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An Examination of the Spatial and Temporal Transferability of Crash Prediction Models in Florida

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Title:
An Examination of the Spatial and Temporal Transferability of Crash Prediction Models in Florida
Creator:
Haas, Phillip R
Place of Publication:
[Gainesville, Fla.]
Florida
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University of Florida
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english
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1 online resource (122 p.)

Thesis/Dissertation Information

Degree:
Doctorate ( Ph.D.)
Degree Grantor:
University of Florida
Degree Disciplines:
Civil Engineering
Civil and Coastal Engineering
Committee Chair:
SRINIVASAN,SIVARAMAKRISHNAN
Committee Co-Chair:
ELEFTERIADOU,AGELIKI
Committee Members:
WASHBURN,SCOTT STUART
YIN,YAFENG
BEJLERI,ILIR
Graduation Date:
5/2/2015

Subjects

Subjects / Keywords:
Calibration ( jstor )
Datasets ( jstor )
Divided highways ( jstor )
Modeling ( jstor )
Parametric models ( jstor )
Population density ( jstor )
Roads ( jstor )
Statistical estimation ( jstor )
Transportation ( jstor )
Two lane highways ( jstor )
Civil and Coastal Engineering -- Dissertations, Academic -- UF
accident -- crash -- safety -- transportation
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bibliography ( marcgt )
theses ( marcgt )
government publication (state, provincial, terriorial, dependent) ( marcgt )
born-digital ( sobekcm )
Electronic Thesis or Dissertation
Civil Engineering thesis, Ph.D.

Notes

Abstract:
This research examines the spatial and temporal transferability of crash prediction models on rural multilane divided highways and rural two-lane roads in Florida. Spatial transferability is investigated through calibration of the Highway Safety Manual and the development of local safety performance functions across statewide conditions and three intra-state grouping methods, Florida Department of Transportation district boundaries, population density groups, and average annual rainfall groups. Crash prediction models are developed and applied across four different temporal combinations, two cases of model estimation and application from the same time period and two cases of model estimation and application from different time periods. To assess and compare the results of each crash prediction method, the mean squared error and variance of the squared error, as well as an error regression model, are analyzed. Results of the error analysis prove that there is significant benefit in statewide calibration, but no additional improvement from calibration within intra-state groups. Locally developed safety performance functions result in improved crash prediction accuracy for population density based models on rural two-lane roads and district and population density based models on rural multilane divided highways. All crash estimation methods show an increase in prediction error at higher traffic volumes. Results of temporal transferability analysis show that there is no significant difference in crash prediction accuracy between any of the temporal estimation and application specifications. Crash estimation models estimated or calibrated based on the three years before or after the application time period were just as suitable as those based on the same application time period. ( en )
General Note:
In the series University of Florida Digital Collections.
General Note:
Includes vita.
Bibliography:
Includes bibliographical references.
Source of Description:
Description based on online resource; title from PDF title page.
Source of Description:
This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Thesis:
Thesis (Ph.D.)--University of Florida, 2015.
Local:
Adviser: SRINIVASAN,SIVARAMAKRISHNAN.
Local:
Co-adviser: ELEFTERIADOU,AGELIKI.
Statement of Responsibility:
by Phillip R Haas.

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UFRGP
Rights Management:
Copyright Haas, Phillip R. Permission granted to the University of Florida to digitize, archive and distribute this item for non-profit research and educational purposes. Any reuse of this item in excess of fair use or other copyright exemptions requires permission of the copyright holder.
Resource Identifier:
960940217 ( OCLC )
Classification:
LD1780 2015 ( lcc )

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AN EXAMINATION OF TH E SPATIAL AND TEMPORAL TRANSFERABILITY OF CRASH PREDICTION MOD ELS IN FLORIDA By PHILLIP HAAS A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE R EQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2015

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© 2015 Phillip Ryan Haas

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To my family

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4 ACKNOWLEDGMENTS I thank my parents and my wife for their endless support and encouragemen t . I thank my advisor, Dr. Siva Srinivasan for his guidance and support of my educational development. I thank my dissertation committee, Dr. Lily Elefteriadou, Dr. Scott Washburn, Dr. Yafeng Yin, and Dr. Ilir Bejleri for their input and feedback in this research. I thank Benjamin Jacobs and Tina Hatcher from the Florida Department of Transportation for their assistance in accessing roadway geometry and crash databases.

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5 TABLE OF CONTENTS page ACKNOWLEDGMENTS ................................ ................................ ................................ ............... 4 LIST OF TABLES ................................ ................................ ................................ ........................... 7 LIST OF FIGURES ................................ ................................ ................................ ......................... 9 LIST OF ABBREVIATIONS ................................ ................................ ................................ ........ 11 ABSTRACT ................................ ................................ ................................ ................................ ... 12 CHA PTER 1 INTRODUCTION ................................ ................................ ................................ .................. 14 Motivation ................................ ................................ ................................ ............................... 14 Highway Safety Manual ................................ ................................ ................................ ......... 15 2 LITERATURE REVIEW ................................ ................................ ................................ ....... 17 HSM Crash Estimation Models ................................ ................................ .............................. 17 Methods for Comparing Crash Estimation Models ................................ ................................ 19 Calibration of Crash Estimation Models ................................ ................................ ................ 20 Calibration versus Localized Model Development ................................ ................................ 24 Variables Used in Crash Estimation Modeling ................................ ................................ ...... 27 Summary and Conclusions ................................ ................................ ................................ ..... 31 3 DATA ................................ ................................ ................................ ................................ ..... 32 Data Sources ................................ ................................ ................................ ........................... 32 Data Assembly ................................ ................................ ................................ ........................ 35 Data Descriptives ................................ ................................ ................................ .................... 37 4 TRANSFERABILITY USING CALIBRATION FACTORS ................................ ................ 44 Analysis Framework ................................ ................................ ................................ ............... 44 HSM Calibration Methodology ................................ ................................ .............................. 47 Analysis of Rural Multilane Divided Highways ................................ ................................ .... 49 Calibration Results for Rural Multilane Divided Highways ................................ ........... 49 Validation and Comparison Analysis for Rural Multilane Highways ............................. 50 Analysis of Rural Two Lane Roads ................................ ................................ ....................... 52 Calibration Results ................................ ................................ ................................ .......... 52 Validation and Comparison Analysis for Rural Two Lane Roads ................................ .. 53 Summary and Conclusions of Calibration Transferability ................................ ..................... 55

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6 5 TRANSFERABILITY USING LOCAL SAFETY PERFORMANCE FUNCTIONS .......... 66 Analysis Framework ................................ ................................ ................................ ............... 67 Analysis o f Rural Multilane Divided Highways ................................ ................................ .... 69 Locally Derived SPFs ................................ ................................ ................................ ...... 69 Model Validation and Comparison Analysis ................................ ................................ .. 69 Analysis of Rural Two Lane Roads ................................ ................................ ....................... 71 Locally Derived SPFs ................................ ................................ ................................ ...... 71 Model Validation and Comparison Analysis ................................ ................................ .. 71 Summary and Conclusions of Local SPF Development ................................ ......................... 73 6 TRANSFERABILITY THROUGH VARYING MODEL FORM ................................ ........ 85 Analysis Framework ................................ ................................ ................................ ............... 85 Analysis of Rural Multilane Divided Highways ................................ ................................ .... 87 Model Estimation ................................ ................................ ................................ ............ 87 Model Validation and Comparison Analysis ................................ ................................ .. 89 Analysis of Rural Two Lane Roads ................................ ................................ ....................... 90 Model E stimation ................................ ................................ ................................ ............ 90 Model Validation and Comparison Analysis ................................ ................................ .. 91 Summary and Conclusions of Varying Model Form ................................ .............................. 92 7 SUMMARY AND CONCLUSIONS ................................ ................................ ................... 107 Summary of Research ................................ ................................ ................................ ........... 107 Data Summary ................................ ................................ ................................ ............... 107 HSM Calibration Summary ................................ ................................ ........................... 108 SPF Development Summary ................................ ................................ ......................... 109 Conclusions and Future Expansion ................................ ................................ ...................... 111 APPENDIX COUNTY CALIBRATION GROUPS ................................ ................................ 114 LIST OF REFERENCES ................................ ................................ ................................ ............. 116 BIOGRAPHICAL SKETCH ................................ ................................ ................................ ....... 122

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7 LIST OF TABLES Table page 3 1 Data collected from the RCI ................................ ................................ .............................. 39 3 2 Segment length and cra sh data for rural two lane roads ................................ .................... 39 3 3 Roadway characteristics for rural two lane two way roads ................................ ............... 40 3 4 Segment length and crash data for rural multilane divided highways ............................... 40 3 5 Roadway characteristics for rural multilane divided highways ................................ ......... 40 4 1 HSM SPF regression par ameters for fatal and injury crashes ................................ ........... 57 4 2 HSM CMFs for rural multilane highways ................................ ................................ ......... 57 4 3 HSM CMFs for rural two lane roads ................................ ................................ ................. 57 4 4 Statewide and localized calibration factors for rural multilane highways ......................... 58 4 5 Rural multilane highways MSE and variance of SE by crash e stimation method ............. 58 4 6 Rural multilane highways MSE by calibration method and AADT range ........................ 59 4 7 MSE error regression by crash estimat ion method for rural multilane divided highways ................................ ................................ ................................ ............................ 59 4 8 Statewide and localized calibration factors for rural two lane roads ................................ . 60 4 9 Rur al two lane roads MSE and variance of SE by crash estimation method .................... 61 4 1 0 Rural two lane roads MSE by calibration method and AADT range ................................ 61 4 11 MSE error regression by crash estimation method for rural two lane roads ..................... 62 5 1 AADT distribution by analysis group for rural multilane highways ................................ . 75 5 2 AADT distribution by analysis group for rural two lane roads ................................ ......... 76 5 3 Rural multilane divided highway SPFs ................................ ................................ .............. 77 5 4 Rural multilane divided highways MSE and variance of SE by SPF ................................ 78 5 5 Rural multilane highways MSE by SPF and AADT range ................................ ................ 78 5 6 MSE regression by SPF for rural multilane divided highways ................................ .......... 79

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8 5 7 Rural two lane roads SPFs ................................ ................................ ................................ . 79 5 8 Rural two lane road MSE and varia nce of SE by SPF ................................ ...................... 80 5 9 Rural two lane road MSE and variance of SE by SPF and AADT range .......................... 80 5 1 0 MSE regression by SPF for rural two l ane roads ................................ .............................. 81 6 1 Rural multilane divided highway AADT bins ................................ ................................ ... 94 6 2 Rural two lane road AADT bins ................................ ................................ ........................ 94 6 3 Rural multilane divided highway two parameter and three parameter SPFs .................... 95 6 4 Rural multilane divided highway binned AADT model ................................ .................... 95 6 5 Rural multilane divided highway low and high AADT grouped model ............................ 95 6 6 Bordering intersection distributions ................................ ................................ ................... 96 6 7 Rural multilane divided highway 2005 2007 intersection grouped models ...................... 96 6 8 Rural multilane divided highway 2008 2010 intersection grouped models ...................... 96 6 9 Rural multilane divided highways MSE and variance of SE by crash estimation method ................................ ................................ ................................ ................................ 97 6 10 Rural multilane divided highway MSE regression ................................ ............................ 97 6 11 Rural two lane road two parameter and three parameter SPFs ................................ ......... 98 6 12 Rural two lane roads binned AADT model ................................ ................................ ....... 98 6 13 Rural two lane road low and high AADT grouped model ................................ ................ 98 6 14 Rural two lane roads 2005 2007 intersection grouped models ................................ ......... 99 6 15 Rural two lane roads 2008 2010 intersection grouped models ................................ ......... 99 6 16 Rural two lane MSE and variance of SE by crash estimation method .............................. 99 6 17 Rural two lane roads MSE regression ................................ ................................ ............. 100 A 1 List of county calibration groups ................................ ................................ ..................... 114

