UFDC Home  Search all Groups  UF Institutional Repository  UF Institutional Repository  UF Theses & Dissertations   Help 
Material Information
Subjects
Notes
Record Information

Full Text 
SLOWING AN EXPLANATION FLUID ] WITH AGE AS FOR AGE CHANGES INTELLIGENCE ADRIAN TOMER A DISSERTATION PRESENTED TO T OF THE UNIVERSITY O IN PARTIAL FULFILLMENT OF FOR THE DEGREE OF DOCTOR 'HE GRADUATE SCHC F FLORIDA THE REQUIREMENTS OF PHILOSOPHY UNIVERSITY OF FLORIDA )OL ACKNOWLEDGMENTS I would like express deep gratitude the chairman supervisory committee and academic advisor, Walter Cunningham. The present study conception approach relies heavily on his work as well as on innumerable talks have had with him on the subj ects treated here. guidance, continuous encouragement and openness constituted a vital support this major endeavor. I would like also to thank and express appreciation supervisory committee members: James Algina, Richard Griggs, Patricia Miller Robin West their continuous support assistance different stages the dissertation. Thanks are extended Christopher Hertzog from Georgia Tech whose help the design and analysis this study was extremely important. Appreciation also extended fellow graduate students whose support helped me all along the way achieving a difficult task. Finally, wife who was patient and supportive A~~~~~~~~~~~~~~~ at seA fll 1 ar a 4.aaaS .. A~ ni 'nab.4.1 AnC 4 ~1 hrJ LI CIL YIA II ~I ClIf C rrwni TABLE OF CONTENTS page ACKNOWLEDGMENTS .............. .......... ............i i ABSTRACT..............................................v CHAPTERS 1 INTRODUCTION AND OVERVIEW.......................1 The Speed Hypothesis............................ 3 Alternative Views and Criticisms................7 The Present Study..............................10 2 LITERATURE REVIEW.............................. 13 Cerella's Approach.............................14 Factor Analytical Studies......................15 Tentative Conclusions on the Dimensionality of Slowing.............. .....................21 Slowing in Relation to Psychometric Abilities..22 Speed and Memory Abilities...................32 Alternative Interpretations....................34 Summary................... . . ....... . 39 3 THE PROPOSED MODELS............................42 4 METHOD........ ...... .. .. . .. .... ........ ..58 Subjects.............. . . ....... . . .58 Tasks and Tests................................59 Speed Tasks...................... ...........59 Fluid and Crystallized Intelligence.........64 Other Variables...................... .......65 Procedure............. ...... ... ................ 66 RESULTS.... ..... ... .. . . ... ....... . ... 68 Confirmatory Factor analysis of Speed Mea n r s    s     ......  7 Models with Speed.... Models with Multiple Second First Order Order Speed Speed Factors Factors. Factors. S. .99 .....102 DISCUSSION..................... ...... ......... 108 The Speed Hypothesis.. Fluid and Crystallized Integration and Future Intelligence Directions.. APPENDICES GOODNESS OF FIT INDICES ..... ........... ..... The Normed The LISREL' The Adjuste The LISREL' ChiSquare Diagnostics Other Indic Relationshi Indices of Fixed Index. s Goodnesso d Goodnesso s RootMean and ChiSqua of Fit..... es of Fit... ps Fit between for the * fFit f Fit Squar re/df Indices User of Index (G.I Index (AGF eResidual ....... of Fit.. LISREL. ;FI)..... 1 . (RMR)..1 * ..... .1 * .4....1 * .. .. .1 . . .1 e 1 RAW REFERENCES.. BIOGRAPHICAL ...SKETCH...... . . . .. ........ .148 .00.... . .... ...109 ..... .. ... 118 ...........120 DATA......................................133 Abstract the Dissertation University Requirements Presented Florida the Degree the Partial F of Doctor Graduate School fulfillment of Phil osophy SLOWING WITH AGE AN EXPLANATION FOR AGE CHANGES FLUID INTELLIGENCE ADRIAN August TOMER 1989 Chairman: Major Walter Department R. Cunningham : Psychology Ph.D. The speed hypothesis attempts to explain changes intellectual functioning with increased postulating mechanism level of the central nervous system decline thi mechanism with age assumed to affect speed of performance of various tasks and cognitive functioning in general. Correlational anal yses measures of speed suggest that more than one mechanism may involved . Correlational or regres sion analyses relationship between speed and fluid intelligence were general consistent with the speed hypothesis. In thi study the issue of structure measures speed was addressed conducting confirmatory factor analy ses of fi rmt 1 avel order then the level of second S. R nL n.l l crystallized intelligence (Gc) were estimated several path models which included age, education subjective health as exogenous variables. Speed, a mediating variable, was modeled as a first order factor or as a second order factor, agreement with the confirmatory analysis. The analyses were performed a sample elderly adults aged 73 and a sample of 147 young adults aged Confirmatory factor analyses found , as hypothesized, five first second order order factors speed of speed factors both were age necessary groups. Three to account the relationships between the first order speed factors. The path models investigated supported, general, a speed hypothesis the older sample. The evidence this young subjects was weaker. Also, the analysis indicated that, old subjects, two factors of speed mediated independently the effect age on Gf, suggesting the existence of a multitude of speed mechanisms. CHAPTER INTRODUCTION AND OVERVIEW Intellectual abilities, as amply documented cross sectional , longitudinal and sequential approaches Botwinick , 1977; Cunningham 1987 Schaie, 1983; Schaie Hertzog, 1983) vary among adults as a function age. Sequential analyses show that beyond certain ages, which might be different different abiliti there steady decline differences with the increased respective independent abiliti of cohort (Schaie & Hertzog, 1983). There also evidence, most cross sectional, suggesting a decline problem solving ability with Reese & Rodeheaver , 1985) secondary memory with increased , Poon, 1985) Convergent evidence indicates that a decline with larger and seen earlier speeded than unspeeded intellectual tasks , Cunningham, 1988) . Thus, Schai and Strother (1968) found steep longitudinal declines two highly speeded abilitiesVerbal Fluency and Psychomotor Speed. Cunningham (1988, 1989) found pronounced declines negligible cohort differences the longitudinal Florida Expressional Fluencyalso decreased with but showed larger cohort differences . In a subsequent study Cunningham and White (1984) found the factor scores of Figural Perceptual two Speed samples to correlate old higher (ages than and .7 with young age (ages across to 33) adults . Symbolic sensitive Perceptual . Thi Speed pattern appeared of relatively to be 1 y steep ess declines with age speeded tasks consis tent with the pattern a steeper between increase unspeeded covariances intellectual between factors speeded which than been demonstrated cross sectional (Cunningham, 1980) longitudinal analy ses (Cunningham, Smook, Tomer, 1985) The pattern of pronounced decline speeded intellectual factors consistent with a large body studi showing slowing with reaction times responses to different stimuli times exe cution almost any activity which has been tested , Birren, Woods, & Williams, 1980; Salthouse, 1985a) . A few exceptions pattern, however, have been found . Vocal suggested at least part of the evidence does not slow with increased Salthouse, 1985a) . Lexical access time as shown priming studi Cerella & Foza 1984 . Salthouse, 1985b) affected systematically age. forming sentences which incorporate a given pair nouns (Nebes & AndrewsKulis , 1976) . Finally no age differences were found Waugh (1980) the rate of reading words. The Soeed Hypothesis A major attempt to explain the decline cognitive functioning Birren s hypothesis (e.g. , Birren, 1964, 1965; Birren, Woods, & Williams, 1980) . According to this hypothesis: There a decline central nervous system with increased age, and As a result there decline intellectual functioning. The hypothesis was first conceived Birren the late and forties his and colleague inspired s in the many research fifties projects sixties of Birren (Cunningham, press). It reflects, part a realization Birren the importance of the evidence showing that the wellknown finding slowing with cannot be attributed peripheralinput or outputslowing. In fact, had become clear that slowing of encoding processes and of movements executed response to stimuli explain only a small part the overall slowing a variety tasks (Birren, 1964, 1965). factors To the than extent that periphera slowing 1 ones was attributed was treated to other as a dependent variable, a result of cognitive adaptations o behavior and can used as an explanatory variable. The computer metaphor used Birren (Birren, 1965) according which speed of behavior similar to operation speed computers and may be similarly used as a "primary descriptive characteristic" (Birren, 1965, 195) has been proved to be a fruitful model describing changes cognitive The seventies functioning speed and ever hypothesis eighties since has from (e.g., received several Salthouse, new 1985b). impetus developments the field of intelligence the field information processing. A first development refers to what Eysenck called "a Kuhnian revolution the theory and the measurement of intelligence" (Eysenck, 1986, 731). It is related the work of Jensen (e.g., Jensen, 1982) the United States and, quite independently, to the work others Europe, especially Germany . Eysenck, 1987) and represents a large degree a return the ideas Sir Francis Galton. The main concept that intelligence a biologically determined cognitive ability . The experimental work supportive this notion indicated substantive correlations between scores reaction times. was also observed that, when the number of choices the amount of information) increases a multiple intelligence resulted in several similar models being proposed (Eysenck, 1987; Jensen, 1982; Vernon, 1987). Thus, Vernon the "neuralefficiency" model (Vernon, 1987, assumed that brain or shortterm or working memory has limited capacity to store process information. addition, there are processes of decay of information absence of rehearsal. speediness these easy circumstances understand . In the m the odel advantage put forward Eysenck (1967, 1987) he asserts that there are three components to the concept of IQ: mental speed, persistence/ and error checking, first one being more fundamental accounting individual differences intelligence (Eysenck, 1967 Eysenck, 1987, 27). The first factor supposed to be biological while the other two are personality factors. A similar approach was adopted Hunt and his colleagues (e.g., Hunt, 1978, 1983). Studying individual differences longterm memory access they found (Hunt, Davidson, & Lansman, 1981) that reaction times from several verification tasks correlated with verbal ability. Moreover, reaction the time reading measures and formed vocabulary a factor measures. which Other was evidence related reviewed Hunt (1978) has shown that encoding processes (measured individual differences cognition are based on three factors: knowledge, individual s ability manipulate information (the "mechanics of information proce ssing" Hunt, 1978, 128) , and strategies. Verbal ability according Cattell, Cattell 1987; Horn, 1978; Horn Horn distinction Cattell, (e.g., 1966), crystallized ability supposedly determined to a considerable degree make cultural inferences, factors. draw Fluid relations, intelligencethe develop ability hypotheses on the other hand, assumed to be essentially genetically determined. Hunt sugge sted that fluid intelligence and mechanistic information processing show conceptual empirical affinities which make study of their relationship Given promising a speed intelligence, (Hunt, 1978, of information natural 125). processing propose theory a processing rate theory aging as has been done Salthouse (1980, 1985b) elaborating on the ideas Birren. The first inclination was assume an aging organism which like the young organism but slower than (Salthouse, 1985b, 296). However, this simplified view does not take into consideration possibility of interactions the information processing system. In fact, the same chapter to thi model, given task memorize words, old people rehearse words more slowly than young people rehearse. There also a process decay memory traces proceeding the same speed the young and the old . Assuming a slow enough rehearsal rate older people, possible reach a point where a trace completely lost before next rehearsal, making strategy no longer a viable option the elderly. A distinction between a strong and a weak version speed hypothesis was made Cerella, Poon Fozard (1981) . In the strong form hypothesis a single age related mechanism the level of the central nervous system slows down the same extent mental processes. A weaker version allows multiple mechanisms which are age dependent different degrees and which affect different sets cognitive variable (Salthouse, 1985b). Finally, a realistic model of cognitive change based the concept of processing rate should include also adjustments slowing, and as well adaptations as other v which may ariabl happen such as a result as strategy information which may affect cognitive performance and may affected (Salthouse, 1985b, . 