possible to conduct conditions until meeting a stability

criterion (e.g., a difference of less than 5% between data points), however, in the applied









setting, it was not always possible to bring each condition to stability before exposing

behavior to another condition (i.e., Alice). Therefore, the matching analyses conducted

in these experiments may not be based on stable responding, and this could account for

some of the variability observed. This may be supported by the observation of closer

approximations to matching towards the end of each condition. Ideally, for all

participants, each set of conditions would have been conducted until meeting stability

criteria.

The present experiments focused on evaluating the rate of reinforcement and the

effects on problem and appropriate behavior. It was designed to determine if the simple

matching equation (1) and the generalized matching equation (2) provided descriptions of

response allocation on concurrent schedules of reinforcement with three individuals with

developmental disabilities who engaged in severe problem behavior.









Table 4-1. Summary of correlation coefficients (r) for all participants using the Simple
Matching Equation and the coefficients of determination using the (r2)
Generalized Matching Equation.
Method of Calculation
Last Response Within 10 s Programmed
Greg Tangible r .80 .80 .59
(All sessions)
r .98 .98 .99
(Means)
r2 .45 .28 .60
(All sessions)
r2 .92 .40 .81
(Means)
Greg Escape r .49 .92 .41
(All sessions)
r .97 .78 .95
(Means)
r2 .30 .85 .22
(All sessions)
r2 .60 .88 .69
(Means)
Audrey r .79 .87 .72
(All sessions)
r .98 .95 .96
(Means)
r2 .23 .84 .44
(All sessions)
r2 .28 .99 .86
(Means)
Alice r .77 .75 .71
(All sessions)
r .77 .84 .84
(Means)
r2 .25 .32 .45
(All sessions)
r2 .23 .01 .41
(Means)















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69



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BIOGRAPHICAL SKETCH

Carrie S. W. Borrero was born in Easton, Pennsylvania, in 1973 to Donald and

Santa Wright, and grew up in Bethlehem, Pennsylvania. Carrie attended the University

of Pittsburgh, and in 1995 graduated with a Bachelor of Science degree in psychology.

In 1997, she entered the graduate program in counseling and human services at Villanova

University in Pennsylvania. Carrie was awarded her Master of Science degree in 1999.

She then entered the graduate program in psychology (behavior analysis) at the

University of Florida.