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9 LIST OF FIGURES Figure page 3 1 FDOT district boundaries (FDOT 2013). ................................ ................................ .......... 41 3 2 Population density group creation. ................................ ................................ .................... 41 3 3 Map of population density groups. ................................ ................................ .................... 42 3 4 Florida average annual rainfall (Weisburg and Daly 1997). ................................ .............. 42 3 5 Creation of homogeneous seg ments (Srinivasan et al. 2011). ................................ ........... 43 4 1 Rural multilane divided highway calibration by FDOT district. ................................ ....... 63 4 2 Rural multilane divided hi ghway calibration by county population density. .................... 63 4 3 Rural multilane divided highway calibration by average annual rainfall. ......................... 64 4 4 Rural two lane road calibration by FDOT district. ................................ ............................ 64 4 5 Rural two lane road calibration by county population density. ................................ ......... 65 4 6 Rural tw o lane road calibration by average annual rainfall. ................................ .............. 65 5 1 Rural multilane highway 2005 2007 SPFs by district. ................................ ...................... 82 5 2 Rural multilane highway 2005 2007 SPFs by population density group. ......................... 82 5 3 Rural multilane highway 2005 2007 SPFs by average annual rainfall group. .................. 83 5 4 Rural two lane road 2005 2007 SPFs by district. ................................ .............................. 83 5 5 Rural two lane road 2005 2007 SPFs by population density group. ................................ . 84 5 6 Rur al two lane road 2005 2007 SPFs by average annual rainfall group. .......................... 84 6 1 Rural multilane divided highway 2005 2007 binned AADT comparison. ...................... 101 6 2 Rural multilane divided highway 2008 2010 binned AADT comparison. ...................... 101 6 3 Rural multilane divided highway 2005 2007 low and high AADT grouped model. ...... 102 6 4 Rural multilane divided highway 2008 2010 low and high AADT grouped model. ...... 102 6 5 Rural multilane divided highway 2005 2007 intersection grouped model. ..................... 103 6 6 Rural multilane divided iighway 2008 2010 intersection grouped model. ...................... 103

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10 6 7 Rural two lane road 2005 2007 binned AADT comparison. ................................ ........... 104 6 8 Rural two lane road 2008 2010 binned AADT comparison. ................................ ........... 104 6 9 Rural two lane road 2005 2007 low and high AADT grouped model. ........................... 105 6 10 Rural two lane road 2008 2010 low and high AADT grouped model. ........................... 105 6 11 Rural two lane roads 2005 2007 intersection grouped mode l. ................................ ........ 106 6 12 Rural two lane roads 2008 2010 intersection grouped model. ................................ ........ 106

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11 LIST OF ABBREVIATIONS AADT Annual Average Daily Traffic AASHTO American Association of State Highway and Transportation Officials BIC Bayesian Information Criterion CARS Crash Analysis Reporting System CMF Crash Modification Factor FDOT Florida Department of Transportation FHWA Federal Highway Administration HSM Highway Safety Manua l IHSDM Interactive Highway Safety Design Module MSE Mean Squared Error RCI Roadway Characteristic Inventory SE Squared Error SPF Safety Performance Function VPD Vehicles per Day

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12 Abstract of Dissertation Presented to the Graduate School of the Uni versity of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy AN EXAMINATION OF TH E SPATIAL AND TEMPORAL TRANSFERABILITY OF CRASH PREDICTION MOD ELS IN FLORIDA By Phillip Haas May 2015 Chair: Siva Sri nivasan Major: Civil Engineering This research examines the spatial and temporal transferability of crash prediction models on rural multilane divided highways and rural two lane roads in Florida. Spatial transferability is investigated through calibrati on of the Highway Safety Manual and the development of local safety performance functions across statewide conditions and three intra state grouping methods, Florida Department of Transportation district boundaries, population density groups, and average a nnual rainfall groups. Crash prediction models are developed and applied across four different temporal combinations, two cases of model estimation and application from the same time period and two cases of model estimation and application from different time periods . To assess and compare the results of each crash prediction method, the mean squared error and variance of the squared error, as well as an error regression model, are analyzed . Results of the error analysis prove that there is significant benefit in statewide calibration, but no additional improvement from calibration within intra state groups. Locally developed safety performance functions result in improved crash prediction accuracy for population density based models on rural two lane r oads and district and population density based models on rural multilane divided highways. Further crash estimation improvements are evident using locally derived models with alternate functional forms; however, this result is only seen for rural

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13 multilan e divided highways. All crash estimation methods show an increase in prediction error at higher traffic volumes . Results of temporal transferability analysis show that there is no significant difference in crash prediction accuracy between any of the te mporal estimation and application specifications. Crash estimation models estimated or calibrated based on the three years before or after the application time period were just as suitable as those based on the same application time period.

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14 CHAPTER 1 INT RODUCTION Motivation In recent years, improving roadway safety has been a primary goal for many state and federal agencies. This can be seen through the national effort created by the Federal Highway Administration (FHWA) entitled Toward Zero Deaths: A De cade of Action for Road Safety . Under this program, the goal is to develop a national strategic highway safety plan based on the premise that even one traffic related fatal ity is unacceptable (FHWA 2012). In moving towards this goal several safety relate d tools have recently been released for implementation. These include crash prediction method software packages such as SafetyAnalyst and the first edition of the Highway Safety Manual (HSM) , recently published by the American Association of State Highway and Transportation Officials (2010) . Along with the HSM, a software tool has been developed through FHWA for the implementation of the HSM by state departments of transportation, the Interactive Highway Safety Design Module (IHSDM). Due to the release o f the IHSDM, many states are making efforts to implement the methods recommended in the HSM. As states seek to improve their roadway safety, they must address important questions regarding the transferability of crash prediction models and how to assess t he performance and accuracy of these models. The efforts of this research are both beneficial to state agencies and engineers in their efforts to apply crash prediction models to ultimately reduce crashes and valuable in presenting original contributions t o the field of safety analysis. These contributions to the field of safety analysis focus on both methods of improving the transferability of crash prediction methods and the development of systematic processes to assess the transferability of crash predi ction models. The evaluation of existing means of transferring crash prediction models, the development of

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15 improved transferability methods, and the construction of new, locally specifi c, crash prediction models are addressed through this research effort. This dissertation includes an introduction to the HSM, a description of previous related research, a description of the data collection and assembly procedures, analysis of spatial and temporal transferability of calibration factors, analysis of spatial and temporal transferability of locally developed crash estimation models, and a summary of the conclusions and work completed . Highway Safety Manual The HSM has become the current standard for crash estimation modeling in practice today. It has been wid ely adopted due to its ease of use through its simplification of otherwise complex procedures in both Part C, regarding crash prediction methods, and Part D , regarding the use of crash modification factors (CMF s ). Part C of the HSM provides guida nce for crash prediction on three broad facility categories: (1) rural two lane two way roads, (2) rural multilane highways, and (3) urban and suburban arterials (AASHTO 2010). For each facility type within Part C, the HSM provides a safety performance function ( SPF) which relates the AADT of a given segment to the expected crash frequency. This SPF is then multiplied by multiple CMFs to account for differences in roadway characteristics, such as lane width and shoulder width, between segments for which the model was developed and the specific segments where the model is being applied. The SPF is also multiplied by a calibration factor in order to account for various spatial and temporal differences between when and where the model was developed to its local appl ication. These differences include driver population, crash reporting thresholds, animal populations, weather patterns, and geogra phical variations. In addition to providing a method for calculating a calibration factor, simply dividing the observed cras hes by the predicted crashes, the HSM notes

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16 that states may want to explore the development of their own SPF to bett er fit their local conditions (AASHTO 2010). While a calibration factor provides a linear modification to force the total predicted crashes towards the total observed crashes, it does not address the potential for differing relationships between annual average daily traffic (AADT) and crash frequency. In order to address the possibility that the implementation area has a different relationsh ip between crashes frequency and AADT than that of the model development location, new model parameters for the SPF must be estimated. In comparison to calibration, which according the HSM required a minimum of 30 segments with at least 100 crashes, the d evelopment of a new SPF requires significantly more data . As states are left with the difficult decision of whether to calibrate the HSM or invest the time and effort to develop a new SPF, there is not currently a great deal of information to aid their dec ision making process. State agencies are faced with the dilemma of how to evaluate or compare a given model for implementation , and they are also often unaware of alternatives beyond the provided HSM statewide calibration that may offer improved predictio n accuracy without significant additional effort.

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17 CHAPTER 2 LITERATURE REVIEW This section provides a review of p revious work completed on the development of crash estimation models. This provides a background from which to develop safety performance fun ctions for Florida roadway segments and investigate the differences between calibration and model estimation. Discussions of roadway variables, model forms, and complications identified through previous research efforts are included in this chapter . HSM C rash Estimation Models Numerous research efforts have been completed to develop safety performance functions or crash estimation models on a variety of facility types. These models can take a variety of functional forms and range from containing only AADT as the independent variable to utilizing numerous geometric and environmental highway characteristics to estimate crashes. While there are many differences amongst crash models due to varying data sources, methodologies, and assumptions, there are select elements which have remained consistent across past research efforts. These consistent aspects include the use of AADT as the primary measure for exposure, the separation of crash prediction based on area (rural or urban) and number of lanes, and a commo n output varia ble of the crash model (AASHTO 2010) . The common output variable used for safety evaluation purposes is expected crash frequency, which can be for total crashes or separated by crash severity and crash type. Crash frequency is modeled rathe r than crash rate in order to allow the relationship between crash frequency and traffic volume to be nonlinear (Harwood et al. 2007) . The current state of practice in developing crash estimation models includes regression modeling using the assumption of a negative binomial error distribution of crash frequencies (AASHTO 2010) . Negative binomial regression is used rather than a Poisson regression in order

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18 to account for the overdispersion of estimated crash frequency (AASHTO 2010) . These negative binomia l regression models take two general forms: either with the model only including length and AADT and utilizing crash modification factors (CMF) to account for different roadway characteristics, as seen in Equation 2 1 , or with the regression process incorp orating the variation of these roadway characteristics in the development of the model, as seen in Equation 2 2 (Harwood et al. 2007) . ( 2 1 ) Where: N = predicted crash frequency per year for a specified segment ADT = average dail y traffic volume (veh/hr) for the segment L = length (mi) of the segment b 0 b n = regression coefficients X 1 X n = segment characteristics (2 2 ) Where: N = predicted crash frequency per year for a specified segment ADT = aver age daily traffic volume (veh/hr) for the segment L = length (mi) of the segment b 0 and b 1 = regression coefficients CMF 1 CMF n = crash modification factors based on segment characteristics Segment length is a variable common to all crash models; howeve r, in the past it has been included through two different methods. Some researchers, including Harwood et al. (2007), Tegge et al. (2010), Garber et al. (2010), and Lord et al. (2008), have incorporat ed length as a

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19 scalar, with a coefficient of 1.0 , so th at the estimated crashes are proportional to the site length. Alternatively, Hadi et al. (1995), Strathman et al. (2001), Persaud et al. (2003), and Saito et al. (2011) each developed crash models estimating a coefficient for segment length not equal to 1 .0. In the application of such a model, the estimated crashes for a segment of a given length would not equal the sum of the estimated crashes of the same segment split into two parts. However, this application does allow for the model to account for the situation in which the data suggests that shorter segments experience a higher crash frequency than similar longer segments. Currently all safety performance functions in the HSM assume a fixed coefficient of 1 on segment length. Methods for Comparing Crash Estimation Models Prior to the discussion of alternate approaches for transferring the HSM models to local conditions (via methods such as calibration and local estimations), it is useful to discuss metrics used for comparing alternate model specific ations. In both developing a new crash estimation model and applying an existing model to a new data set, it is important to evaluate the goodness of fit of multiple models. Each of these two scenarios involve a model comparison, whether it is through th e course of variable and structure selection for a new model or model selection and calibration method for the transfer of an existing model. There are many possible methods that have been suggested for use in order to assess the goodness of fit of a give n model. The first step for model comparison is to identify a distinct data set for validation. This common practice is evident in many different types of research efforts, including state department of transportation recommendations (Hamidi et al. 2010), local model development (Lu 2013), and HSM model development (Harwood et al. 2000) and (Vogt and Bared 1998). However, in the case of model calibration, several past studies have not used a separate data set