295 319) Alternative Views Criticisms cognitive changes aging have met with various criticisms. Sternberg (1985, 301304) argued against the view that speed emphasized a critical that what aspect critical intelligence is resource . He allocation speed selection rather than speed per se. Thus, more intelligent persons tend to spend relatively more time than less less intelligent on lowerorder persons planning on higherorder (Sternberg, planning 1981). and Similarly, more intelligent tend spend relatively more time encoding the terms of a problem (Sternberg, 1977) and tend to spend more time trying to solve insight problems (Sternberg & Davidson, 1982) conditions of unlimited time than less intelligent persons While these other examples advanced Sternberg highlight importance "metacomponent" intelligent (Sternberg, allocation 1985) dealing resources, with not issue clear that they conclusively show that "sheer speed" not important at all. when First, performing the ability simple tasks to respond such quickly as reaction important time perceptual speed tasks. Second, and poss ibly more important, Sternberg s argument seems to confound two distinct issues: the speed answer issue and the speed information individual faster than they are executed a slower individual. The speed hypothesis as an explanation of cognitive change with increased has also been criti cized on the basis of the exceptions the phenomenon of slowing, on the basis of the existence of a multitude of slowing models (Botwinick, 1984), and also reason that the opposite approach basis which on other tries to explain cognitive changes changes makes speed more on the sense (e.g ., Arenberg, 1980) Kausler a speed (1982, mechanism . 258), truly u example, Universal then mentioned there that should exceptions to the phenomenon of slowing . There are, however, notable (1984), exceptions reviewing which the were mentioned evidence diff above. erent Botwinick models slowing (additive, multiplicative, exponential), concluded that some functions may described better models one type while other functions are best described models different kind. This suggested the existence more than one mechanism slowing. Botwinick maintained that this weaker form the speed hypothesis loses much value 239). Also, Arenberg (1980) suggested that more plausible to consider speed a result of effi cient cognitive Other authors tended to play down significance exceptions or the significance of having many possible models competing to explain data. Part these results may prove not to be genuine (Salthouse, 1985b) . Should they stand scrutiny of additional and more powerful tests still seems that most them may be subsumed under the general category automatic processing (e.g lexical access a very well trained function). might well the case that automatic processing, because does not require many information resources, qualitatively different from active processing (Hasher & Zachs, 1979; Salthouse, unaffected 1985b). In "consequence 1985b). aging addition view" automatic processes there (Botwinick, (Cerella, no strong 1984, processing 1985; S evidence 230) ac might althouse, cording which slowing of behavior with a consequence changes declines the perceptual and cognitive systems (Salthouse, 1985b, 302). The Present Study The present study was conceived as an investigation two main aspects speed hypothesis: An examination the issue of the structure measures of speed and examination, the context of a causal model, testing a longitudinal study on memory and intelligence (White & Cunningham, 1987). Several first order and one or more second order factors of speed are assumed to subsume the intercorrelations among scores on various tasks and tests which were administered a group old and a group young adults. These include reaction time and card sorting tasks as well as perceptual speed tests. Confirmatory factor analyses ( hypotheses Gorsuch, 1983) regarding the were undertaken structure of the test the measures of speed and make comparisons between the two groups. LISREL (Joreskog & Sorbom, 1984) the maximum likelihood estimation method (Hayduck, 1988 Mulaik, 1972 were used these analyses. The second part of the study uses structural equation models (Hertzog, 1987) order to evaluate models pertinent to a speed hypothesis. these models several independent variables such as age and level of education are assumed affect fluid and crystallized intelligence either directly or indirectly through a speed factor. A speed hypothesis would predict that most of the decline fluid intelligence mediated through a decline speed . The inclusion theoretical variable crystallized intelligence makes Again, LISREL procedure were and the maximum method likelihood of choice estimation estimation these models with multiple indicators. The following chapters provide a detailed literature review as well as a description of the methodology, analyses, results and interpretations. Chapter presents literature review the main findings regarding the two general issues this study: the dimensionality measures of speed and explanation of declines cognitive abilities on the basis of declines speed information investigated processing the . Chapter hypotheses depicts examined. models A description sample of the tasks and procedure provided Chapter Chapter 5 presents the main analyses and findings which are later interpreted discussed Chapter addition, reader may find Appendices a general presentation variancecovariance topic matrices indices of fit on which as well analyses are based. CHAPTER LITERATURE REVIEW The speed hypothesis explains parsimoniously the fact that behaviors mediated the central nervous system, almost without exception, slow down the aging organism and that covariances between speed factors increase with age. Thi chapter surveys the literature relevant the issue of change in the structure of speed measures with increased possibility . The that speed a general hypothesis slowing makes mechanism plausible evidenced a general factor speed . The ques t after such factor has been conducted on young mainly subjects regressing scores and old factor subjects analyze ' scores speed and other measures . The literature relevant to this reviewed chapter . In addition, speed hypothesis may explain changes intellectual functioning with increased age. Given that there are individual differences rates of agerelated change and that these changes have common cause (slowing), one can expect increased covariances on the cc (Hertzog, ,gnitive 1985, variable 1987) influenced . Moreover, this partialling cause or partingout (Salthouse, 1985b). The body of literature relevant these issues also reviewed here Cerella s Approach Cerella attempted answer question "How many slowing processes are there?" using a method proposed Salthouse (cf. Salthouse, 1985b) assess the impact age on reaction time. Young subj ects ' reaction times on a given task and older subjects ' reaction time on the same task may be considered determine a point a twodimensional space. Various tasks within a given experiment or across experiments determine a multitude of points and linear models relating young and older subjects ' reaction times may evaluated as to their accuracy in reproducing points the space. Cerella, Poon, and Williams (1980) used information processing conditions (points the two dimensional space) taken from 35 studies. They found that simple regression Old=1.36*Young accounted the variance subject data. Further refinements are possible based on a distinction between sensorimotor and mental each tasks. one Two of these regressions were categories. constructed The results the indicated tasks that regression coefficient sensorimotor tasks was much lower than regression coefficient the mental tasks operating at a peripheral level, and a second one central level. These results are basic agreement with Birren's hypothesis. In a subsequent article Cerella (1985) considered more general terms the topic of fitting models to points a twodimensional space relation the issue of how many factors or mechanisms of slowing should postulated order to account the data. Instead using a onefactor or a twofactor linear model, one can increase number of parameters or factors the model and gain power. One can assume, example, a distinct regression line each experiment . The number parameters this case two multiplied the number studies. Conducting this kind of analysis Cerella was able to predict the variance old subjects' scores. However, as Cerella has shown, this result may be reproduced assuming mental D that different processes experiments different contain proportions sensorimotor and that these processes slow with age to different degrees. Different proportions, in addition to sampling error, produce different regression lines. Cerella s conclusion that, reasons parsimony, one should adopt simple two factor model involving one central mechanism of slowing. Factor Analytical Studies of other measures as well. Given a multiplicity of speed factors, an assumption of multiple slowing mechanisms plausible. regarding A speed the hypothesis structure also of these enables factors some with predictions increased these predictions are somewhat different the case a single slowing mechanism than the case of multiple mechanisms. Given that individuals slow down with increased at different rates and given that a central mechanism slowing responsible this phenomenon with increased age, several predictions are possible (Hertzog, 1985 , 1987). Factor Similarly, covariances may increased be expected factorial to increase variances should with age. result. More comprehensive and/or higher order factors are also more likely multiple variances appear slowing and c with increased mechanisms ovariances are with age. on the at work, increased the age other hand, change should rather nonuniform across different factorsfor example existent some cases and others (Hertzog, Raskind, & Cannon, 1986) one the earlier factor analytical studies, Birren and Morrison on 11 tests (1961) of WAIS performed including, a principal component addition, analysis and education. A sample about subjects, aged 2564 was second component associated positively with several verbal scores and negatively with several performance scores. The performance tests associated with the second component, especially the digit symbol subtest, may be considered reflect speed. This analysis, therefore, has demonstrated the existence a pure speed factor. Possible reasons this are the fact that unrotated solutions tend to produce bipolar factors as well as the fact that WAIS a test that does not emphasize speed. Birren, Riegel, and Morrison (1962) performed a study which measured reaction times stimuli of varying complexity a group young and a group of old subjects. The study used 22 stimuli conditions including tasks of varying complexity as different as choice reaction time versus word