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20 for validation (Xie et al. 2011, Koorey 2011, and Saito et al. 2011). In these studies, validation of the crash prediction methods were either performed on the same data set that was used for calibration or not performed at all. When a validation data set is used, there are three data identificatio n techniques that previous studies have used. The first is to set aside for validation a random sample of the total available roadways (Hamidi et al. 2010, Lu 2013, and Banihashemi 2011). The second method is to use the same roadway facilities as used fo r model development or calibration, but to use future years of available data (Vogt and Bared 1998). Finally, some studies have used a data set from a different state for validation purposes (Harwood et al. 2000 and Vogt and Bared 1998). A variety of va lidation and model comparison metrics have been used in previous crash estimation studies. The most commonly used metrics include the Pearson Correlation Coefficient (r), Mean Prediction Bias (MPB), Mean Absolute Deviation (MAD), Mean Square Error (MSE), paired t test, percent difference between observed and predicted crashes, average of the absolute percent differences between observed and predicted crashes, and visual methods, such as scatter plots and Cumulative Residual (CURE) plots. As evident by the wide variety of validation metrics that have been previously used in model comparison, there is no well established best practice for selecting validation metrics, and the results of the model comparison will often differ based on the metric selected (Lub liner and Schrock 2012). Calibration of Crash Estimation Models Several states have completed studies to calibrate the crash estimation models in the HSM to their local conditions. These studies have identified several challenges and areas for future impr ovement in calibration implementation and assessment. Calibration efforts for all facility types included in the HSM in the state of Oregon were carried out by Xie et al. (2011). In this study, the authors used the HSM recommend sample size

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21 of 30 50 segme nts with a total of at least 100 crashes. This research resulted in three one year calibration factors and one three year calibration factor for each facility type; however, no validation or impact analysis was performed using these calibration factors. The authors also examined the impact of using state specific crash type distributions for rural two lane roads. The resulting calibration factors with state specific crash distributions did not significantly differ from the calibration factors calculated using the HSM default crash distributions. Based on their efforts the authors recommended improvement in the calibration methods through severity based calibration. Additionally, further investigation was advised into locally derived SPFs and the potenti al for variations in SPF functional form. A calibration project in Louisiana for rural multilane highways found a wide variation in yearly calibration factors, ranging from 1.07 to 1.41 in the five years used in the study. While the authors did not examin e any system wide validation or comparison of the calibrated model, they found that in the network screening process, the calibrated HSM models produced a similar list of top ten sites for improvement as a less sophisticated crash frequency method. The bi ggest challenge in calibration was identified as data collection and processing (Sun et al. 2011). The authors of a study in North Carolina examined HSM calibration specifically on curved segments of rural two lane highways (Zegeer et al. 2012). Their res earch showed that the AADT, curve radius, and curve length of each segment were required for accurate calibration, but assumed values may be used for other HSM segment inputs without a great decrease in the accuracy of the predicted crash value. In valida ting the calculated calibration factor of 1.33, a paired t test showed that the difference between the actual and HSM predicted crashes was not significant, resulting in a recommendation that assuming a calibration factor of 1.0 might be reasonable.

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22 Lublin er and Schrock (2012) examined calibration of the HSM for rural two lane highways in Kansas, including alternatives to the linear calibration factor in the HSM. The authors used 190 miles of highway for calibration out of the roughly 8,600 miles of two la ne rural highway in Kansas. Uncalibrated HSM models were compared to statewide calibrated models and two methods of alternative calibration that accounted for the frequency of animal related crashes within a given county or segment. Models were compared using a variety of goodness of test, percent difference of crashes, and average absolute percent difference of crashes. Different calibration methods showed better results acros s the differing comparison metrics. Ultimately, the authors concluded that a single statewide calibration factor provided the best results for aggregate system wide analysis, while the calibration method accounting for county animal crash frequency provid ed the best results for project level analysis. Research conducted by Trieu et al. (2014) examined calibration with respect to the necessary sample size. They found that the recommendations provided by the HSM could be improved upon by increasing the numb er of segments used for calibration, from 10% of the population to 30%. They also recommend against using a minimum threshold value for number of crashes in the sample set, as this may introduce bias. Research efforts to calibrate crash prediction models have also taken place internationally, including those by Koorey (2011) in New Zealand. This study calculated calibration factors on multiple levels: nationwide, by terrain type, by AADT category, and by region. Validation of the calibration factors was attempted on three highways with differing characteristics; however, the impact and accuracy of the calibration factors was difficult to determine due to the small sample size for validation. The author also reports that crash

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23 prediction for fatal and inj ury crashes was more accurate than for non injury crashes, and he suggests that the greater accuracy for fatal and injury crashes is more socially and economically important due to the severity of these crashes. Research conducted by La Torre et al. (2014) on the calibration of crash estimation models for freeways in Italy found that the models were transferable to the Italian road network. They noted some bias in the calibration factors, particularly with the tendency to underestimate crashes in locations of high crash frequency. A potential solution recommended for this issue was the specialization of calibration factors, including calibration for different CMFs. International HSM calibration was also examined in Italy and Canada by Sacchi et al. (2012). Calculated calibration factors for fatal and injury crashes on rural two lane roads were found to be significantly less than 1.0, 0.44 in Italy and 0.74 in Ontario, Canada. In order to assess the goodness of fit of these models to their respective locat ions, the mean absolute deviation, cumulative residual plots, and recalibrated dispersion parameters were calculated. Results of a higher mean absolute deviation and higher recalibrated dispersion parameter in Italy than in Canada, lead the authors to sug gest a poorer model fit in Italy, which also is consistent with the relative size of the calibration factor itself. The cumulative residual plots were only constructed for the Italy sample and showed an acceptable fit with regards to AADT, but poor fits w ith respect to degree of curvature, driveway density, and grade, suggesting that the influence of these variables may not be transferable from the HSM models to Italy conditions. Ultimately, the authors recommend that HSM implementation efforts in Italy s hould be directed towards local SPF and CMF calculation.

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24 Calibration versus Localized Model Development There have been a small number of recent studies that have attempted to examine if it is preferable for a local or state agency to calibrate existing cr ash estimation models or develop new models for their specific region. In Kansas, Bornheimer et al. (2012) built upon the previously discussed Kansas HSM calibration project to develop local SPFs for rural two lane highways. The authors used 29 segments to develop SPFs and 9 segments for validation. An alternative definition of rural highways was used, as it was determined that sections within small towns had very different characteristics than sections outside of any towns. Models examined included st ructures similar to those in the HSM, although roadside hazard rating was included in the model. A model variation which included a coefficient on the length variable was also considered. The model coefficient, t test, MPB, and MAD. Validation results did not show any clearly preferred model, with different models performing strongly across each metric. Two models were identified to work best for Kansas, HSM calibration based on county animal crash rate and a Kansas specific SPF that only considered crashes without animals. Brimley et al. (2012) carried out a research project in order to compare the calibration of HSM models to four different locally developed SPFs for rural two lane roads in Utah. The four local SPFs included two with a linear AADT relationship and two with a natural log transformation used on AADT. Within each of these model types, models with a variable selection confidence level of 75 percent and 95 percent were each developed. Across all four SPFs, AADT, segment length, speed limit, and truck percentage were found to be significant. The Bayesian information criterion (BIC) was the sole criterion used to compare the four local SPFs and the HSM calibration. The local SPF devel oped at a 95 percent confidence level had

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25 the lowest BIC, primarily due to the fact that it had the fewest number of variables, and it was recommended for use in Utah. Banihashemi (2011) compared the crash prediction accuracy of locally developed SPFs and HSM calibration for rural two lane highways in Washington. Using half of the data set for model development and half for validation, the author calculated a statewide calibration factor of 1.501. For the locally developed SPF, locally derived CMFs were a lso included as part of the crash prediction method. In order to compare the new models to the HSM model, segments were aggregated under three scenarios. The first option was to consider each data point as an individual entity (no aggregation), the secon d was to aggregate all sites into sections of at least 10 miles, and the third was to aggregate based on the geometric and traffic characteristics of the MSE. Result s showed very little difference between the new models and the calibrated HSM model; therefore, the author recommended the use of the calibrated HSM model for Utah. However, he also did specify that locally developed SPFs should be revisited if improved d ata on geometric characteristics became available. In Alabama, research performed by Mehta and Lou (2013) examines HSM calibration, calibration by negative binomial regression, as well as several state specific SPFs with varying functional forms for rural two lane and rural multilane segments. The model with the best fit was found to be a state developed model that included lane width, speed limit, and year as variables. Further research was recommended to understand the resulting model, as the derived co efficients showed some counterintuitive results and parameters that switched signs between models.

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26 Research performed by Kweon et al. (2014) compared calibrati on and locally developed models in Virginia. This study also analyzed intra state geographic inf luences by testing district based SPFs and calibration. They recommended using state specific SPFs because they were different from the default HSM SPFs. They also found significant variation within the state to recommend district based calibration facto rs. While not addressing calibration, research conducted by Kim et al. (2013) examined grouping within the data sample to develop models for groups with similar characteristics. It was found that sites with similar AADT and geometric characteristics share d similar relationships between AADT and crash frequency. The models that allowed for the categorical impacts of AADT, and also other grouped characteristics, performed with better accuracy than base models. Also not addressing calibration, research by L u et al. (2013) compared locally developed two parameter SPFs with multivariate SPFs. Models were estimated for four lane freeways and compared using the mean absolute deviance and mean square error, as well as comparisons of the variation for high ranked locations. Results showed the two prediction methods performed very similarly for both crash prediction and network screening. Each of the three comparisons for calibration vs. locally developed models discussed in this section have come to different re sults. In the three research efforts, one recommends local model development, one suggests that HSM calibration provides sufficient results, and one selects a combination of calibration and new model development. The three studies also showed that consis tent comparison metrics are not applied, perhaps leading to the variation in results. Additionally, when multiple validation metrics are used, they often provide inconsistent results across the models being analyzed.

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27 Variables Used in Crash Estimation Mod eling While the overall regression method employed for the development of crash estimation models is similar across many studies, the estimated models are often contradicting with respect to specific variables. Many studies have examined the connection bet ween lane width safety; however these studies have not come to consistent conclusions, especially when analyzing urban roadways. Lane width has the potential to impact safety through multiple relationships. Wide lanes serve to both separate vehicles to r educe sideswipe crashes and to provide room for drivers to perform crash avoidance maneuvers (Harwood et al. 2007) . However, wide lanes may also foster a false sense of security amongst drivers and encourage higher speeds, potentially increasing the possi bility of severe crashes (Harwood et al. 2007) . The affect of lane width on rural roads has been well documented through several previous research efforts. Work by Harwood et al. (2000) analyzing the factors affecting the safety performance of rural two l ane roads found that crash frequency increased with lane widths narrower than twelve feet. This conclusion confirms the findings of Griffin and Mak (1987) and Zegeer et al. (1988), as well as many others. These results can found implemented in the Intera ctive Highway Safety Design Module (IHSDM) and the Highway Safety Manual (HSM). One of the most comprehensive studies on the factors affecting crashes on rural multilane highways, performed by Lord et al. (2008), found mostly consistent results that crash frequency decreased with increasing lane width on undivided highways. This relationship was the case for three out of the four state specific regression models that were estimated. Alternatively, the same study found that there was no relationship betwe en lane width and crash frequency on rural multilane divided roads. Despite this result, CMFs showing an increase of crashes for narrow lane widths on both divided and undivided segments were recommended for implementation in

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28 the HSM. These CMFs were ada pted from the previous efforts of Harwood et al. (2003) and Harkey et al. (2008). There have been very few research studies examining the effects of lane width on highways in urban areas, presenting varying results across the different projects. Hauer et al. (2004) developed regression models to estimate crash frequency by severity and by crash location, either occurring on the road or off the road. Lane width did not have any impact on crash frequency for crashes of any severity level occurring off the r oad. In the model for on the road property damage only (PDO) crashes, wider lane widths were very weakly related to higher crash frequencies. In examining the impacts of design attributes on crashes in Oregon, Strathman et al. (2001) found that the aver age segment lane width was not related to crash frequency for non freeway urban roads. Shankar et al. (1997) developed regression models to predict crashes on principal arterials in Washington, finding that lane widths less than 3.46 meters were related to a higher crash frequency. Hadi et al. (1995) used negative binomial regression models in order to estimate the safety effects of cross section design on a variety of highway types in Florida. For both two lane urban roads and four lane undivided urban ro ads, wider lanes were related to a decrease in crashes, up to widths of twelve feet and thirteen feet, respectively. This relationship was strongest for the urban four lane undivided roads and was found for both total crashes and midblock crashes, as well as for both injury crashes and total crashes. Using the dataset that was collected in order to develop the regression models for use in the urban and suburban arterial chapter of the HSM, Potts et al. (2007) examined the relationship

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29 between lane width an d crashes. In this study, lane width was treated as a categorical variable, presenting a method not generally used in previous studies. Overall, there was no consistent significant relationship between lane width and crash frequency. However, crash freq uency was found to increase on urban four lane undivided arterials and urban four lane divided arterials with lane widths of ten feet or less and nine feet or less, respectively. As no consistent relationship was found between lane width and crash frequen cy, it was not included as a CMF in the urban and suburban arterial chapter of the HSM (AASHTO 2010) . Shoulder width as a factor impacting roadway safety is similar to lane width in that it has been studied extensively on rural segments, yielding consisten t results; however, the affect of shoulder width in urban areas remains uncertain. Studies focusing on rural areas, across both low volume roads (Zegeer et al. , 1981) and high volume roads (Zegeer et al. 1988), have shown that narrower shoulder widths inc rease crash frequency. These results were further confirmed by expert panels recommending CMFs for rural two lane roads (Harwood et al. 2000) and rural multilane highways (Harwood et al. 2003). Among the studies that have examined the potential relationsh ip between shoulder width and crashes in urban areas, consistent results have not been found. Hadi et al. (1995) found that wider shoulder widths reduced crashes, especially on urban freeways and two lane urban highways. Harwood (1986) found similar resu lts on multilane suburban highways. His findings showed that the safety benefit of providing full shoulders as opposed to curb and gutter treatment was a reduction in crash rate of ten percent. Through the development of regression models to estimate cras h frequency on urban four lane undivided roads by severity and by crash location, either occurring on the road or off the road, Hauer et al. (2004) found that increasing shoulder width was related to an increase of

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30 crashes; however, the presence of a shou lder rather than curb and gutter lead to a decrease in crashes. Total crashes, injury crashes, and PDO crashes all were found to increase with wider shoulders in the case of off the road crashes. For on the road crashes, wider shoulder widths were relate d to an increase in injury crashes, but did not have a clear relationship to PDO crashes. Hauer concluded that the relationship between both shoulder type and shoulder width was of minor importance for urban multilane roads. A similar conclusion was reac hed by Stratham et al. (2001), finding that the relationship between shoulder width and crash frequency was not significant. Finally, these conclusions are reflected in the HSM, as there is not a CMF for shoulder width for crashes on urban and suburban ar terials (AASHTO 2010) . There are several other roadway characteristics that have been found to be useful in crash estimation models. These attributes include access density (Levinson and Gluck 2000), speed (Mayora and Rubio 2003 and Harwood et al. 2007), surface quality (Persaud 1994), roadside hazard rating (Harwood et al. 2007 and Harwood et al. 2000), truck percentage (Saito 2011 and Hauer et al. 2004), parking (Harwood et al. 2007 and Greibe 200 3 ), median width (Harwood et al. 2007 and Bowman et al. 19 95), horizontal curvature (Strathman et al. 2001 and Milton and Mannering 1996), grade (Strathman et al. 2001 and Milton and Mannering 1996), land use (Bonneson and McCoy 1997 and Greibe 200 3 ), and AADT categorization (Koorey 201 1 ). The potential effects of these variables on crash estimation are well documented in the cited studies as well as in other research efforts. While each of these roadway characteristics is not represented in every crash estimation study, there have not been multiple studies resu lting in conflicting variable influences. While there may be many roadway characteristics that impact the prediction of crash frequency, it is not ideal to use as many variables as possible. The use of too many variables can

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31 result in overfitting the expe cted crashes to the data as well as the use of variables that may be correlated with each other (Saito et al. 2011). Summary and Conclusions Overall, there have been numerous studies in the field of crash prediction modeling; however, as the implementat ion of crash modeling continues to become more popular, questions continue to arise. Many of these questions focus around the spatial and temporal transferability of crash prediction models. It is important to understand if and how a model developed in o ne location can be accurately applied to another location; also, if a state has the capability, are they better served to develop their own specific SPF or implement some form of model calibration. In order to address these issues, it is essential to esta blish a consistent method to compare or evaluate crash prediction models. Finally, the temporal transferability of crash estimations must also be addressed in order to examine the recommended frequency for model updates.

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32 CHAPTER 3 DATA This chapter des cribes the data sources, the steps taken to prepare the data for analysis, and the selection of facility types to be used in analysis. The data described in this chapter is used for the analysis performed in Chapter 4 and Chapter 5. Data Sources In both t he development of new crash estimation models and the calibration of existing models, there are three broad categories of data that are required: (1) roadway attribute data, (2) historical crash data, and (3) segment location data. These data are required for both of the two facility types that were selected for analysis, rural multilane divided highways and rural two lane two way roads. These two facility types have sufficient data available for analysis and have also been identified by FDOT as emphasis facility types for the implementation of crash prediction methods (Srinivasan et al. 2011). Roadway attribute data were collected through the Florida Roadway Characteristics Inventory (RCI), which is maintained by the Florida Department of Transportation ( FDOT). The RCI contains a wide variety of roadway data for all roads that are maintained by FDOT. End of year archived copies of the RCI were obtained for the years 2005 through 2010. These archived copies include the roadway characteristics as of Decem ber 31st each year. As the RCI includes roadway segments that are no longer in use, as well as segments that are not part of the state s qualification was made because inactive and non SHS roadways do not have complete crash and geometric data that is necessary for analysis. Roughly 10% of the total number of roadway segments in the RCI qualify as active on the SHS, while roughly 80% of the segments are active, but not on the SHS.

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33 Historical crash data for Florida were extracted from the Crash Analysis Reporting System (CARS), which is also maintained by FDOT, for the 2005 through 2010 study period. The resulting crash related data set s extracted from CARS were classified in three levels: (1) crash level files, (2) vehicle level files, and (3) occupant level files. While most of the relevant data required for crash prediction modeling, such as location and overall severity level, were extracted from the crash level files, data from the vehicle level files were also used, primarily in identifying the crash type and for consistency checks. In order to examine the spatial transferability of crash estimation models, different spatial county constructs were created for use in calculating localized calibration and inclusion within multivariate crash estimation models. The introduction of the county groups seeks to further improve crash estimation methods through more specific calibration fact ors and roadway characteristic impacts. The three localized county groups analyzed include: 1) FDOT districts, 2) population density, and 3) average annual rainfall. The FDOT district localization is a geographically based county grouping. On a broader scale, geographic grouping is the basis for statewide HSM calibration factors. It is also suggested by the HSM for use within states. While Florida does not have the distinct terrain based regions that would be present in more mountainous states, separa ting sites by FDOT district does offer the potential to account for different driver behavior, animal populations, or weather that may be evident in different geographic clusters within the state. Figure 3 1 displays the seven FDOT district groups by coun ty, and a complete list can be found in Appendix A. The second localized county grouping is a division by population density. This localization specification provides a slight modification to the purely geographic division. While population density is he avily geographically based, it seeks to group together counties who may

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34 have similar characteristics despite not being physically close to each other, such as counties surround several of the larger cities within the state or counties that contain small to medium sized cities. For separation by population density, four population density groups were created using population data from the 2010 census. The groups were sorted as follows. Group 1 las, in which there were no applicable rural segments), from Broward (1,445 per sq. mile) to Duval (1,134 per sq. mile). Group 2 included the next ten counties, from Lee County (788 per sq. mile) through Leon County (413 per sq. mile). The next eighteen c ounties comprise Group 3, spanning from Hernando County (365 per sq. mile) to Santa Rosa County (150 per sq. mile). The fourth and final group consists of the remaining thirty two counties, from Nassau County (113 per sq. mile) through Liberty County (10 per sq. mile). A complete list of the county population density groups is provided in Appendix A, while Figure 3 2 and Figure 3 3 illustrate the boundaries of the group sizes quantitatively and geographically. The final localized county grouping is based on historical average annual rainfall. This county grouping is considered for analysis due to the fact that weather is specifically referenced in the HSM as a reason for model calibration. Within Florida, the defining weather characteristics throughout t he state that could potentially impact driving conditions are caused by rain. As historical rainfall data are not as strictly defined around county borders as population density and FDOT district location are, estimations were made to assign each county t o one of four average annual rainfall groups . Figure 3 4 shows the statewide average annual rainfall that was used to create the county based groupings. Group 1 consisted of thirteen counties averaging an annual rainfall of roughly 58 inches per year or greater. Group 2 included fifteen counties with approximate annual rainfall averages between 54 and 58 inches per year. Group 3

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35 contained twenty five counties that had approximately 50 to 54 inches of rainfall per year. Finally, Group 4 included the rem aining fourteen counties that averaged an annual rainfall less than 50 inches per year. A complete list of the four average annual rainfall groups is provided in Appendix A. Data Assembly For each year in the study period, forty three segment attributes w ere extracted from the RCI . Table 3 1 show s the variables collected and the roadway attribute to which they relate. These attributes included all of the mandatory HSM elements for rural two lane roads and rural multilane highways; however, data for some of the non mandatory roadway characteristics for these facility types are not available through the RCI. For these unavailable data elements, HSM recommended default values were assumed during the calibration procedure. The unavailable variables include grade, centerline rumble strips, roadside hazard rating, and driveway density, which are all part of the rural two lane road analysis. In the case of lighting presence, the RCI contained information on the number of luminaries along a given segment. In order to convert this data into whether or not the segment was to be considered lit, two lights were subtracted from the segment total for each boarding intersection, and the remaining lights were required to have a density of at least 21.1 lights per mile (one light every 250 feet), in order to be designated as a lit segment. In the identification of composite shoulders (a combination of paved and turf shoulders), multiple shoulder type and shoulder width variables were used for rural two way two lane ro ads. While the HSM gives CMF values for a composite shoulder that is half paved and half turf (the resulting CMF is halfway between the CMF for a paved shoulder and the CMF for a turf shoulder), composite shoulders not conforming to this ratio are not add ressed. For the purposes

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36 of this analysis, shoulders were determined to be composite if the ratio of paved shoulder width to total shoulder width (paved plus turf) was between one third and two thirds. The data in the RCI are in the form of database table s with each table representing an attribute. The rows in each table identify locations along the roadway where the corresponding attribute (such as number of lanes or shoulder width) changes value. As all attributes do not change value at the same locati ons, a segmenting procedure was developed to create homogenous roadway segments needed for crash modeling. This involves systematically splitting the roadway at points in which any of the attribute value changes ( See Figure 3 5 for a schematic illustratio n of this procedure). As a result, the majority of Florida highways were divided into segments of less than half of a mile in rural locations. While the HSM does not establish a minimum segment length for model calibration, a minimum of 0.10 miles was us ed in this study for rural segments; this was the minimum used in the research efforts to develop the HSM SPFs (Harwood et al. 2000 and Lord et al. 2008). Segments shorter than these minimum thresholds were not used in the analysis. The segmentation proce dure incorporated several consistency checks, including the removal of segments with missing and/or internally inconsistent attributes. It was ensured that segments do not include intersections, and curves were also removed from the analysis. The entire segmentation procedure was automated using a Python script, and the output of this program was a set of homogenous roadway segments with all the of the previously identified roadway attributes. Only segments that remained homogenous for all years of data were retained for analysis in order to ensure consistency in year to year comparisons and to remove any segments with changing physical characteristics during the study period.

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37 After the homogeneous segments were identified, the crashes extracted from CARS were crashes within a given distance from an intersection due to t he potential for queuing influences to extend great distances away from an intersection. The remaining crashes were then assigned to roadway segments depending on their locations relative to the starting and ending mileposts of the segments. Crash repor ting in Florida is a three tier system: long form reports, short form reports, form reports must be completed for any crashes involving injuries or fatalities, hazardous materials, government owned property, or the act of commiting a criminal offense; whereas, short form reporting is used for property damage only crashes. Only crashes recorded using the long form reports are included in the CARS database (Benac at al. 2006). Due to this limitation, only crashes with injuries or fatalities were included for analysis in this study, as the majority of the property damage only crashes are not readily available for analysis in Florida. The concentration on only fatal and injury crashes is not detrimenta l to statewide safety analysis due to the proven social and financial impact of crashes to be skewed heavily torwards fatal and injury crashes (Council et al. 2005). Data Descriptives The following data descriptive tables provide an overview of the rural t wo lane segments used for model estimation . Table 3 2 gives the segment length and crash data , and Table 3 3 shows an overview of the roadway characteristics for which Florida data was available. There are a total of 6,499 segments included in the data s et for rural two lane roads. As expected, the majority of the segments experience no crashes in a given year, showing the importance to collect multiple years of data to aggregate crash estimation over several years.