association. In all cases subjects had press a button according to instructions. A principal components analysis the data demonstrated the existence of a general speed factor old but not the young subjects. The general factor had high loadings on tasks varying complexity and character and explained variance. The existence of a general factor of speed was also examined Salthouse (1985b). Two studies conducted tachistoscopic tasks. A second study included same types tasks with the exception of the perceptual speed tasks. The median correlations were low both cases: first and the second study. The modest intercorrelations suggest a multitude of speed factors, least the young ages represented these studies. These results highly should selected qualified samples however as those the used observation Salthouse that s studies are likely to be accompanied restrictions range and, as a result, reduced correlations. White factor and analysis, :unningham found a (1987), multitude using an exploratory of speed factors group young and a group of old subj ects who were tested (among other tasks) on simple , choice Sternberg and card sorting . In both groups card sorting was a separate factor. the young group Sternberg tasks loaded on the same factor and simple RT and choi on another factor. The factorial structure was more complicated elderly subjects. Most important, Sternberg RT tasks including spatial stimuli and Sternberg RT tasks including verbal stimuli formed two distinct factors. A multitude of speed factors was also reported adults. A twogroup confirmatory factor analysis established the existence of a semantic memory access speed factor distinct single from reaction a choice time reaction factor. time Moreover, factor this and from factor showed similar pattern both age groups . The correlation between this factor and the choice reaction time factor was greater the old group than young group. However the semantic speed factor correlated less with simple RT in the older group. This lack of uniformity the behavior the matrix factor covariances (excluding some kind selection effects) not consistent with the existence single mechanism of slowing. an additional study to be reviewed in some detail the next section, Hertzog press) measure found and measures an answer shee of speeda t measuret perceptual o be highly speed correlated suggesting the existence a second order factor of speed. Cunningham and White (1983) analyzed a battery tests including measures of fluid and crystallized intelligence figural symbolic perceptual speed abilities group subjects. young The to 33 years) confirmatory and factor in a group analysis old indicated equal number of factors with a similar pattern across groups. More important present context, the In the White and Cunningham (1987) study factorial covariances were relatively large the young subjects. However, the different factor structure the two age groups (see above) precludes a significant comparison. Longitudinal data collected over a period seven years showed also increase the covariances between highly speeded tests. Cunningham, Smook, and Tomer (1985) presented data based on 100 older subjects who had taken battery speeded tests twice over interval of 7 years. The factors analyzed this paper were Symbolic Perceptual Speed, Figural Perceptual Speed, Expressional Fluency and Word based Fluency. on tests Each from factor had the three indicators, of Factor most Referenced of them Tests (Ekstrom, French, & Harman, 1976). A longitudinal confirmatory factor analysis has been performed using LISREL. A model, restricting the factor loadings but not factor variances and covariances, was significantly better (p<.o1) than a model that restricted both to be equal but only marginally .05) worse than a model that allowed both factor free. loadings The changes factor the m variances agnitude and covarlances of factor to be covariances and intercorrelations confirmed the results obtained the earlier cross sectional analysis (Cunningham, 1980) : factor covariance Perceptual between Speed. Figural Another Perceptual result Speed and of interest Symbolic this study refers to the magnitude of stability coefficients (correlations stability within coefficients factors were across occasion) high .90) , . While figural perceptual speed had a relative stability .73) indicating that this variable interindividual differences intraindividual rate change are maximal. Tentative Conclusions on the Dimensionality Slowina While Cerella's approach produced one single central factor slowing, evidence suggested the factor analytical studies more congenial to the hypothesis multiple speed mechanisms, other words to a weak form (Cerella, Poon, Fozard, 1981) of Birren s hypothesis. The reasons this discrepancy need still to be explored. Several observations on this point seem pertinent . It possible that the regression method used Cerella and his colleagues not very sensitive the existence more than one central mechanism of slowing, especially when there onei predominant central factor, or when speed factors (processes) are represented different tasks comparable proportions and/or change with age to a similar degree. the other hand is not impossible that behind the higher order factor rather than a first order factor. The magnitude intercorrelations among different speed factors important judging the plausibility general (second order) speed factor. In White and Cunningham s study the correlations were about .6 for young subjects and the older subjects. High but "imperfect" correlations between a perceptual speed factor and a Thurstone PMA Answer Sheet speed factor are reported unpublished Hertzog results. press), In Salthouse referring s studies some in young subjects (1985a) intercorrelations between the speed variables were relatively low. Together these findings suggest exist, that a general although, higher given order great speed factor variability might of speed tasks, abstraction Slowin'a difficult Relation . Salthouse Psychometric , 1985b). Abilities Several groups of findings make a causal relationship between a reduction speed a decline intellectual functioning plausible. First , as shown many cross sectional studies, there are positive correlations between measures 1985b). speed While measures magnitude of intelligence of these (Salthouse, correlations generally very high, and while there are large differences Another of relevant findings regards the fact that, general, a r intellectual education functioning speed t . Thus, :ends to precede Schaie & Stroth declines er (1968) using sequential different cohorts data for found those longitudinal variables age (word changes fluency across and psychomotor Subsequent speed) where analyses have response confirmed speed this was important. pattern (Schaie, 1983) Some other results come closer the examination causal model of relationships . Witt and Cunningham (1979), analyzing data from second author' master' thesis (Cunningham, 1974; Cunningham Birren, 1976) , showed that pattern of intercorrelations between a highly speeded relations factor and two unspeeded factors verbal and numerical consistent factor with from the Army assumption Alpha Examination) of a causal relationship between speeded factor an early time and the unspeeded factors at a later time. The subj ects were males and females tested when they were young and then retested years later. The speeded factor time one was highly co abilities related time (about two .65) whereas with each the one verbal of the and two numerical abilities at time one was only weakly correlated (about .25) with The assumption a causal relationship implies increased covariances between speed factors and other factors of psychometric intelligence with increased age. This between increase different similar speed to the variables increase or factors covariances which already been discussed. However, the focus this section on the relationship between speed variables and other intelligence factors which have no direct or evident connection to speed. There are several pieces of evidence suggesting that there indeed an increase covariances correlations) with increased age. Birren (1965) reported that Wechsler Memory Scale the speed of writing digits young group showed adults of old essentially but no correlation a significant adults. .01) correlation longitudinal a group .52) comparisons with Army Alpha Examination (Cunningham & Birren, 1980) showed increased intercorrelations between a highly speeded relations factor and a verbal factor. The increase was particularly dramaticfrom independence to 50% of the variance results shared based the two on the factors. factor Other, system cross showed that sectional the covariances between symbolic perceptual speed and figural perceptual speed on one hand fluid intelligence on the were smaller. Additional longitudinal results showed also increased covariances between these two factors perceptual speed and expressional fluency and word fluency factors (Cunningham, Smook, & Tomer, 1985). The last group of findings to be reported this section relates to the prediction that, given a causal relationship relationship between between speed and and fluid intelligence, intelligence should be weaker after controlling speed. The rationale behind this approach was presented Salthouse (1985b) . Salthouse argued that the best method to control statistically speed partial correlation which enables an examination the relationship between a cognitive variable after removing speed related variance from both. Other authors, however (e.g., Horn, Donaldson, Engstrom, 1981) , argued that artificial remove variance from and that part semipartial) correlation that removes speedrelated variance The only location from cognitive processes which variable mediates should changes used. fluid crystallized intelligence one of the main interests work Horn and his colleagues (Horn, Donaldson, Engstrom, 1981; Horn, 1982). They tested three samples middleaged and older adults aged 20 to 60, residents apprehension, shortterm memory, encoding organization, attentiveness, concentration, hypothesis generation, speediness, carefulness persistence. The speed measures included perceptual speed measures (two measures symbolic speed and one measure of figural perceptual speed) and also measures based on the time spent providing (correct or incorrect) responses to items. Fluid intelligence was measured using the Raven Progressive Matri ces Test, a letter series test, a paper folding test one study only) visual organization. Crystallized intelligence was measured with vocabulary tasks, analogies and remote assoc iations. Variables factor level were defined as simple unweighted linear combinations of the relevant scores. The method of analysis was based on part correlational procedures: the linear component predicted one or several removed from process the variable relationship (e.g., between perceptual age speed) and intelligence. If the process variable which partedout mediates entirely relationship between and fluid intelligence, a nonsignificant part correlation can expected. however, the part correlation different from zero but significantly lower than bivariate correlation between intelligence, the conclusion intelligence: was found to decline some analyses (Horn, 1982 75 IQ points per decade. Controlling perceptual speed reduced this rate points. Interestingly, speed to correct or to incorrect answer was not found to have same effect. Thi kind of speed correlated also at a low level with the perceptual speed. Horn indicated that relation between perceptual speed and fluid intelligence might be mediated an attentional factor of concentration. This factor accounted a similar decline Gf and also much decline perceptual speed. Other processes were also found to contribute to the decline Gfthe ability to eliminate irrelevancies concept attainment, and also processes involved hypothesis formation. similar finding was obtained Hertzog press) using tests from the Educational Testing Services Reference and Thurstone Thurstone Primary Mental Abilities (PMA) test a group of older adults, ranging in age from through years. The speed factors