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38 Table 3 4 and Table 3 5 show the same summary statistics for the rural multilane divided highways model estimation data set. For this data set, there are 2,056 available segments included.

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39 Table 3 1. Data c ollected from the RCI Roadway Characteristic RCI Variable(s) Rural Two Lane Road s Rural Multilane Highways Number of Lanes NOLANES Functional Classification FUNCLASS Intersection Location INTDIR Horizontal Curve Location HRZPTINT N/A Segment Length BEGMP, ENDMP AADT SECTADT Median Type RDMEDIAN Median Width MEDWIDTH N/A Surface Width SURWIDTH S houlder Type SHLDTYPE, SHLDTYP2, SHLDTYP3 Shoulder Width SLDWIDTH, SHLDWTH2, SHLDWTH3 Number of Luminaries NOHMSLUM, NOSTDLUM, NOLOCLUM, NOUDKLUM Automated Speed Enforcement No automated speed enforcement was used in Florida during the study period Speed Limit MAXSPEED Table 3 2. Segment l ength and c rash d ata for r ural t wo l ane r oads Facility Attribute Year Sum Mean Median Minimum Maximum Length (mi.) All 2769.06 0.426 0.27 0.1 0 6.27 Total Fatal and Injury Crashes 2005 1159 .0 0.178 0 .0 0 .0 8 .0 2006 1147 .0 0.177 0 .0 0 .0 8 .0 2007 1145 .0 0.176 0 .0 0 .0 11 .0 2008 1116 .0 0.172 0 .0 0 .0 6 .0 2009 1063 .0 0.164 0 .0 0 .0 6 .0 2010 1092 .0 0.168 0 .0 0 .0 8 .0

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40 Table 3 3. Roadway c haracteristics for r ural t wo l ane t wo w ay r oads Roadway Ch aracteristic Year Mean Median Minimum Maximum AADT 2005 5069 .4 4300 500 22500 2006 5210 .6 4300 600 26000 2007 5229 .8 4200 450 32500 2008 5213 .2 4200 400 25000 2009 4935 .4 4017 350 25000 2010 4854 .3 4000 450 23000 Lane Width (ft.) 11. 9 12 11 18 Shoulder Width (ft.) 5.0 5 0 20 Speed Limit (mph) 55.8 55 25 60 Number of B ordering Intersections 1. 1 1 0 2 Table 3 4. Segment l ength and c rash d ata for r ural m ultilane d ivided h ighways Facility Attribute Year Sum Mean Median Minimum Maximum Segmen t Length (mi.) All 790.56 0.385 0.24 0.10 7.06 Total Fatal and Injury Crashes 2005 860 .0 0.418 0 .0 0 .0 23 .0 2006 854 .0 0.415 0 .0 0 .0 12 .0 2007 843 .0 0.410 0 .0 0 .0 18 .0 2008 780 .0 0.379 0 .0 0 .0 21 .0 2009 775 .0 0.377 0 .0 0 .0 20 .0 2010 757 .0 0.368 0 .0 0 .0 10 .0 Table 3 5. Roadway c haracteristics for rural m ultilane d ivided h ighways Roadway Characteristic Year Mean Median Minimum Maximum AADT 2005 14766 .7 12700 2500 58900 2006 15345 .1 13200 2800 63800 2007 15259 .4 13100 2700 66000 2008 15123 .1 12600 2900 66900 2009 14235 .2 12100 2700 66000 2010 14059 .6 12100 2400 59627 Lane Width (ft.) 23.9 24 21 27 Shoulder Width (ft.) 5.3 5 1 13 Speed Limit (mph) 60.9 65 35 70 Number of B ordering Intersections 0.8 1 0 2

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41 Figure 3 1. FDOT d is trict b oundaries (FDOT 2013). Figure 3 2. Population d ensity g roup c reation.

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42 Figure 3 3. Map of p opulation d ensity g roups. Figure 3 4. Florida a verage a nn ual r ainfall (Weisburg and Daly 1997).

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43 Figure 3 5 . Creation of h omogeneous s egments (Srin ivasan et al. 2011).

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44 CHAPTER 4 TRANSFERABILITY USING CALIBRATION FACTORS This chapter examines the spatial and temporal transferability of crash estimation models through different methods of calculating localized calibration factors and the comparison o f these calibration factors across different time periods. Three localized calibration groups (population density, average annual rainfall, and FDOT district), as well as statewide calibration of HSM crash estimation models are analyzed in this chapter. In comparing the performance of each of these calibration scenarios, their applications across four different temporal specifications are tested. The four temporal specifications include two cases where the model estimation years are the same as the model application years, one case where the estimated model is forecasted to future years, and one case where the estimated model is backcasted to past years. Chapter 3 provides an explanation of the data collection and processing procedures used to construct the data sets used for this analysis on both rural two lane roads and rural multilane divided highways. Summary statistics for both facility types can also be seen in Chapter 3. This chapter includes an analysis framework, a description of the HSM crash estimation procedure and calibration methodology, results of HSM model calibration for each of the calibration options, analysis of the error in predicted crashes for each crash estimation method, and summary and conclusions of the results from this chapte r. Analysis Framework The calibration methods examined in this chapter are based on the procedures given in the HSM. As discussed in Chapter 1, calibration factors are used to address crash differences caused not only by crash reporting procedures that ma y vary by state, but also a variety of other potential local differences, such as driver behavior, animal populations, topographic conditions,

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45 to provide results t hat are reliable for each jurisdiction that uses them, it is important that the importance of calibration is clearly stated, the level of detail for the local juri sdictions is not specified. The HSM, cites crash reporting thresholds that vary by state, while also mentioning, weather patterns and driving conditions that vary within a state. The analysis framework specified in this chapter is used to analyze the spa tial transferability of calibration factors within several different local categorizations that can be created within Florida. In Chapter 2, previous work was discussed that has addressed the statewide calibration of the HSM. However, the analysis and val idation of this calibration has traditionally been conducted using a data set with a consistent and limited time frame. The analysis framework used in this chapter addresses the temporal transferability of calibration factors by comparing how calibration factors perform when applied to both future and past years as well as the traditional same year data sample. To examine the spatial effects, Florida was stratified in three different ways (1) based on FDOT districts (there are seven such districts); (2) ba sed on population density (counties were grouped into four levels of population density), and (3) based on rainfall (counties were grouped into four categories based on average annual rainfall). With the addition of the statewide calibration factor, there are a total of 16 calibration groups used in this analysis. In addressing the temporal transferability of these calibration factors, calibration factors for each of the 16 groups were developed for two different time periods, 2005 through 2007 and 2008 t hrough 2010, resulting in the calculation of 32 calibration factors. This process was performed for each of the two facility types addressed in this dissertation, rural multilane highways and rural two -

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46 way two lane roads. This stratification results in a total of 64 calibration factors developed in this analysis. All calibration factors were calculated using 70% of the available data (model estimation data set), while the remaining 30% was used to compare the relative accuracies of the alternate calibrat ion factors (model validation data set). The prediction errors are calculated as the difference between the observed and predicted crashes for each segment in the validation dataset. Aggregate statistics such as the mean squared error (averaged over all s egments), mean absolute deviation, the variance of the squared error, and the absolute deviation are examined. In addition to examining the errors averaged over all segments, they were also examined by stratifying the segments to three categories based on AADT (low, medium, and high). This allows for the analysis of the relative performance of the calibration factors at different levels of traffic volumes. The calculated calibration factors were applied to the validation data set for four different temp oral scenarios; future years (2005 through 2007 applied to 2008 through 2010), past years (2008 through 2010 applied to 2005 through 2007), and same years (both 2005 through 2007 applied to 2005 through 2007 and 2008 through 2010 applied to 2008 through 20 10). Using a different timeframe for the model estimation and the model application data sets provides a more realistic approach to crash estimation error analysis, as when applied in practice the estimated crashes for a given segment will be based on a m odel and/or calibration factor computed based on data from previous years. For this research, applying the estimated crashes to both future years and past years allows for analysis in cases where the system wide total crashes experience both an increase a nd a decrease from the estimation years to the application years.

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47 In addition to the commonly reported aggregate measures, the error results are also used to develop an error regression model. In the error regression analysis, every segment in the valid ation dataset has ten predicted crash rates (one each from each of the four types of calibration, well as the uncalibrated model, applied over the two time periods of analysis). This MSE regression model relates the MSE to distinctive segment characterist ics and the type of calibration method used. Therefore, the error regression model allows us to determine whether there is any statistically significant difference in the relative performance of the alternate calibration approaches. HSM Calibration Metho dology The HSM base models for rural two lane roads and rural multilane divided highways both use the same SPF functional form, which is given in Equation 4 1: (4 1) Where: N SPF = predicted average segmen t crash frequency for base conditions; = regression parameters; AADT = average annual daily traffic volume (vehicles per day); L = length of roadway segment (miles). The regression parameters estimated in the SPF are provided in the HSM and vary ba sed on the facility type and crash severities being modeled. Table 4 1 gives the regression parameters used in the HSM SPFs for fatal and injury crashes on rural multilane highways and rural two lane roads. While the SPF yields the predicted crashes for each segment under base conditions, the crash frequency predicted by the HSM for a specific segment is also impacted by the crash modification factors. The CMFs for which there is Florida data for application in this

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48 research include lane width, shoulder type and width, presence of lighting, and presence of two way left turn lane. CMFs for which data was not available and the HSM default values were used include grade, roadside hazard rating, driveway density, and centerline rumble strips. Table 4 2 give s the CMFs that are applied as part of the crash estimation method for rural multilane highways, and Table 4 3 gives the applicable CMFs for rural two lane roads. The number of predicted crashes for a given severity level for a specific segment is calcula ted using Equation 4 2: (4 2) Where: N Predicted = predicted segment crash frequency for an individual segment; N SPF = predicted average segment crash frequency for base conditions; C = calibration facto r; CMF n = crash modification factor for site condition n . The calibration factor shown as a component of Equation 4 2 is computed by dividing the sum of the observed crashes across all segments in the study area by the sum of the predicted crashes across all selected segments. This calculation is shown in Equation 4 3. (4 3) For the analysis presented in this chapter, five different methods of calibration factor calculation are examined. The first method uses a constant calibrat ion factor of 1.0 across all sites, this is referred to as the uncalibrated HSM model, the next method uses a calibration factor based on all segments in the state, and the final three methods use local county groups to develop localized calibration factor s. The three localized methods, discussed in detail in Chapter 3,

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49 consist of a geographic based specification which includes seven county groupings formed from the seven FDOT districts, a population density based specification which includes four county g roupings, and a weather based specification which includes four county groupings formed from historical average annual rainfall records. Analysis of Rural Multilane Divided Highways Calibration Results for Rural Multilane Divided Highways Resulting calibra tion factors from the four different calibration methods (statewide, population density, FDOT district, and average annual rainfall) for rural multilane highways are displayed in Table 4 4. The statewide calibration factor for the years 2005 2007 is 0.736 while the factor for years 2008 2010 is 0.669. The fact that both of these are less than one indicates that the HSM equations when directly applied to Florida would over predict crashes. The observation that the calibration factor for 2008 2010 is less than that for 2005 2007 is consistent with the overall reduction in crashes in Florida over the same time period (see Chapter 3). These calibration factors are also shown graphically in Figure 4 1, Figure 4 2, and Figure 4 3. In these figures, it is easie r to compare trends across the two time periods and for each calibration method. Within the district groupings, there is substantial variability among the calculated calibration factors, suggesting that it is possible that district calibrations will offer improved crash predictions when compared to using the statewide calibration factor. The population density calibration factors show a slight, but steady, decrease as population density decreases. This trend is intuitive and shows that the roads in more densely populated counties experience more crashes than those in less densely populated areas. While there is some variation in the resulting calibration factors by average annual rainfall groups, the results show somewhat counterintuitive values. It is unexpected to see that the group that experiences the highest average annual rainfall rate also has the lowest calibration factor. Additionally, the

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50 calibration factor does not show an increasing or decreasing trend across the rainfall groups. This sugge sts that crash differences within Florida are likely not due to any difference in weather characteristics. Validation and Comparison Analysis for Rural Multilane Highways In order to validate and compare the accuracy of crash estimates provided by each ca libration method, each calibration is applied to the validation data set. To analyze the temporal transferability of the different spatial calibration specifications each estimation method is applied to four different estimation and application timeframe combinations, using the 2005 through 2007 and 2008 through 2010 data sets. The mean square error (MSE) and the variance of the squared error for these applications are calculated . The results for the MSE and variance of the squared error are shown in T able 4 5. These metrics provide insight as to the aggregate effectiveness of each crash prediction method. In viewing the spatial analysis of the calibration factors, the most noticeable result is the finding that the uncalibrated HSM model has substantia lly higher M SE values than any calibration method . Within the localized calibration factors, t here is not a single calibration method that provides reduced errors for each application condition. For two of the application cases, the statewide calibration has lower MSE values than any of the localized calibrations. In the other two cases, the district calibration method results in the smallest errors. For all four cases, the difference between the calibrated and uncalibrated cases is substantially larger than the differences among the different calibration types. There is a small temporal variation in the observed MSE values that is consistent across each calibration method. The errors when applied to the 2008 2010 validation data are smaller than when applied to the 2005 2007 data. This is due to the fact that there are fewer crashes during the 2008 2010 period, reducing the number of instances where extremely large errors are

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51 observed on segments with very high observed crashes. A large portion of th e prediction error originates from the few segments with a high number of observed crashes, as the crash estimation models are skewed to the high number of segments with zero observed crashes. The validation segments were then classified into three categor ies based on AADT. Low AADT is defined as less than 10,000 vpd, and high AADT is defined as greater than 20,000 vpd. AADT values in Florida ranged from 2,700 vpd to 63,000 vpd, this falls within the recommended HSM application range of 0 to 89,300 vpd. Table 4 6 provides the MSE from each calibration method for each of the three AADT groups. While the MSE values are nearly identical for each crash estimation method in the low and medium AADT groups, at the high AADT range, there is some variability in t he MSE based on the calibration method used. Additionally, the magnitude of the MSE increases as the AADT range increases. As also seen in the overall MSE values, there is once again no consistent crash estimation method that offers improved predictions over multiple temporal specifications. While the MSE calculated on subsets of the application sample provides a slightly more disaggregate approach, it is still not clear if the spatial transferability of the HSM crash estimation model is improved by fur ther localization. In order to examine the estimation error on each individual segment and fully explore the potential for reduced errors within localized regions, regression models are used to relate the MSE to the type of crash estimation method used. The regression model includes model parameters to account for length, AADT, and dummy variables for the prediction method used; these can each be seen in Table 4 7. In examining the significance of each of these dummy variables it is evident that none of t he localized calibration methods result in a statistically significant improv ement of the MSE. Each of the localized calibrations is just as effective as the statewide calibration, which does

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52 offer s ignificantly reduced MSE values when compared to the unc alibrated model. Overall, the results support the development of a statewide calibration factor, but further stratifications were found to be not beneficial. Even in cases where a localized calibration factor appears to differ significantly from the stat ewide calibration factor, there is not a significant resulting difference in the MSE. Additionally, it is clear that there is not a significant difference in the temporal transferability of the model between calibrations based on the same years or neighbo ring years. This supports the immediate temporal transferability of the calibration factors. The regression model also indicates that the errors are systematically larger with longer segments and increasing AADT (irrespective of the calibration procedure used). This suggests improvements may be needed in the fundamental safety performance functions as the single adjust factor by calibration is not able to improve predictive accuracy for longer segments and those with greater traffic volumes. Analysis of Rural Two Lane Roads Calibration Results Resulting calibration factors from the four different calibration methods (statewide, population density, FDOT district, and average annual rainfall) for rural two lane roads are displayed in Table 4 8. These cali bration factors are also shown graphically in Figure 4 4 through Figure 4 6. Among the rural two lane segments, the difference between the two time periods is negligible. The statewide calibration factor shows a difference of only 0.011 between the 2005 2007 and 2008 2010 calibration factors. This negligible difference is illustrated in Figures 4 4, 4 5, and 4 6, as within each set of calibration groups there is not a time period that consistently has a higher calibration factor. The calibration factors by district for rural two lane roads show some variation, but are overall much more consistent than their rural multilane counterparts. Population density based calibration factors are also more consistent for rural two -

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53 lane roads, as there is only a ver y slight decrease in calibration factor as population density decreases. Finally, the average annual rainfall calibration factors are also very consistent across the four groups for rural two lane roads. In addition to showing less temporal variability, crash frequency on rural two lane roads in Florida appears to have much less spatial variability as compared to crash frequency on rural multilane highways. Finally, it is also useful to point out that all calibration factors are fairly close to 1.0 sugge sting that rural two lane roads of Florida are not much different from the facilities used to develop the HSM equations. Validation and Comparison Analysis for Rural Two Lane Roads In order to validate and compare the accuracy of crash estimations provide d by each calibration method for rural two lane roads, each calibration is applied to the validation data set. To analyze the temporal transferability of the different spatial calibration specifications, each estimation method is applied to four different estimation and application timeframe combinations, using the 2005 through 2007 and 2008 through 2010 data sets. The mean square error (MSE) and the variance of the squared error for these applications are calculated . The results for the MSE and varian ce of the squared error are shown in Table 4 9. These metrics provide insight as to the aggregate effectiveness of each crash prediction method. Within the localized calibration factors, the calibration by population density group offers the smallest MSE values for each time period combination; however, the margin between the population density errors and errors from other calibration methods is very small. There is a small temporal variation in the observed MSE values that is consistent across each cali bration method. As was also evident with rural multilane highways, the rural two lane road errors when applied to the 2008 2010 validation data are smaller than when applied to the 2005 2007 data. The temporal combinations using the same estimation data set produced very

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54 similar results. When the validation data set is held constant and different estimation data sets are applied, there is very little impact on the resulting crash estimation errors. In order to investigate the underlying causes in the mod el estimation errors and find potential benefits for a specific prediction method, the MSE s are calculated for specific subsets of AADT in the application data set. Low AADT is defined as less than 2,500 vpd, and high AADT is defined as greater than 7,500 vpd. AADT values in Florida ranged from 500 vpd to 25,000 vpd, this extends outside of the recommended HSM application range of 0 to 17,800 vpd. Table 4 10 provides the MSE of each calibration method separated into the three AADT groups. It is clear th at over the low and medium AADT groups there is no variation in MSE between time period or calibration method. In the high AADT group, there are some minor differences in MSE, and calibration using population density groups appears to offer the best resul ts in most cases. As seen with the rural multilane highway results, the magnitude of the MSE increases as the AADT range increases. While the MSE calculated on subsets of the application sample provides a slightly more disaggregate approach, it is still not clear if the spatial transferability of the HSM crash estimation model is improved by further localization. Calibration by population density appears to result in somewhat consistently lower MSE values; however the magnitude of the reduced error is s mall. In order to examine the estimation error on each individual segment and fully explore the potential for reduced errors within localized regions, regression models are used to relate the MSE to the type of crash estimation method used. The regressio n model includes model parameters to account for length, AADT, and dummy variables for the prediction method used; these can each be seen in Table 4 11.

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55 The negative sign seen on the population calibration variable would indicate that calibration by popula tion density does result in reduced MSE values; however, this result is not statistically significant. I t is evident that none of the localized calibration methods result in a statistically significant improv ement of the MSE. Additionally, it is clear th at there is not a significant difference in the temporal transferability of the model between calibrations based on the same years or neighboring years. As was also evident in the error regression performed on rural multilane highways, the parameters whic h do prove to be significant are segment length and AADT. The positive coefficients on both of these parameters show that as segment length and AADT increase, the crash estimation error also increases. Error regression analysis performed on each individua l group of the localized calibration specifications supported the same results seen across all segments. Even in cases where a localized calibration factor appears to differ significantly from the statewide calibration factor, there is not a significant r esulting difference in the MSE. Summary and Conclusions of Calibration Transferability This chapter examined the spatial and temporal transferability of crash estimation models through the use of calibration factors on rural multilane divided highways and rural two lane roads in Florida. Spatial effects were analyzed through the comparison of the uncalibrated HSM model, a statewide calibration, and three localized calibration methods (FDOT districts, population density groups, and average annual rainfall groups). Through aggregate and segment specific crash estimation errors, localized specifications did not offer statistically significant improvements to state calibration. Statewide calibration itself is beneficial, but further fine tuning of calibratio n for specific regions did not provide a significant added benefit to the accuracy of crash estimation. Error results across AADT subsets of the application data set

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56 showed that estimation errors increase on high AADT segments and the variability of the a ggregate errors for each estimation method also increases within the high AADT group. Results of the error regression models also showed that increasing AADT, as well as increasing segment length, contributed to increased crash estimation errors. This sh ows the potential for future model specifications to improve upon crash estimation on these high AADT sites. Temporal transferability of crash estimation methods was investigated through the estimation of model parameters and calibration factors for diffe rent combinations of estimation and application data periods. In this analysis, two cases were used where the estimation and application time period were the same, and two cases were considered for the forecast or backcast of the estimation data period ap plied to validation data from a different time period. Crash estimation did not vary significantly whether using same year calibration factors or projecting to a different year. With the validation data set held constant, similar error results were found for either model estimation time period. This downplays the importance of frequent updates to calibration factors, as small changes in the calibration factor did not offer significantly improved accuracy of crash estimations. The results of both spatial and temporal transferability highlight the significance of statewide calibration while also providing assurance that for states with limited resources, it is not necessary to provide detailed localized calibration factors or update calibration factors on a yearly basis.

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57 Table 4 1. HSM SPF r egression p arameters for f atal and i njury c rashes Facility Type Value Value Rural Multilane Divided Highways 8.837 0.958 Rural Two Lane Roads 9.364 1.000 Table 4 2. HSM CMFs for r ural m ultilane h ighways HSM CMF Number CMF Description HSM Reference 1 Lane Width Equation 11 16, Table 11 16, Figure 11 10 2 Ri ght Shoulder Width Table 11 17 3 Median Width Table 11 18 4 Lighting Equation 11 17, Table 11 19 5 Automated Speed Enforcement Page 11 32 Table 4 3. HSM CMFs for r ural t wo l ane r oads HSM CMF Number CMF Description HSM Reference 1 Lane Width Table 10 8, Figure 10 7, Equation 10 11 2 Shoulder Width and Type Tables 10 9 and 10 10, Figure 10 8, Equation 10 12 3 Horizontal Curves: Length, Radius, Transition Table 10 7 4 Horizontal Curves: Superelevation Equations 10 14, 10 15, 10 16 5 Grades Table 10 11 6 Driveway Density Equation 10 17 7 Centerline Rumble Strips Page 10 29 8 Passing Lanes Page 10 29 9 Two Way Left Turn Lanes Equation 10 18, 10 19 10 Roadside Design Equation 10 20 11 Lighting Equation 10 21, Table 10 12 12 Automated Speed Enforc ement Page 10 31

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58 Table 4 4. Statewide and l ocalized c alibration f actors for r ural m ultilane h ighways Calibration Area Number of Segments Mileage Calibration Factor 2005 2007 Calibration Factor 2008 2010 Statewide 1441 557.52 0.736 0.669 FDOT Distric t 1 198 88.48 0.749 0.631 2 438 169.25 0.656 0.605 3 258 84.13 0.586 0.573 4 109 47.49 0.948 0.778 5 312 131.32 0.799 0.717 6 15 5.92 0.924 0.837 7 111 30.93 0.528 0.714 Population Density Group 1 77 37.00 0.832 0.849 2 237 80.67 0.761 0.743 3 603 237.47 0.725 0.61 0 4 524 202.38 0.705 0.675 Rainfall Group 1 130 43.23 0.551 0.527 2 407 154.51 0.810 0.774 3 605 218.69 0.654 0.611 4 299 141.09 0.833 0.717 Table 4 5. Rural m ultilane h ighways MSE and v ariance of SE by c rash e stimatio n m ethod Estimation Data Set Validation Data Set Prediction Error Metric HSM Calibration Type Uncalibrated Statewide District Population Density Rainfall 2005 2007 2005 2007 Mean Square Error (MSE) 0.431 0.260 0.241 0.262 0.255 Variance of SE 4.471 1.941 1.466 1.979 1.448 2005 2007 2008 2010 Mean Square Error (MSE) 0.397 0.214 0.223 0.229 0.233 Variance of SE 6.370 1.023 1.493 1.876 1.893 2008 2010 2005 2007 Mean Square Error (MSE) 0.431 0.246 0.228 0.258 0.232 Variance of SE 4.471 1.892 1.5 77 2.081 1.560 2008 2010 2008 2010 Mean Square Error (MSE) 0.397 0.200 0.202 0.231 0.200 Variance of SE 6.370 0.720 0.897 2.170 0.906