included were Perceptual test Besides Speed figural speed, (based on two perceptual the tests speed) psychometric and batter of symbolic and AnswerSheet y provided m one Speed. multiple measures Verbal Comprehension, Inductive Reasoning, variables restandardization. The two measures of speed correlated highly with each other supporting the existence a higher order factor speed. Regression analyses have been conducted variables and using speed ability factor factor scores scores as dependent as independent variables. Age (and age squared) have been entered a second step, sex the a third, regression and interactions analysis. Both the Perceptual last two Speed steps and Answer Sheet ability Speed predicted factor. Although significantly and adding independently the speed the predictors resulted a significant improvements magnitudes of this improvements were minimal. Of special interest are the results Induction. unadjusted age differences (based on the regression analysis) Induction were about standard deviation from age Adjusted speed, the age differences were only half a standard deviation. Numerical Facility and Verbal Comprehension showed when levelling consistent adjusted off with old the for sp age. I results eed a positive n general obtained age these Horn gradient results and are his colleagues. A detailed comparison difficult because methodological differences between two studies . It seems, however, that the relationship remaining between The results are interpreted Hertzog as supportive general position that cognitive slowing associated with declines of intellectual abilities. However, independent contribution of the speed factors the variance cognitive variables suggests that more than one mechanism of slowing involved. Hertzog also mentions unpublished factor analytical work showing that while Answer Sheet factor correlated highly with Perceptual Speed factor these two factors had different pattern correlations strengthens with the c other onclusi cognitiv on that abilities. multiple This processing finding g speed factors are involved an explanation of slowing. Schaie press) analyzed crosssectional and longitudinal data from Seattle Longitudinal Study with respect primary to Perceptual mental Speed abilities: and Verbal relationship Meaning, the Spatial Orientation, Inductive Reasoning , Number and Word Fluency. The subjects included two large samples more than 1600 adults. Longitudinal data were available over adults from first sample. The ages represented were to 91. Perceptual speed was measured using two indicators: Identical Pictures test and Finding test. Partial correlations between age and the five abilities were reduced also the correlations but to a lesser extent. additional analysis the author examined the behavior residuals abilities after regressing them on speed. the case Inductive Reasoning the trend of decline with age which had been found with usual measure of Inductive Reasoning was found with residualized measures but reduced degree. Moreover, this trend of reduced decline with was apparent both longitudinal and the cross sectional analysis. An examination of the figure presented author shows that the range about to 80 years the longitudinal the crosssectional curves are virtually identical show almost no decline. Schaie interpreted Salthouse's data slowing as providing of processing "limited speed support" model. Stankov (1988) has examined relationship between fluid and crystallized intelligence and attentional abilities a group subj ects aged One attentional factors Perceptual/Clerical Speed this with study salient was Search loadings from Number Comparison, Letter Comparison, And Search Time tests. Other attentional Flexibility. factors author f were ound Concentration a correlation and of .31 Attentional between fluid intelligence, indicating a loss of about particular, partingout Search reduced the correlation from .31 .08 decline .08 points per decade). even greater effect was obtained when Flexibility was partedout. Partingout three attentional factors to a positive relationship between age and The results obtained using same technique examine the relationship between and crystallized intelligence showed of about a different .7 IQ trend. points Gc evidenced of crystallized an increase intelligence with per decade Search which and C increased to 3 concentration anm .6 and d to 4 .7 after after p partingout artingout Flexibility indicating . These that results changes are interpreted in attentional Stankov processes mediate changes in fluid and crystallized intelligence. Salthouse (1985b) examined the relationship between age, speed, perceptualspatial abilities. Two tasks were selected this purpose: the Gestalt Closure Test from a task involving the identification of computer generated incomplete figures. In both cases subject had to identify the object represented a distorting drawing. Two groups and pointbiserial correlations were used. Speed was measured a digit symbol substitution test . The findings showed no major reduction magnitude the indicating that closure ability dependent on speed but an independent correlate (Salthouse, 51). Soeed and Memory Abilities As is case with psychometric abilities, the speed hypothesis predicts that controlling speed should reduce substantially correlation between age and memory. the same time, controlling should affect much the correlation between speed and memory performance. Salthouse (1985) reviewed relevant research regarding these predictions providing also data from a number of studies performed own laboratory . Salthouse' work was based on samples of 16 young adults aged to 30 and comparable numbers of older adults aged to 84. The digit symbol substitution test, a reasonable indicator of symbolic perceptual speed, served as the speed measure. Different memory tasks were used: digit span, letter span, dual span (including both digits and consonants), supra span (involving the pre sentation seven pairs of letters and seven pairs digits several trials), free recall, paired associates and spatial recall. The analysis based on a comparison the correlations between age and performance correlations on the between various n the s tasks ame with variables partial after partialling The results showed that, general, the span measures are consistent consistent Morrison with (1961) with similar and predictions. findings Goldfarb These obtained (1941). The results Birren are and results regarding free recall were less convincing, possibly because increased importance of strategies mediation this task. The spatial recall performance the paired associate performance were inconsistent with the processing rate hypothesis. Salthouse attempted to explain the first inconsistency on the basis the assumption that spatial recall a pass task whereas measure speed (digit symbol) a measure active processing. satisfactory explanation was found second inconsistency. The fact that age still accounted substantial performance part after the variance controlling the speed paired (about ociate versus about the zero order correlation) but only much lower percentages the span measures was attributed Salthouse relative complexity first versus the simplicity the latter. In free recall strategies mediation, elaboration and organization may play important role and may overshadow some extent the effects of speed. This interpretation fits the rate processing model section. They included measures of primary memory, secondary memory, free recall and incidental memory. In general these measures behaved as predicted the speed hypothesis. Alternative Interpretations The findings reviewed here, while supporting general a speed hypothesis (especially the area of fluid intelligence), possible do not to view exclude alternative a reduction spee interpretations. d as a consequence rather than as a cause of cognitive changes (e.g Botwinick, 1984; Salthouse, 1985a, 1985b). Cognitive factors that are frequently mentioned this context are strategy changes, differential motivations and age differences familiarity with tasks (Salthouse, 1985b). While this kind hypothesis between can a reduction account positive speed a decline correlations intelligence, cannot easily account the large reductions the correlations between and intelligence after controlling for one speed. should Moreover, be able t make :o provide such an hypothesis evidence showing plausible a drastic reduction the correlation between age and intelligence after controlling for, say, strategy. However studi this topic are lacking (Salthouse, 1985a, 1985b) Another possible interpretation begins with the confound of two phenomena: chronological time and cohort. Accordingly, possible that the relationship agefluid intelligence reflected the first place mainly cohort differences which were reduced after controlling speed because a possible relationship between speed and cohort. Semipartial correlations equivalent statistics) which have been often used these studies seem particularly susceptible this criticism. The reason that (the square a semipartial correlation this context represents proportion of variance in Gf accounted beyond that accounted speed this necessity Gf without necessarily smaller the the than statistical case the proportion control partial accounted of speed. correlations This (or age path coefficients) partialled from are from both used. age, and In this only still latter from leaves case speed . Partialling substantial speed portions variance unaccounted and one can expect, given that cohort explanation correlation should true, obtain. that a In other substantial words (partial) an explanation based exclusively on cohort differences seems unlikely partial correlation between small. It is also possible to consider the lationship problems may determined a test that measures how fast one can solve simple problems. According to this argument, speed of processing information may be not a good predictor of the may ability a good relatively solve very predictor trivial difficult the problems. problems intelligence Such an argument shown may although solving rely Horn s finding that speed to correct answer a poor predictor of ability level (Horn, 1981, 1985) and that part of the psychometric tests are of low difficulty . However, some tests contain items of increasing difficulty to high levels difficulty. As Cunningham (1987) indicated, what stops subjects timed tests of this nature the difficulty of the items rather than time itself. These later items place greater information processing demands on the person attempting them and, as a result, success on them more likely at increased speeds information processing (Vernon, 1987). Some empirical results confirm this interpretation: The correlations of RTs with untimed scores have been shown (with exception of performance tests) to be of a similar magnitude as the correlations RTs with timed scores (Vernon, 1987; Vernon, Nador, Kantor, relevant 1985; Vernon research may & Kantor, be criti 1986) cized . While part Sternberg, the 1986) , the intelligence: tests may emphasize speed too much and, as a result, may penalize older subj ects (Lorge, 1936; Cunningham, 1989). seems that Cunningham' counterargument holds this case as well. The empirical evidence on this point rather scant. Hertzog press) obtained an interaction between age and Answer Sheet Speed analyzing PMA Verbal Meaning subtest indicating that the speed marking the answer sheets become increasingly more important with increased age determining the score. However such an interaction was found other and subtests. Also, as Hertz remarks, the invariance number and pattern of intellectual factors across adult ages (Cunningham, 1981, Hertzog & Schaie, 1986) rather inconsistent with this type of interaction. Another possibility that both speed of information processing cognitive abilities, such as fluid intelligence, decline with increased age because both are influenced the same agerelated mechanism. A candidate this attention (Horn, 1982, 1985; Horn et al., 1981). Some other findings are rather inconsi stent with such possibility. (1983) Cornelius, performed Willis, a confirmatory Nessellroade, factor and analysis Baltes on data obtained from a group older people. The analysis was variables have been measured using tests. Other tests measured attention attention attention factors: switchin decoding g and co processes, ncentration. selective The loadings were fixed the ability factors the levels indicated a previous analysis while the attention variables were allowed load freely on these four factors. The expectation was that they will load mainly on fluid intelligence on short term acquisitionretrieval. However, three of the four attentional factors loaded highly on the perceptual speed factor. The authors interpreted these findings as showing that changes in attention with age occur independently of changes fluid intelligence, crystallized intelligence or memory. Finally, the results reviewed this chapter are compatible with more complex models relating age, speed information processing and additional variables. The additional variables complexity (age, may etc.) be at allowing level variables of the other independent than per se to affect Birren s notion speed of information of a secondary processing. factor reflecting An example disease processes (Birren, 1965) . Also variables reflecting strategy, motivation, adjustments, etc. may affect and/or mediate the relationship between speed and cognitive considered more comprehensive models. Indeed one should explain why, example, there are declines fluid intelligence corresponding to reductions speed but apparently there are no analogous declines crystallized intelligence with (e.g. , Horn al., 1981). Finally, even an influence of cognitive declines on speed information processing, possibly via additional variables such as depression, not incompatible with the claim that main path of causality goes the opposite direction. Obviously the scientific community still away from being able to construct evaluate properly complex models this type. Summarv The studies reviewed this chapter allow several tentative conclusions regard to the two main issues discussed : the dimensionality of the speed measures relation plausibility an explanation cognitive change based on a reduction the speed processing information. Most speed the measures evidence (e.g., favors White a multidimensional Cunningham, view 1987). addition, measures while the covariances factor level between typically different increase w speed ith multidimensionality of speed measures and lack homogeneity the rate change with suggest the existence of multiple mechanisms of slowing possibly mediating relationship age with other cognitive variables (Hertzog, press). . Other evidence, however, favors a more parsimonious view. Cerella s results, particular, are consistent with existence one central mechanism slowing addition to a peripheral mechanism explaining slowing at the inputoutput level). Cerella s results may conceivably reconciled with other results obtained with factor analytical procedure at a higher level of analysis: possible that a higher order factor of speed represents captures the central mechanism of speed. Although difficult from the perspective one higher order factor interpret nonuniform changes in factorial covariances those obtained Hertzog, parsimony considerations require examination the possibility that higher order speed factors are better measures of information processing. There of the evidence intercorrelations (most between of it age, based speed on the and analysis cognitive abilities) suggesting that a reduction in speed processing information mediates the decline cognitive relationship are possible. In particular, arguable that other factors than speed, possibly attentional factors, explain both the decline speed and the change cognitive abilities with increased age (Horn, 1982; Horn al., 1981). CHAPTER PROPOSED MODELS The approach described a general way the introductory chapter is a twostage approach. the first stage the factorial structure the speed measures considered. Of particular importance in this stage is the stence of a higher order speed factor . The prediction based on the speed hypothesis of increased covariances with increased may be examined the level of first order factors and also the level of second order factors. In the second stage a model based on the speed hypothes and on the theory of crystallized and fluid intelligence (Cattell, 1987) examined. A basic question addressed part whether a model that assumes that speed mediates intelligence the and relationship that fluid between intelligence fluid mediates relationship between speed crystalli intelligence fits the data reasonably well . Given that further important question refers to the magnitude path relating processing age rate directly theory to fluid as well intelligence. as empirical The findings suggest bulk the influence age on fluid intelligence passes through a speed variable. Figure depicts the model defining five first order factors speed : Symbolic Perceptual Speed (SPS), Figural Perceptual Speed (FPS), Choice Reaction Time (CRT), Sternberg Reaction Time (STRT), and Card Sorting (CS). Four factors have three indicators each. Sternberg Reaction Time has four indicators . The tests on which these indicators are based are described Chapter The model assumes a simple structure loading f : each ixed variable zero loads on the on one other factor factors. and This model suggested the previous analyses of these data (Cunningham & White, 1983; White & Cunningham, 1987). Confirmatory factor analyses using LISREL (Joreskog & Sorbom, 1984) can be conducted both groups order to estimate free parameters of the model (factor loadings, specific variances corresponding the error terms of each observed variable, correlations between factors) as well as to obtain an evaluation correlations the or covariances model between to the the data observed (matrix variables) on which model based . Correlation matrices are used input and the scale the latent variables (factors) established fixing variances the factors to unity 44 Ct 0 H 0 4 *~ I a r , (0 PC 00 ) c I 0 r .C VO ^ PU # S C 0 C *H ..C O I IIH H C E 0 r P **n 0 ) C U3 >lQ .4 C C oQC 0 *HM r4 l C0 I S 00 CO 0 0 r ** 9t4 0) S 03 0)0 0)a 0 DQ ) fO O 0 I 5P0 4 S04 0I 0 000I I * kW UI P  n.dir e s c fO 4 II P S a) n3 we I I0 a IU O WIU 0 0 W041)  I* UCO C #CM * <0 C ~0E.4.r4 WH40 T3C 0 Vt *r4'OC (H 0 V II I I I rBl 11r40 4 c 0 40 I Wv * r >Q *O C O) C E^r 0 'CO 00 13 .0 r't0) r^ n r^ C< I e POI C 03I 04 tU MI > *. r U 0~0 S4J W ) 'too fP r1 0 I U2 r4Q4 C I f P M i 4.4) 0)idE MI ^ Q> 0 IJJW ^ C PI PI CI ) 0 I II IS6 a .I 04 I I 0) U O CQ & 0 0 C SI I P1 > 0 EH*. I I k I II . I.E1 H OC ** . a) .0 C 0 IO I r E* . S4 O 0 I S** 0 04 4lW I(0 >  3 H *( CI V1 I; program. The LISREL program supplies a Chisquare statistic which model can be used to the data as a test (Hayduck, the 1988; correspondence Joreskog & Sorbom of the , 1984). This Chisquare may be also related to the degrees freedom the model to obtain an index of goodnessoffit and other indices of goodness are provided the program or may be computed (see Appendix Moreover, possible to perform simultaneous confirmatory factor analyses both groups test the hypothesis increased covariances the older subjects. This hypothesis may be considered versus a null hypothesis of equal variancescovariances. more general terms, models with constraints on their parameters across the two groups may be compared with models without or part these constraints. Previous anal yses this kind (Cunningham, Smook, & Tomer, 1985) have shown that very restricted model which assumes equality of factor loadings, as well as equality of factor variancescovariances and equality specificities the observed variables across two groups does not data well. Moreover, such model may be improved relaxing some constraints. Thus, a model which does assume equality specificities may be expected to fit data better. Chisquares This reported difference the itself LISREL program a Chisquare as a statistic. distribution with number of degrees of freedom equal the difference between number of degrees freedom of the compared models. repeating this operation a series of models nested one within another obtained. According to previous results is expected that a model may be sequentially improved relaxing first the constraint on specificities and next the constraint on equality of variancescovariances. No further significant improvement expected as a result of relaxing the constraint on factor loadings. The comparative analyses are based on variancecovariance matrices which have been rescaled using the pooled mean variances age groups (Cunningham, 1978). Figure depicts a model based on a second order factor of speed. In this simple model the second order factor explains intercorrelations covariances) between the first order factors. In the LISREL notation second order factor an exogenous, variable determining first order factors which are endogenous Eta variables. One path coefficients from the second order factor to the first order factors fixed one order to determine the scale the second order factor. Speed than to other factors and Choice Reaction Time more similar to Sternberg Reaction Time than to other factors. possible conceive a model where there a second order factor explaining only part of the relationships between factors. In this more complicated model there are specific intercorrelations between the residual terms "similar" factors: between Figural and Symbolic Perceptual Speed and between Choice RT and Sternberg Formally, this model equivalent to a model postulating three second order factors (Figure 33) . A second order factor Perceptual Speedhas as corresponding first order factors Figural Perceptual Speed and Symbolic Perceptual Speed. Another second order factor correspond to Choice Rt and Sternberg as first order factors. Finally, this case the "second order" factorCard Sorting identical with the first order factor. In this model three second order factors "explain" the correlations between the first order factors and the offdiagonal covariances between the residuals (specificities) the first order factors are zero the matrix. A second order factor model may considered nested a first order factor model therefore can be evaluated relation to it the usual way. Moreover, the first, more factors are correlated. The model with three second order factors, being equivalent to the less restricted model with one second order factor, may not be considered explanation of this latter model and cannot be validated the usual way showing that fits the data as well the singlefactor model. However, this model presents some interest since allows use of alternative latent variables speed path models. The basic path models relating to fluid intelligence (Gf) and cry stallized intelligence are illustrated Figures 34, 35. They may be described terms the model of their paths components: between referring the latent to the structural variables relationships model the between referring measurement the latent variables the observed variable (Joreskog & Sorbom, 1984). the model depicted Figure (omitting measurement model) and education are independent, exogenous variables. Gf and variables. Speed mediates education are Speed, mediates the allowed and the are relationship relationship to relate to GC. to all endogenous between In addition three latent and , age latent variables. In a slightly more complicated model presented Figure (omitting again measurement model) 51 U) a H 0 0 0 j *rI 01 0 a4 *r4 4ir / I ( / \ 0) 0) C 0 0) f Y/ \ ^*r ti 3 its 0 52 II) 0 0 Cn 0 0) f \Jo \ S 0 In ICI 0) 'C a) *In C) en l (A (U 'C 01 H 4, IC a) a) with subjective health of particular importance older subjects. The two basic path models are constructed on the basis the speed hypothesis. particular interest, explained above, is the path from to Gf. According speed hypothesis this path should be of modest magnitude such that most of the effect to Gf pas ses through latent variable of speed. A strong version speed hypothesis will predict fact that this path not significantly different from zero. The LISREL program provides tvalues estimated parameters which allows us to confirm or disconfirm this