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59 Table 4 6. Rural m ultilane h ighways MSE by c alibration m ethod and AADT r ange Estimation Data Set Application Data S et AADT Range MSE by Calibration Method Statewide Calibration District Calibration Population Density Calibration Rainfall Calibration 2005 2007 2005 2007 Low 0.081 0.078 0.080 0.083 Medium 0.187 0.175 0.184 0.192 High 0.674 0.620 0.693 0.644 2 005 2007 2008 2010 Low 0.068 0.066 0.067 0.067 Medium 0.163 0.162 0.161 0.162 High 0.579 0.628 0.657 0.676 2008 2010 2005 2007 Low 0.080 0.078 0.078 0.081 Medium 0.176 0.164 0.170 0.175 High 0.639 0.583 0.705 0.574 2008 2010 2008 2010 Low 0.0 66 0.066 0.066 0.066 Medium 0.161 0.156 0.157 0.159 High 0.516 0.536 0.680 0.519 Table 4 7. MSE e rror r egression by c rash e stimation m ethod for r ural m ultilane d ivided h ighways Regression Parameter Coefficients Significance B Std. Error Const a nt 0.590 0.036 0.00 Length 0.849 0.024 0.00 AADT 3.3 61 E 05 1. 218 E 06 0.00 Population Method 0.015 0.039 0.70 Rainfall Method 0.000 0.039 1.00 District Method 0.006 0.039 0.87 Uncalibrated 0.184 0.039 0.00 Temporal Change 0.001 0.023 0.95

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60 Table 4 8. Statewide and l ocalized c alibration f actors for r ural t wo l ane r oads Calibration Area Number of Segments Mileage Calibration Factor 2005 2007 Calibration Factor 2008 2010 Statewide 4591 1978.39 0.986 0.974 FDOT District 1 723 385.20 1.020 0.932 2 1415 565.23 0.999 1.029 3 1537 627.39 0.961 0.966 4 147 60.53 0.871 0.747 5 468 212.36 1.013 0.984 6 134 66.04 0.951 1.176 7 167 61.64 0.947 0.811 Popluation Density Group 1 168 81.22 1.068 1.016 2 429 184.28 1.096 1.056 3 1169 524.28 1.01 0 0.956 4 2825 1188.61 0.930 0.957 Rainfall Group 1 1180 493.64 0.948 0.964 2 1238 506.45 0.999 1.070 3 1465 634.65 1.001 0.952 4 708 343.65 0.974 0.924

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61 Table 4 9. Rural t wo l ane r oads MSE and v ariance of SE by c rash estimation m ethod Estimatio n Data Set Validation Data Set Prediction Error Metric HSM Calibration Type Statewide District Population Density Rainfall 2005 2007 2005 2007 Mean Square Error (MSE) 0.108 0.108 0.105 0.106 Variance of SE 1.117 1.144 1.010 1.056 2005 2007 2008 20 10 Mean Square Error (MSE) 0.074 0.075 0.073 0.074 Variance of SE 0.079 0.079 0.073 0.077 2008 2010 2005 2007 Mean Square Error (MSE) 0.108 0.107 0.106 0.106 Variance of SE 1.117 0.968 1.072 1.020 2008 2010 2008 2010 Mean Square Error (MSE) 0.074 0 .074 0.074 0.074 Variance of SE 0.079 0.076 0.076 0.076 Table 4 10. Rural t wo l ane r oads MSE by calibration m ethod and AADT r ange Estimation Data Set Application Data Set AADT Range MSE by Calibration Method Statewide Calibration District Calibr ation Population Density Calibration Rainfall Calibration 2005 2007 2005 2007 Low 0.030 0.030 0.030 0.030 Medium 0.075 0.076 0.075 0.076 High 0.313 0.316 0.298 0.305 2005 2007 2008 2010 Low 0.029 0.029 0.029 0.028 Medium 0.065 0.065 0.065 0.065 High 0.162 0.163 0.155 0.159 2008 2010 2005 2007 Low 0.030 0.030 0.030 0.030 Medium 0.075 0.076 0.075 0.076 High 0.303 0.295 0.296 0.290 2008 2010 2008 2010 Low 0.032 0.032 0.032 0.032 Medium 0.065 0.065 0.065 0.065 High 0.159 0.158 0.156 0.155

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62 Table 4 11. MSE e rror r egression by c rash e stimation m ethod for r ural t wo l ane r oads Regression Parameter Coefficients Significance B Std. Error Constant 0.167 0.012 0.000 Length 0.210 0.008 0.000 AADT 3.307E 05 1.07 5 E 06 0.000 Statewide M V 0.002 0.012 0.896 Population Density MV 0.003 0.012 0.783 District MV 0.000 0.012 0.968 Temporal Change 0.001 0.008 0.901

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63 Figure 4 1. Rural m ultilane d ivided h ighway c alibration by FDOT d istrict . Figure 4 2. Rural m ultilane d ivided h ighway c alibration by c ounty p opulation d ensity .

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64 Figure 4 3. Rural m ultilane d ivided h ighway c alibration by a verage a nnual r ainfall . Figure 4 4 . Rural t wo l ane r oad c alibration by FDOT d istrict .

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65 Figure 4 5. Rural t wo l ane r oad c alibration by county p opulation d ensity . Figure 4 6. Rural t wo l ane r oad c alibration by a verage a nnual r ainfall .

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66 CHAPTER 5 TRANSFERABILITY USING LOCAL SAFETY PERFORMANCE FUNCTIONS This chapter examines the spatial and temporal transferability of crash estimation models through the development of localized SPFs. Table 5 1 and Table 5 2 show the AADT distributions for each of the Florida analysis groups on rural multilane divided highways and rural two lane roads, respectively. While the range of AADT values for rural m ultilane highways observed in Florida falls within the modeling range specified in the HSM of 0 to 89,300 vehicles per day, the average Florida AADT of 14,794 is substantially greater (a 25% increase) than the average AADT from HSM modeling conditions of 1 1,777 vehicles per day. Additionally, it is clear that there is significant variation in the AADT values observed within each Florida analysis group. Within these groups, the average AADT varies from 10,000 to over 20,000 vehicles per day. On rural two lane road segments, the average AADT in Florida, 5,060 vehicles per day, is a 74% increase compared to the average across segments used for HSM model development. There is also great AADT variation evident within the Florida analysis groups, as average v alues range from below 4,000 to above 10,000 vehicles per day. Additionally, the range of AADTs observed in Florida fall outside of the recommended application range specified in the HSM of 0 to 17,800 vehicles per day. It is useful to note here that the statewide calibration factor for rural two lane roads for Florida was estimated to be very close to 1. The substantial difference in AADT between the conditions observed in Florida and the segments used in HSM model development suggest the possible benef its of developing models that not only reflect the local (Florida) relationship between crash frequency and AADT but also are applicable over the range of AADTs observed in Florida. Further, the MSE results by AADT

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67 category and error regression results fr om Chapter 4 indicated that even after calibration, the models are systematically more erroneous at higher values of AADT. Developing location specific SPFs is a topic that is suggested as a method for possible improvement, but not discussed, in the HSM ( AASHTO 2010). With access to the full inventory of rural two lane roads and rural multilane divided highways in Florida, the potential for statewide and localized SPFs in Florida can be investigated. Therefore, we examine whether the transferability of H SM models to Florida can be improved by estimating localized SPFs. Models developed using the same three local county subsets (FDOT district, population density, and average annual rainfall), as well as statewide models, are analyzed in this chapter. In the application of these locally developed SPFs, the four combinations of temporal applications are again considered. These include two cases of model estimation and application to the same three year period and two cases of model application to the three year period before and after the model estimation time period. The results of the statewide HSM calibration from Chapter 4 are used as a benchmark for crash estimation performance and a comparison point to the crash estimation from locally developed SPFs . Chapter 3 provides a description of the data and data collection procedure for both rural multilane divided highways and rural two lane roads used in this analysis. This chapter includes an analysis framework, resulting model parameters for locally de veloped SPFs, analysis of the crash prediction error for each crash estimation method, and the summary and conclusions of the results from this chapter. Analysis Framework The HSM base models for rural two lane roads and rural multilane divided highways bo th use the same SPF functional form, which is given in Equation 5 1:

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68 (5 1) Where: N SPF = predicted average segment crash frequency for base conditions; = regression parameters; AADT = average annual daily traffic volume (vehicles per day); L = length of roadway segment (miles). The two regression parameters (alpha and beta) shown in Equation 5 1 are calculated directly using negative binomial regre ssion. Model coefficients were calculated with the IBM SPSS Statistics software, using the negative binomial generalized linear modeling tool. The overall analysis framework is similar to the one adopted for in the context of calibration in Chapter 4. To examine the spatial and temporal transferability of the HSM crash estimation procedure using locally derived SPFs, the categorization of the estimated and applied models was the same as specified in Chapter 4. This includes statewide model analysis, as w ell as the three localization methods of FDOT districts, population density groups, and average annual rainfall groups. For SPF development in this chapter, FDOT District 4 and District 6 did not contain a sufficiently large enough sample size individuall y for rural multilane divided highways. These two districts, located adjacent to each other with similar population and geographic characteristics in South Florida, were combined for rural multilane highway analysis. With this district combination and th e full spatial and temporal stratification specified in Chapter 4, there were a total of 62 SPFs developed in this chapter. In the application of these locally developed SPFs, the four combinations of temporal applications are again considered. These in clude two cases of model estimation and application to the same three year period and two cases of model application to the three year period before

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69 and after the model estimation time period. The MSE and variance of the SE, as well as error regression mo dels, were again used to assess and compare the crash estimation capabilities of each predictive method. The results of the statewide HSM calibration from Chapter 4 are used as a benchmark for comparing the crash estimation performance of the locally deve loped SPFs. As outlined in Chapter 4, the validation and comparison analysis of these SPFs included the four combinations of temporal estimation and application time periods. Analysis of Rural Multilane Divided Highways Locally Derived SPFs The resultin g rural multilane divided highway SPFs, developed for the entire state, as well as each subset of the FDOT District, population density, and average annual rainfall groups, are displayed in Table 5 3. Based on the model parameters, there is a noticeable v ariation in the relationship between estimated crash frequency and AADT. This spatial variation can be better seen in Figure 5 1, Figure 5 2, and Figure 5 3, which display the 2005 2007 SPFs within each localized group over the AADT range for which they a re applicable in comparison to the HSM SPF and the statewide SPF. While the wide range of relationships between AADT and estimated crash frequency is visually apparent, the next section examines the impact of these varying relationships on the accuracy of crash frequency predictions. Model Validation and Comparison Analysis In order to validate and compare the accuracy of crash estimations provided by each crash estimation method, each model is applied to the validation data set. To analyze the temporal t ransferability of the different spatial SPF specifications each estimation method is applied to four different estimation and application timeframe combinations, using the 2005 through 2007 and 2008 through 2010 data sets. The mean square error (MSE) and the variance of the squared error for these applications are calculated .