prediction. An equivalent formulation the strong prediction the following: The nested model obtained fixing path coefficient path ageGf zero not significantly worse then the more speed relaxed model. hypothesis A somewhat allows for weaker a significant interpretation path of the coefficient path from to Gf but requires that most of the effect age on Gf will through mediation one more speed variables measuring speed mechanisms. The latent variable of speed these models may any first order speed factors or second order speed factors obtained the confirmatory factor analysis. also possible The models also integrate elements of the theory fluid which and crystallized predicts intelligence a relationship between (e.g., the Cattell, two 1987) forms intelligence as well as a causal influence from education crystallized intelligence. can be expected fact that the effect of education on Gc is larger than the effect The paths from education Gc and were allowed be estimated on speed the program. information process A possible sing impact suggested of education some findings (Botwinick & Storandt, 1974), and this path coefficient also estimated these models. One the two basic models includes health based self assessment as an exogenous variable (subjective health). There evidence indicating that impaired health, as indicated cardiovascular disorder related to slower reaction times (Birren, Wood & Williams, 1980). Since subjective health was found to be a valid predictor mortality Shapiro, variable health (LaRue, 1982), w in these and Banks, re can model intellectual Jarvik, expect . Although Hetland to affect the functioning 1979; the Mossey speed relationship yet clear, between there evidence suggesting that physical health predictive maintenance of intellectual functioning (Schaie & Hertzog, In LISREL' terminology path coefficients going from exogenous the endogenous variables are included the Gamma matrix. The Beta matrix includes relationships among endogenous variables. these terms Gamma matrix was specified to be free and allowed to be estimated . In Beta matrix were estimated the paths from speed to Gf and from Gf to Gc. Other coefficients were fixed this matrix zero. error between The terms. n these endogenous To obtain residuals variables identified should be also model fixed have s the to z residuals covariances ero. In LISREL this done using matrix which includes the variancescovariances of these residuals. Accordingly, diagonal elements this matrix were fixed zero. The diagonal elements representing residual variances were allowed to be estimated. The structural models with second order factors speed are somewhat more complicated. A second order factor itself an endogenous, variableis related to Gf, Gc and to the exogenous variables the same way a first order factor related. However, addition, this factor determines first order factors speed . The paths from second order factor to the first order factors are represented Beta matrix. The residuals of the first off the level of the measurement model the path models several comments are necessary. Age, education subjective health are measured on the basis of self report and are considered be measured without error. The relationships between the exogenous latent variables and their indicators are expressed the Lambda X matrix variancescovariances of the residuals the exogenous variables latent Theta variables Delta are matrix. "identical" our with case the in which observed variables the identity realized fixing unit diagonal Lambda X matrix and fixing zero elements of the Theta Delta matrix. Multiple indicators, especially case of subjective health would have been preferable. However, there evidence that a single self report item like one used the Memory and Intelligence study see Chapter has good validity and reliability Mossey & Shapiro, 1982 The endogenous variables each have several indicators. The relationships between these indicators endogenous latent variables are represented the Lambda matrix. The observed matrices have also "specificities" "whose" variancescovariances form Theta Epsilon matrix. measured four indicators, and Gc is measured Chapter The indicators speed (three or four) vary according the speed factor used the model are also wellestablished measures. A description of them provided Chapter The indicators speed a first order factor) allowed Lambda fixed latent and fluid to load Y matrix to unity variables and freely with order (Joreskog crystallized on the appropriate exception to determine & Sorbom, intelligence factors loading metrics one the 1984). All are the which the other loadings are fixed zero. The variances the specificities the observed variables are estimated assuming that the specificities are intercorrelated. The Theta Epsilon program. The matrix covariances therefore between diagonal these and free. residuals Theta Epsilon matrix were fixed zero. cases where a second order factor was used this factor corresponds to a column zeros the Lambda matrix while first order factors correspond to columns defined way explained above. The path models were applied to the two age groups However, since almost no variability subjective health was found among young subjects, model including subjective health were estimated only old subjects. CHAPTER 4 METHOD Subi ects The subjects were young adults aged old subjects aged 73 which have been tested the Intelligence Memory study (White & Cunningham, 1987) . Both young and the old subjects were residents Gainesville area who responded advertisements local newspapers and were paid their partic ipation study . Four subjects, three young and one old with ssing data on two or more variables corresponding given factor were deleted . For eight other subjects with ssing data, corresponding means groups have been used . The analyses reported here are based on 147 young subjects (Mean age= 24.9 SD=4 and old subjects (Mean age=65 SD=4 . The young group included 69 mal females . The group include 50 mal and females. The young subjects had a mean education 15.3 years school SD=3 . Eighty four of them .1%) were students . Those of them who were attending school were general younger than the othersthe average was about (SD=3 .4) . 21 of them .1%) were still studying. The subjective from health the (excellent) subjects (poor). was The evaluated mean on a scale subjective health the young subjects was 1.64 (SD=. 54) while corresponding mean older subjects was (SD=.73). difference not significant. Subjects were asked report various subjects cardiovascular reported problems. hypertension About versus of the of the younger older subjects who reported These results are close the incidence this condition the general population U.S., 1981 respective groups: the age category to 44 and 37.9% the age category . Bureau of the Census, 1984). Other cardiovascular conditions respective are ages also typical : less than the (one general ; subject) populationn had of the a stroke, no one had a heart attack about suffered from angina. The corresponding rounded percentages the old subj ects are: strokes, heart attacks and angina. Tasks and Tests Speed Tasks The belong speed to five measures categories included s that r the present present distinc analyses t factors Symbolic Perceptual Speed represents the ability scan and compare quickly patterns of symbols. Figural Perceptual comparisons Speed between represents patterns the a with ability to make a figural fast content. Tests perceptual speed are often used as measures of speed Horn et al., 1981) but are considered mark also intellectual ability (Ekstrom, French, & Harman, 1976). Earlier work produced equivocal results regarding the separation Figural and Symbolic Perceptual Speed (Ekstrom et al., 1976) . Work of Cunningham and his assoc iates (Cunningham Richardson, 1978; Cunningham & White, 1983) demonstrated existence two separate factors predicted Guilford (1967) his Structure of Intellect model. This conclusion was further externally validated finding of higher correlations between and Figural Perceptual Speed (Cunningham, 1989; Cunningham & White, 1984; Schaie, press) The reaction time tasks were presented on the screen a TRS80 Radio Shack microcomputer. They included simple choice reaction times which were assumed load on the same factor (White & Cunningham, 1987). Sternberg reaction times with symbolic content were assumed to form a different factor. The Intelligence and Memory Study included also .g., structure may be different the old contrast the young adults (White & Cunningham, 1987). The reaction time tasks are often used the study of slowing of behavior with increased as well as in the study of speed relation to intellectual functioning. Card sorting tasks were considered to define additional fifth factor (White & Cunningham, 1987) . These tasks are also used the study of slowing with increased and, more generally, the study of selective attention. The following list details the tasks each one five categories. Symbolic Perceptual Speed included: Finding s Test (Pl) , (French, Price, Ekstrom, 1963). The subjects had to find which words of a given list contain the letter . Number Comparison Test (P2) from the Educational Testing Service (ETS) kit of reference tests cognitive factors (French, Price, & Ekstrom, 1963) involved a comparison pairs of numbers to establish identity. Letter Comparison Test (P4). This an unpublished test developed Walter Cunningham at the University of Florida. The test requires subjects to make comparisons between pairs Identical reference Pictures tests Testpart cognitive (P31) factors. from the Subjects had decide which of five possible figures are identical given figure. . Identical Picture Testpart . This part from the test referenced above was used as an indicator of figural perceptual speed addition part . Perceptual Speed Test (PSC) , (Guilford & Zimmerman, 1948). The test requires subjects to match objects arranged groups of four at the left of the page to identical objects arranged groups five at the right of the page. Choice included Simple Reaction Time (SRT). Subjects were instructed respond to the onset of the letter which appeared on the screen on each trial one second after a warning signal There and the were Sthe depend: five practice following s nt variable trials imple was and the and choice median test trials. reaction time time this tasks to respond the onset of the stimulus on the screen. Response times less than msec were not included the computation of median reaction times. Choice Reaction Time (CRT1). Subj ects were instructed press a key when letter was presented but to refrain Choice Reaction Time (CRT2). Subjects were instructed press a key when the letter or "J" was presented but refrain from pressing the key when the letters or "W" were presented. There were 7 practice trials and test trial 13 of them positive. Sternberg reaction time tasks based on a modified version of Sternberg's (1975) memory scanning tasks included four tasks with a symbolic contenttwo with a word content, one with a letter content and one with a number content. these of th tasks ree subj ects stimuli which were h was instructed presented to retain twice a memory ensure better recall. They had press a "yes" key when the stimulus the screen was a positive instance the memory and "no" when stimulus was not included memory set. Each task included practice trials and eighteen test trials, nine requiring positive responses and nine requiring negative responses. Median times were recorded correct positive and negative responses as well as for incorrect positive negative responses. The analyses here are based on the positive correct responses. The four tasks were: Sternberg Reaction Time (MFW). This task was based words taken from the Thorndike and Lorge (1944) word . Sternberg Reaction Time (HFW). This task was similar MFW but lists stimuli the were Thorndike selected and Lorge from word high frequency frequency norms. Sternberg Reaction Time (NPR). In this task the memory included number pairs. Sternberg Reaction Time (LPR). In this task the memory include letter pairs. Card sorting. The tasks involved sorting playing cards into several categories. The times completion was measured using a stop watch. Three tasks were included: Card Sorting (CS1) required to sort the cards into two piles according to color. Card Sorting (CS2) required to sort cards into four piles according to suit. Card Sorting (CS3) required to sort the cards into thirteen piles according to rank. Fluid Crystallized Several of the intelligence tests used Intelligence (Cattell, and 1987; Memory Horn, 1 project 978) between the c fluid classic distinction intelligence (Gf) and crystallized intelligence (Gc) and were used present study the purpose of measuring these two dimensions Intelligence on time. Subj ects were encouraged however not to dawdle too long on difficult questions. . Letter Series (LS) from Guilford and Hoepfner, 1971. The test requested subjects solve as many series letters as they could a limited amount time. Number Series Completion (NS) from the Army Alpha Examination (Guilford, 1938). The subjects had to complete several series of numbers a limited amount time. Figural Relations Diagnostic Test (FR), (Plemons, Willis, & Baltes, 1978). Subjects were given sequences of three patterns and, each one were requested to select out five possible patterns one that best completed the sequence. Crystallized intelligence was measured using three tests: Vocabulary Subtest (VOC) the Wechsler Adult Intelligence Scale, (Wechsler, 1955). Advanced Vocabulary Test (V5) from the Educational Testing Service Kit of Factor Referenced Tests (French, Ekstrom, & Price, 1963) Information Subtest (INF) the Wechsler Adult Intelligence Other Scale. Variables Education was measured on the basis the answer the question: "How many years did you to school" . Subjective health was determined using the question: general, would you that your physical health has been: excellent, good, fair poor, very bad? " score of 1 was used indicate excellent questions health, were to indicate asked good case health, education etc. and Additional subj ective health but they were used present analyses. Procedure All tasks were administered individually during two consecutive days, each one of about three hours testing. Several testing breaks procedure provided subjects included opportunity tasks described to rest. above The as well as additional tasks which were not analyzed here. the reaction time tasks card sorting were administered during the first day testing. The reaction times tasks and the card sorting tasks were administered order increasing level of complexity ensure gradual familiarization the subjects with the tasks. Fixed order standard procedure in correlational studies (White Cunningham, 1987). The perceptual speed tasks and crystallized intelligence tasks were administered during thoc arrnr1 14mt,~~I n.F; Jr .ll Ci, * ... r^x ^f 1kjTr i4 rrC Ckn other Army Alpha tests was administered during the first day. CHAPTER RESULTS This chapter presents the main results from the estimation of the structural models delineated chapter The observed variables on which the analyses are based have been presented Chapter All reaction time and other variables their measured reciprocals. time In this units way a have double been transformed purpose using been attained: transformed variables have a distributions closer to the normal distribution and speed variables are measured a similar way. An approximate normality variables statistics important provided one LISREL use maximum meaningfully likelihood estimates (Mulaik, 1972). path models with first order factors speed and comparative analyses are based covariances matrices as input. In several cases which second order factors were incorporated a causal model use of correlation matrices served avoid problems encountered Confirmatory running factor the analyse models s not using co including variance matrices. comparisons were based on correlation matrices (Tables and 52). V 0 0 H 1 X In  0)  (0 I C 69 ) HNWANMO0WNHFO~cammoONCOW ONO M rMit nowo^ Om m On In in eOmm rono O OflnONfnu1UnmncnEcrs r 0 # ONANOU~roNODnr4Hc1Oc & U * * * * * * * I II H C) Su S Su S3 SV( i ~O))C) t~ d V( 0 * * * * * * SII I Hr E NO^^D OO4 OimormnnOmnaocomo Co SrlONM O M4 5 5 9 ma 9 6 5 5 S n5 n 5 4 A * * * * * * U mO o or o 8 btfo iNo cu otor O I rin \o 04 5 5 5 4 5 5 5 4 4 5 5 5 4 5 4 S S S S S 9 5 4 6 5 i H ii NC r r ICo r iOn NInn r) IV(VOUfl U t folnrnnnin nrrrln nnr innn nr O N * a a a ** r( O 10I NMMM O O t Yb NMM MMMin cu MN cu YICI. . . . . ..)V)V~dd~CV(r SO cSnSo O m4oro4n4 5 S s oir5 4 m c5r 55m55i5o OC(^ l U)0L o olc^^ r) o in In rFin rt 'ro 'i ^' 'iJrn n UJ* * * * ncMOnNOHMONfOrmNMno'inrt 0N M O OB nWr n oiSiIO oinnrr MMM wwwr wNr Nlc r P) nc t dooi rcn o tn D SOfOQ) WC1 1ot^oo onio rH OeNoi 0Uif OfMlUnnciq Q4in.4c nt S* * * * * * * NOON N H0Nr ( woinor 4oio son < 7 NHONHsCrHH100rr rOOOOOH OHrrHOnMMrnrM ntO M I 1  W oon onn O comucoa ti c'niooNNcHN 4. OOHHNc MnirMHHNN31fM r zc eS04HMH l HHH ri* 5 6 5 5 4 4 5 9 5 SI il I I I I I I I I I I I I I I I I I I I I I I I I 0 Oi n fNNWHWfnC nNfrlC i rHNNiCOD*<( ' OONO HONr4NOOOOOr4OH MOH(OHHr ni t f t f f t In ~(V~lo ~I ^*Mol tin o^'Vm r lo~roinDon'~~nri oHoot F1400 fltAO HrOHOOH@OmO 2 HH1L MnMNNnnMnNOcnOnq O 1 4 * * * * HWLAO >OOOCHOHrwumLAca rO rl oi com r0 1o o Or0trorOrrrlcnooQr Uinino I U UNo H LAnr oO(o OoOr'coiOOO 03 HH nNHNcmnNnqMnNN^ nu @4n00oo I WH NH A mIO OHO4Hr io cNor r0o0ocnO * ri nc '* ^ nMNnMnnnn nLOcnino n * * * * * * ** oNb i 1o O nc Ha b MNr) rcn cvtnobr4 c1 OMMn ^^^xo nnnMncs ^o itiM r z * * * * * * * H WH0DnWM oHNWH o OM~om SII H o II Hifinntn n c^' ^O oomn U 1 I r^ I I HJ N N NH0WHLAHOOOOW OnH I U II H l N ONHO I m Nn cnao iOm )mo c 4^no l l i ONHo V) Vm wS O wmmom ** U C)9 H ifnOH o OMOM\ wrooooof mco o rmooHrN co02mer jl orn mitn Uo rr t nfn U * * * * * * * coooiiwn oi~votomnNonooM in Stnr^m tf Or!o na* ^^c ^' \o \o rzo o r, nr^ 'nrhoocu II ^*OaflOtnooinLAnO n ft ........... * ~NWNZONnLANnu MMtHt O O 3 93 3 9) 9) 9 9r 9 6O 0nil 9 9I 99OC N 9M C * * * * 'dHU S0 dH 0 I *I I o ENW r00 I t rI0 Qa0 0 W  0 0 I (0 01 UC023 w I0 oCO04 r ll *HU XI COI 0) *r eaCI HZ C HiPt rO I T( 0) H , OIC 3  .1I IH0X C C 0 O< L 0J m 3 *r P 984 b, I a Ed 0, (0 > H rn k 0 (N 4I I In x H 0 $4 I0 0 ca 02 0 H rt 4) 0 O 0 C' ~ONONOhqOfWoOwMw~NommMme S Nr***% *O*fnooo .cv) mNNo cMOru EC 0 0 0 0 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Ot HO r ONNNO n oHoWDin^ mroorQf 2l O * o o * * E ............ N OHOOinM nOomin4ioa unior (0 * * *0 * 9 0 0 9 0 0 0 I H i(( CI) 0 0 0 9 0 0 0 O9 9 000o 0 0 0 0m o0o o 0 * * * * * E rMcoMNSONHOMWinr~orWfmnrr~isoir o A OrHr Hclr%4Ir Mrruoa^InNNrM NNoortH Ca * * *0* * U NN NCO'%OOHOIOtOflOr. H CO rO1nMe r^oo 02 OHm mONHnno m inin inn 'nMcn & * * 0 0 0 0 N MO1 OMHOONmms ewaem 0 H0 0 m 0 M0 0 0 nM 0 0M o 0 0me 0 0 0 00a (ij *. .. .. *. *IJ *I *. *3 *1 *. * * rH fnNOio~rioornNnNHiorto~r^or^Oaut m rl r(m dlno co vor nn) r> \n Vomic r rS mnrl ci 04 *0 0 0 6 0 0 0 0 0 9 0 0 0 6 0 0 0 0 0 0 0. I H ^' ocN e Norri ooa m mcci nr co^ co 'oom cu 4 OrmiomsonHMANNjM^xn^nywN * * * **0*4* * N OCN ONiON f lrmmH nonAioHWHocoNin 040 *o* * * *** *n e a go3e 0 0 0 0 0 0 0 0 0 0 0 9 0 0 0 0 6 0 0 0 0 0 0 0 0 riV o or( rV o rle ) r mcoMuri rlco 'inr^^n ^ 04 ONOMiM flrMr4MNNeMNvrIMNN I u 1 rIOCM^ cOr Ol^CQr ^O ^' O cCO cV(Vrl U) rl CU CJ 0 ONN c NH Nr OHNrlI HHlHOr4NNHN rInrmw GE *0** *.. ... H( 1 O r0 ' oMo a OOH tHO HHrl l r1NH NaCHN ar rIl nH Er rin t ir)CM o oorcrtu H U, flMflOmoNwamwocNW~ om > nC)NNNHHNHOOHOrIOOrnoHaoo * * * * 0* 0 0 N mV 04C (0 V, '0 4  ia M n g g C U H 4" * C HOW 4'oW< f0 (Q  0)*^ 9 *0 04 SOH COG) 90 9) 0 0 0V D 9O t 9O 0 0 r 10 9t 9t 9) 0D 0O 9 0 0 0 O iaN omi'cm^'^ocotnooa e m woionoom r or ErNONo W Nc OWO OWo~enmom0er 0 r4tnoMMWoiNeaoain^'^n omor S* * *0 0 0 0 0 0 4 0 9 0 9 9 0 0 0 0 0 N O OO 0 OO MWOO NO O NN o '0 2N cu M c r mf oo un u, no homn^C 0* **)* * * * *H 43 IND~f~tnNH0HOH'otoomnhoN C 0M orttTNNmcoWNMnmoormne 0 *. * * * * * N E rl O rl^ W Ho0 dN M rOOOCOr OO I 0 HNNM4 wwmtN c nnn nc ogo\Doinm o LA 0* *0 * *94. 0. 0.. 4 0 O 0W 0O O OO O0 oOOOOOO0A (0 .0 ** ** * * **o* * I r rH1 lOOr( COOC OONr o r o rOatnw HHO ifo o o( /2 N cr inM oO r 0 * * * * 0 0O 4 4 nnM O9 0 0 in nOO 0, 0 0 S 0 M 4r) M * * *. ...... * # Or Vt voorre U I O vo r or vtO~omco ocu r( co cM it A Hr NNtNNtAOyOlm0noo ocomq cmNmNn r% 04N MMOMVMMMN 'Uri 8 I 01 I U k 03COrn. 9 $ Va) 0Hc/) 002 OHE 0) 00(i) 0.02 VI a, Aug WFIG O 0) r1a E^' k C Q Gk Sag PI Q) (0 I CO l 0I vl i UIM en I Q) < c% e MI il QOWN HZ C OI0 9!g H 4 3 a a  $ C' C   104 Ma  *0 In 0 U H <0 0) > H  correlation Hayduck, 19 matrices 87; are Joreskog being Sorbo evaluated m, 1984). (Cudeck, All 1989 models estimated here using correlation matri ces were scale free model thus assuring that estimated model has been modified and that the omnibus test statistic corresponding model correct (Cudeck, 1989). The with chapter confirmatory divided factor into analyses two sections, and other one with dealing path analyses. In both cases an additional subdivision has been made between analyses involving first order factors and analyses involving second order factors. Confirmatory Factor Analyses Snesri Maa ~ii mc    ... . . ~ *. a  U  First Order Factor Analyses Five first order factors of speed were hypothesized account variables model the matrix both described of intercorrelations young subjects Chapter Two of the speeded accordance confirmatory with factor analyses were performed each age group. The usual method which treats the observed variable as X variables, the factors as Ksi variables and determines the sca le by fixing diagonal the matrix to unity (Joreskog & Sorbom, 1984) was adopted. The loadings and the intercorrelations ;amnnnrr fa rtnr n ra nra a an4 aA Un~~~~I aI. inani Factor Analyses SCnpere Measures m~a'^ ^.^ EC) T.. ,.%. L Ir 1~ Table 53 LISREL Maximum Likelihood Estimates of Factor Unique Variances and Factor Intercorrelations Loadings, in Old Ss Factor Loadings Variable Unique Variances Symbolic Figural Choice Sternb. Sort .536 .295 .132 .333 .267 .262 .681 .839 .932 .816 .856 .859 SRT CRT1 CRT2 .652 .491 .312 MFW HFW NPR LPR .590 .713 .830 .209 .230 .268 .400 .889 .878 .856 .775 .238 .182 .326 Factor .873 .904 .821 Intercorrelations Symbolic Figural Choice Sternberg Sort Symbolic Figural Choice Sternberg Sort 1.00 .74 .46 .55 .61 1.00 .57 .56 .72 1.00 .88 .66 1.00 .68 1.00 ..  a Table 54 LISREL Maximum Likelihood Estimates of Factor Unique Variances and Factor Intercorrelations Loadings, n Young Ss Factor Loadings Variable Unique Variances Symbolic Figural Choice Sternb. Sort .728 .356 .047 .522 .803 .976 .215 .172 .396 PSC SRT CRT1 CRT2 .886 .910 .777 .710 .473 .258 .539 .726 .862 MFW HFW NPR LPR CS1 CS2 CS3 .388 .357 .316 .399 .782 .802 .827 .775 .308 .286 .218 .832 .845 .884 Factor Intercorrelations Symbolic Figural Choice Sternberg Sort Symbolic Figural Choice Sternberg Sort 1.00 1.00 1.00 1.00 constitutes acceptable fit. The loadings are general high: About of them are above each the two groups. In addition, there are substantial correlations among the five factors young group .80) and the old group (.46 .88). It is possible on the LISREL output to calculate the compound reliabilities factors (Dillon & Goldstein, 1984) and these are presented subjects Table range 55. The from reliabilities young old subj ects from .89. A comparative hypothesis factor of relatively analysis high was undertaken covariances among test factors the older group. Specifically, several nested models were compared. In the covariances, the most restricted factor loadings model the and factor unique variances variances were assumed to be equal the groups. In a second model the restriction equal unique variances was dropped. even less restricted model imposed only the same factor loadings but not equal variances and covariances. In the most relaxed factorial Model pattern only was an identical assumed without simple requiring structure equality factor loadings. The basis this comparative analysis was matrices variancescovariances the groups. Table Reliabiliti of Speed Factors in Old and Young Speed Factor ReliabilityOld ReliabilityYoung Symbolic Perc. Speed .86 .89 Figural Perc. Speed .88 .89 Choice RT .83 .76 Sternberg RT .91 .87 Card Sorting .90 .89 compared using the differences between the corresponding Chisquares as a statistic which has a Chisquare distribution with a number degrees freedom equal the difference restrictive restrictive between model model the the the Degrees degrees comparison of freedom freedom (Herting, the of the 1985) most less . As Table shows, Model which does not impose equal unique variances fits the data better than the most restrictive Model However, no further significant improvement has been achieved relaxing Model the equality condition on factorial variances and covariances. A visual inspection of the two matrices variancescovariances obtained the most relaxed model shows (Table 57) that variances and 8 covariances are higher the old subjects, a total 5 variances 10 covariances. Second Order Factor Analyses Two second order factor models have been hypothesized and tested. the most simple model (Model one second order first factor order of speed speed explains factors. the In LISRE correlations L terminology between the the second order factor a Ksi variable without indicators and the first order factors are Eta variables with multiple indicators. The scale defined the second order factor * a * i ft II i 1 A Table The Results Simultaneous in Young Confirmatory and Old Ss Factor Analyses Model Restrictions Chisq. GFI" Same Same Same Same Same Same Same Same Same factorial pattern factor loadings factor var./cov. unique variances factorial pattern factor loadings factor var./cov. factorial pattern factor loadings 347.45 281.83 271.09 .869 .887 .890 Same factorial pattern 257.19 .894 Model 2 offers a significant improvement i Model 1, Chisquare=60.62, df=16, p<.001. Goodnessoffit index for the whole model. over Table 57 Variances and Covariances of Speed Factors Young and Old Subjects Factor Symbolic Figural Choice Sternberg Sort Young Symbolic Figural Choice Sternberg Sort 45.99 34.94 3.94 5.63 1.00 1.08 Old Symbolic Figural Choice Sternberg Sort 45.33 5.20 9.94 3.27 30.44 3.22 5.05 1.48 1.91 more complex model (Model was obtained allowing some the residuals the matrix to correlate. this case correlations were allowed between the two reaction time factors and between two perceptual speed factors. All other correlations remained null. Model nested Model 2 which itself nested the five first order factors model which has been examined previous section. The evaluation of Models and the old and the young subjects presented Tables 58, 59. In both cases al resulted lowing factor large residuals t significant o correlate improvements Model the goodness of fit. the subjects the goodnessoffit index was .89 and young subjects . Root mean square residuals .043 the old and .046 the young were also acceptable as well as ratios below the Chi squares respective number degrees freedom. The difference Chisquares between Model and the first order factors model both younger older subjects not significant. Table 510 presents the factor loadings the specificities (unique variances) first order factors corresponding to Model loadings, both groups, with one exception, are above . On the other Table A Comparison of First Models Order Old Second Order Factors Subjects Model Description Chisquare (df) Diff.(df) 1 One second order factor 203.85 (99) 53.30 (2)* Null covariances in PSI 2 One second order factor 150.75 (97) 4.01 (3) Free covariances in PSI" 3 Five first order factors 146.74 (94) The mode Chisquare 1 Covariances Speed, on o RT, on the difference gnificant between ne hand, other han between , p<.001. Symbolic and betwe w and ere set this Figura Choice model and the next Perceptual RT and Sternberg free. &en d, Table59 A Comparison of First Models Order and Second in Young Subjects Order Factors Model Description Chisquare (df) Diff.(df) One Null second order covariances factor in PSI 164.49 (99) 53.26 (2)* One Free second order covariances factor in PS Ia 111.23 (97) 0.78 Five first order factors 110.45 (94) The Ch model Covari Speed, RT, on is is anc on th quare difference significant, p<. es between Symbo one hand, and b e other hand, we be 001 lic etw re twee and een set n this model Figural Choice RT free. the next Perceptual and Sternberg Table 510 Model with a Second Subjects Order Speed (Standardized Factor Old and Young Solution) First Order Factor Factor Loadings Unique Variances Old Symbolic Perc. Speed .679 .539 Figural Perc. Speed .780 .391 Choice RT .712 .494 Sternberg RT .744 .446 Card Sorting .912 .168 Chisquare=150.75 df=97 p=.000 GFI=.890 Young Symbolic Perc. Speed .584 .659 Figural Perc. Speed .775 .399 Choice RT .624 .611 Sternberg RT .645 .584 Card Sorting .976 .047 Chisquare=111.23 df=97 p=.153 GFI=.918 Table 511 A Three and Second Old Order Factors (Standardized Solution in Young Coefficients) Second Order Factor First Order Factor Unique Variances Old Symbolic Figural Choice R Perc. Speed Perc. Speed Sternberg Card Sorting .804 .924 .915 .957 1.00 .353 .146 .163 .084 .000 Young Symbolic Figural Choice R Perc. Speed Perc. Speed Sternberg Card Sorting .717 .953 .883 .913 1.00 .486 .093 .221 .167 .000 Model Model for for old: young Chi : Chi square=150. square=lll. df=97 df=97 GFId= GFId= Perceptual Reaction T Card Speed. 'ime. Sorting. Goodnessoffit index (Joreskog and Sorbom, 1984) valuable theoretical speed variable and the possibility that some important information existent first order level may be lost at a higher order. An additional model (Model with three second order factors has also been evaluated . In this model one second order factor explains the relationships between perceptual speed factors, a second factor explains the relationships between reaction time factors and a third factor identical with the first order factorCard Sorting. Model 4 cannot explain Model since has the same number degrees freedom and the same fit. was assessed only because possibility of using the three second order factors as latent variables general model. The loadings first order factors on the second order factors and the correlations between the three second order factors the two groups are presented Table 511. Both the loadings and the coefficients are high, first are above the last are the range Path Analyses Models with First Order Speed Factors The models presented Chapter were first evaluated using each one the five first order factors of speed *ha anei Vana r 1 C en ak a A 9 mI.... a St crrrnn~ C~A m A ~L3 A 1 case of older subjects the exogenous variables were age, education and subjective health. the case young subjects there was almost no variability subjective health which was therefore omitted from the analysis. For purposes of comparability the analyses older subjects were performed twice, once without subjective health and once including assessed subjective these subjects health. and Ten they models are were presented thus Tables 512, 513 and Figures 51, The , 53. five models assessed Models are young examined subjects here presented following Table order: 514. five The models without health older subjects ; five models including health older subjects and five models (without health) young subjects. All five models without health older subjects the range data reasonably from well . Two : the goodnessoffit modelswith Symbolic indices Perceptual Speed and with Sternberg Perception Speed have Chisquares relatively ratios large between and the significant Chisquares (p<.05). the However, respective the number degrees of freedom these models well as for other three models) less than indicating sati factory (Herting & Costner, 1985; see also Appendix . In only one Table 512 Standardized Path Coeffi clients Models and Old Indices of Fit Five Model Path" SpeedGf GfGc AgeSpeed AgeGf AgeGc EducSpeed EducGf EducGc Symbolic .592 .585 .111) .110) .199 .253 .319 .294 Figural .673 .585 .328 .044) .199 .260 .292 .294 Choice .558 .598 .199 .063) .201 .042 .444 .288 Sternberg .451 .596 .064) .146) .200 .098) .424 .289 Sort .584 .599 .162) .080) .200 :.160) .375 .287 Fitb Chisquare df probc GFId 63.19 .000 .916 .057 .937 81.39 58 .101 .941 61.78 47 .023 .926 .073 .938 : The coefficients Note t<2. parentheses are not significant, The first to fluid int intelligence and education paths are elligence (Gc) . The (Educ) Beta (Gf) paths and others Speed, from are from Gf Gamma speed factor to crystallized paths from age Gf and Summary Probability value given of goodness for that Goodnessoffit the C the index of fit measures rhisquare model is (Joreskog each to exceed the model. specified true. and Sorbom, 1984) Table 513 Standardized Path Coefficients Model and Old Indi ces of Fit Five Model Path' SpeedGf GfGc AgeSpeed AgeGf AgeGc EducSpeed EducGf EducGc HlthSpeed HlthGf HlthGc Symbolic .590 .603 .129) .107) .204 .226 .316 .244 .314 .026) .061) Figural .666 .604 .338 '.041) .205 .235 .291 .245 .281 .025) .062) Choice .550 .617 .212 .065 .206 (.013) .442 .247 .333 .029) .065) Sternberg .426 .613 .071) .152 .206 (.078) .416 .243 .219 .118) .064) Sort .571 .617 .172 .083) .206 (.135) .373 .284 .283 .050) .064) Fit" square 61.59 88.34 64.16 54 probc GFId .001 .918 .101 .938 .223 .944 .035 .925 .162 .941 The coefficients parentheses are not significant, t<2. The to first fluid intelligence paths are intelligence (Gc) age, education Speed, Gf and . The Beta (Gf) paths and other (Educ) from paths subjective from Gf are the speed factor to crystallized Gamma health paths (Hith) from to Summary Probability value given of goodness for that the the measures Chisquare model is each to exceed the model specified true. Goodnessof fit index (Joreskog Sorbom, 1984) 90 *9 *H (0 3 P a *4 0 cu u SC) s4 *4 0 i *r4 GOl C 4 rd. lr CO *I~ 4 H 0 0 *H1 C 3 04 0 5.4 4 * 0 C 0 Co OQ) 0U U O) (fl r o r 2 0) C 0 0 U (0 P & IP (0 a 04 lr4 4 N c H 0) T3 U <0 Lw CU 0 C. T3 o rH PC* 0 4.3 I" a. 4g^ 91 0 (4C4 ( C < 17 \ Q CJ IC C) Cl \ \ \ / Vt 0 CC / i \ / \ fs/ ** I~~, \ \/ \/ w rl I~~c \ I I 'H a) 44 /~~' '\H\ \ /I( .'/ \/ ^^\ tr O N ^ /\/^ 0 :3 w. 41 H \C 0 o 4c) 0 C 0 /*\ / \\(0 U) o \\4 14J to C 0 \ ct U) I 5) H a, 01 4 C 0~ 3 04 oP I i *rn '0j : rl C) ( U oU C/ UC ( DC N 44 Ilx 92 0'. tr .617 44  o o V sVd I \r / IC 43 C L ~ ^\ \ / 5 H '^ ^ o 0 C^ (V^/ .n1\\\ tr*r4 0 0\ X C 0H K) 0) C)] oo 1 I ^ 1 Q) U C 04r *rII U tn 0 44 o U) U a a ccit 10 I: Table 514 Standardized Path Coefficients Model and Indices of Fit Five Young Model Symbolic SpeedGf GfGc AgeSpeed AgeGf AgeGc EducSpeed EducGf EducGc .464 .626 .130) .293 .279 .341 .174 .244 Figural .570 .623 .220 .226 .277 .261 .183 .245 Choi .425 .616 .328 .212 .274 .320 .197 .247 Sternberg .462 .627 .320 .203 .277 .297 .196 .243 Sort .573 .608 .396 [.126) .272 .311 .154 .250 Fitb Chisquare 80.66 94.54 74.81 probc GFId .001 .916 .000 .913 .002 .918 .002 .915 .006 .925 The coefficients parentheses Note t<2. are not significant, The to first fluid intelligence and education Summary Probability value given Goodnessof paths are intelligence (Gc) . The (Educ) of goodness for that fit the the index Beta (Gf) paths and others from are to Speed, from Gf Gamma speed factor crystallized paths from age and measures Chisquare model (Joreskog each to exceed the model specified true. and Sorbom, 1984) Patha greater than would be expected chance alone, given that the model true. The focus the examination the models first the direct indirect paths from age to fluid intelligence as well as on the path from fluid to crystallized intelligence. Next are examined the paths from the exogenous variablesage, education (and subjective health the models including this variable) to fluid and crystallized intelligence. Symbolic Perceptual Speed: In this model age does seem to be related indirectly : The to fluid intelligence coefficient direct directly path significant the path from to Symbolic Perceptual Speed not significant. The path coefficients the path from fluid crystallized intelligence high significant. Age also related to crystallized intelligence but this case positive, significant coefficient indicates an increase crystallized intelligence with increased age. Education related to all three endogenous variablesspeed, fluid and crystallized intelligence and the corresponding standardized path coefficients are of magnitude .25 .32. Figural Perceptual Speed: A direct path from age 