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70 The results for the MSE and variance of the squared error are shown in Table 5 4. With regards to the error results from the different spatial specifications, there are mixed res ults as to which model results in the lowest errors. The population density SPFs provide the lowest MSE values for the two cases of 2008 2010 application, while the district SPFs give the lowest MSE values for the two cases of 2005 2007 application. The one result that is consistent across all four temporal specifications is that the variance of the squared error is lower for the district SPFs prediction method than for statewide calibration; with the state calibration showing a squared error variance tha t is from 42% to 109% higher than the district SPF squared error variance. As was also seen in the calibration MSE values discussed in Chapter 4, there is once again a small temporal variation in MSE that is consistent across each crash estimation method. The error when applied to the 2008 2010 validation data is smaller than when applied to the 2005 2007 data. Next, MSE s are calculated for specific subsets of AADT in the application data set. Low AADT is defined as less than 10,000 vpd, and high AADT i s defined as greater than 20,000 vpd. Table 5 5 provides the MSE of each calibration method separated into the three AADT groups. The magnitude of the MSE is again substantially higher for the high AADT range than for the remaining segments. For the two cases of 2008 2010 model application, both the statewide SPF and population density SPFs appear to offer improved crash prediction over the statewide calibrated model; however, this improvement is not evident for the 2005 2007 model applications. With the variation in model performance across both spatial and temporal specifications for local SPFs, error regression models were introduced for a disaggregate approach. In order to examine the estimation error on each individual segment and fully explore the potential for

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71 reduced errors within localized regions, regression models are used to relate the MSE to the type of crash estimation method used. The regression model includes model parameters to account for length, AADT, and dummy variables for the predic tion method used; these can each be seen in Table 5 6. The potential improved aggregate crash estimation accuracy seen in the previously discussed portions of the statewide, population density, and district SPFs are not evident in the error regression. Th e error regression shows that none of the locally derived SPFs offer improved crash estimations at the disaggregate level. Analysis of Rural Two Lane Roads Locally Derived SPFs The resulting rural two lane road SPFs, developed for the entire state, as well as each subset of the FDOT District, population density, and average annual rainfall groups, are displayed in Table 5 7. Based on the model parameters, there is a noticeable variation in the relationship between estimated crash frequency and AADT. This spatial variation can be better seen in Figure 5 4, Figure 5 5, and Figure 5 6, which display the 2005 2007 SPFs within each localized group over the AADT range for which they are applicable in comparison to the HSM SPF and the statewide SPF. While the wi de range of relationships between AADT and estimated crash frequency is visually apparent, the next section examines the impact of these varying relationships on the accuracy of crash frequency predictions. Model Validation and Comparison Analysis As was p erformed with the rural multilane divided segments, each crash estimation model is applied to the validation data set in order to validate and compare the accuracy of the crash predictions. To analyze the temporal transferability of the different spatial SPF specifications, each estimation method is applied to four different estimation and application

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72 timeframe combinations, using the 2005 through 2007 and 2008 through 2010 data sets. The mean square error (MSE) and the variance of the squared error for t hese applications are calculated . The results for the MSE and variance of the squared error are shown in Table 5 8. While the magnitudes of the MSE values are very similar across each spatial specification, the population density based SPFs do show a very slight accuracy improvement in each time period. The population density SPFs result in between a 3.2% and 6.6% reduction in MSE and an 11.4% to 21.2% reduction in variance of the squared error. While these accuracy improvements are not as substantia l as seen in previous models on individual application periods, it is important that it is consistent throughout each application and estimation time period. The MSE results were also analyzed for the three AADT subsets. Low AADT is defined as less than 2 ,500 vpd, and high AADT is defined as greater than 7,500 vpd. Table 5 9 provides the MSE of each calibration method separated into the three AADT groups. The magnitude of the MSE is again substantially higher for the high AADT range than for the remainin g segments. It is evident that the previously discussed accuracy improvement seen for the population density based SPFs is entirely due to improvements within the high AADT category. The MSE for population density SPFs ranges from 6.3% to 12.8% lower tha n the statewide calibration models across each temporal specification. Error regression models were also calculated based on the MSE for each spatial and temporal model specification. Table 5 10 provides the resulting model coefficients from the error reg ression analysis. The error regression coefficient on the variable for population density based SPFs is negative, showing an error reduction for these models at a disaggregate level; however, this result is only significant at a 30% confidence level.

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73 Su mmary and Conclusions of Local SPF Development This chapter examined the development of local SPFs for use in transferring the HSM methodology to estimate crash frequency on Florida rural multilane divided highways and rural two lane roads. Spatial effect s were analyzed through the comparison of the statewide calibrated HSM model to local SPFs developed statewide and for FDOT districts, population density groups, and average annual rainfall groups. Models were analyzed and compared through estimation and application across four different temporal specifications with the calculation of MSE, variance of SE, and error regression models. Results for rural multilane divided highways showed that on the aggregate level prediction models using district based SPF s and population density based SPFs performed slightly better than statewide calibration (reduced MSEs for 10 out of 12 and 9 out of 12 AADT categories, respectively). Crash estimations using district SPFs also had the benefit of showing substantially low er variance of the squared errors. A lower variance of crash estimation errors is significant in decreasing the propensity for large estimation errors, and is an indicator of improved predictions on high risk sites with abnormally high AADT or observed cr ashes. Disaggregate model analysis, performed through the calculation of error regression models, did not show any improvement in crash estimation using statewide or locally derived SPFs. Aggregate analysis results for rural two lane roads showed that cra sh estimation with population density based SPFs had improved accuracy compared to statewide calibrated HSM models. These improvements were seen consistently in MSE and variance of SE across each of the four temporal specifications as well through reduced MSE values in 9 out of the 12 AADT categories. The error regression models for rural two lane roads also showed a possible improvement through crash estimation with population density based SPFs; however, this result was only significant at a 30% confide nce level.

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74 The temporal transferability of the crash estimation models, as examined through model estimation and validation with two cases from the same time period and two cases from different time periods, showed that there was no significant difference in errors for either temporal combination. These results mirror those seen and Chapter 4 and highlight the need to accurately model the relationship between AADT and crash frequency, as this relationship is consistent over an extended period of time. Resu lts from this chapter identify the potential for improved crash estimation through the development of local SPFs instead of applying statewide calibration to HSM models. This improvement is driven by the ability for local SPFs to offer flexible relationsh ips between AADT and estimated crash frequency that is not seen in the application of pre existing HSM models. The lack of significant temporal fluctuation results in crash estimation models that can be applied over an extended period of time. The combin ation of these two factors points towards future resources being more efficiently spent at one time to develop local SPFs rather than spread out for frequent calibration of pre existing crash estimation models.

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75 Table 5 1. AADT d istribution by a nalysis g roup for rural m ultilane h ighways Model Area 2005 2007 2008 2010 AADT Min AADT Max AADT Average Crashes AADT Min AADT Max AADT Average Crashes Statewide 2733 62900 15103 1891 2700 56209 14485 1653 FDOT District 1 3733 37000 16714 312 3100 37167 15471 244 2 3233 28667 12094 382 2700 30500 11373 326 3 2733 33167 11283 172 2733 32500 11242 168 4 & 6 4167 35367 14810 251 4400 36733 14926 209 5 3100 62900 21245 706 2900 56209 20144 612 7 4967 25133 16048 68 5567 25611 16147 94 Population Density Group 1 8900 41500 18982 230 8167 56209 19928 235 2 3100 31833 12608 241 2900 29000 12624 233 3 3600 62900 19079 973 3033 50346 17985 782 4 2733 28667 11086 447 2700 30500 10500 403 Rainfall Group 1 2733 331 67 13259 101 2733 32500 12880 94 2 3233 27500 9462 347 2700 26667 9263 320 3 3100 36300 15589 686 2900 37367 15133 620 4 7067 62900 22600 757 6300 56209 20982 619

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76 Table 5 2. AADT d istribution by a nalysis g roup for r ural t wo l ane r oads Model Area 2005 2007 2008 2010 AADT Min AADT Max AAD T Average Crashes AADT Min AADT Max AADT Average Crashes Statewide 533 25833 5145 2401 467 24167 4975 2288 FDOT District 1 1183 21833 5629 533 1250 21667 5225 443 2 600 19733 4443 597 467 19233 4216 576 3 533 16433 3832 522 467 16367 3820 525 4 290 0 11500 5092 71 2878 11767 5163 64 5 1500 20733 7004 347 1550 21233 6789 328 6 2233 25833 12322 183 1700 18500 11793 219 7 833 22933 10151 148 767 24167 10241 133 Population Density Group 1 1867 18567 10754 229 1700 22667 10878 223 2 833 22933 682 8 323 767 24167 6788 308 3 1033 20733 5874 733 1150 21233 5623 663 4 533 25833 4254 1116 467 18033 4080 1094 Rainfall Group 1 533 16433 3982 418 467 16367 3980 426 2 600 18367 4402 534 467 18500 4232 544 3 833 25833 6320 981 700 24167 6109 905 4 1500 20733 5948 468 1617 21233 5583 413

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77 Table 5 3. Rural m ultilane divided h ighway SPFs Model Area Number of Segments Mileage 2005 2007 2008 2010 c c Calibrated HSM N/A N/A 6.504 0.958 1.687 5.912 0.958 1.687 Florida Statewide 1441 557. 52 8.689 1.031 0.447 8.033 0.956 0.459 FDOT District 1 198 88.48 8.594 1.018 0.249 9.659 1.110 0.583 2 438 169.25 4.857 0.613 0.140 4.437 0.557 0.091 3 258 84.13 7.412 0.873 0.111 7.649 0.896 7.6 × 10 8 4 & 6 124 53.41 9.151 1.109 0.383 5. 168 0.679 0.245 5 312 131.32 9.094 1.083 0.721 7.663 0.932 0.764 7 111 30.93 12.709 1.409 0.039 13.835 1.555 0.579 Population Density Group 1 77 37.00 12.833 1.486 0.617 9.952 1.191 0.431 2 237 80.67 5.042 0.654 0.451 4.694 0.610 0.244 3 6 03 237.47 10.594 1.216 0.480 8.867 1.032 0.512 4 524 202.38 6.672 0.811 0.046 7.398 0.886 0.338 Rainfall Group 1 130 43.23 6.371 0.755 0.589 6.755 0.794 7.6 × 10 8 2 407 154.51 7.809 0.953 0.339 8.505 1.022 0.320 3 605 218.69 8.964 1.047 0. 385 5.809 0.717 0.306 4 299 141.09 10.267 1.197 0.471 10.979 1.257 0.772

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78 Table 5 4. Rural m ultilane d ivided h ighways MSE and v ariance of SE by SPF Estimation Data Set Validation Data Set Prediction Error Metric HSM State Calibration FL SPF St ate District Population Density Rainfall 2005 2007 2005 2007 Mean Square Error (MSE) 0.260 0.278 0.259 0.272 0.273 Variance of SE 1.941 2.184 1.226 2.235 1.240 2005 2007 2008 2010 Mean Square Error (MSE) 0.214 0.197 0.215 0.196 0.215 Variance of SE 1.023 0.416 0.631 0.429 0.723 2008 2010 2005 2007 Mean Square Error (MSE) 0.246 0.253 0.228 0.244 0.244 Variance of SE 1.892 1.918 1.330 1.875 1.191 2008 2010 2008 2010 Mean Square Error (MSE) 0.200 0.180 0.185 0.174 0.187 Variance of SE 0.720 0.3 56 0.344 0.351 0.382 Table 5 5. Rural m ultilane h ighways MSE by SPF and AADT r ange Estimation Data Set Application Data Set AADT Range MSE by Prediction Method Statewide Calibration Statewide SPF District SPF Population Density SPF Rainfall SPF 200 5 2007 2005 2007 Low 0.081 0.082 0.079 0.077 0.084 Medium 0.187 0.198 0.178 0.183 0.194 High 0.674 0.737 0.698 0.751 0.720 2005 2007 2008 2010 Low 0.068 0.065 0.065 0.067 0.066 Medium 0.163 0.167 0.165 0.157 0.163 High 0.579 0.461 0.546 0.474 0.550 2008 2010 2005 2007 Low 0.080 0.081 0.075 0.076 0.080 Medium 0.176 0.187 0.162 0.176 0.179 High 0.639 0.650 0.595 0.640 0.623 2008 2010 2008 2010 Low 0.066 0.065 0.063 0.065 0.065 Medium 0.161 0.164 0.159 0.157 0.164 High 0.516 0.391 0. 425 0.375 0.419

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79 Table 5 6. MSE r egression by SPF for r ural m ultilane d ivided h ighways Regression Parameter Coefficients Significance B Std. Error Constant 0.490 0.027 0.000 Length 0.583 0.019 0.000 AADT 2.236E 05 9.5233E 07 0.000 Statewide SP F 0.013 0.028 0.632 District SPF 0.008 0.028 0.776 Population Density SPF 0.008 0.028 0.776 Rainfall SPF 0.016 0.028 0.572 Temporal Change 0.002 0.018 0.906 Table 5 7. Rural t wo l ane r oads SPFs Model Area Number of Segments Mileage 2005 2007 2008 2 010 c c Calibrated HSM N/A N/A 9.364 1.000 N/A 9.364 1.000 N/A Statewide 4591 1978.39 7.577 0.917 0.025 7.496 0.910 0.365 FDOT District 1 723 385.20 5.244 0.654 0.136 5.193 0.634 0.209 2 1415 565.23 8.424 1.021 0.469 7.146 0.870 0.239 3 1537 627.39 6.501 0.782 0.251 6.655 0.802 0.345 4 147 60.53 8.741 1.037 0.140 8.633 1.011 0.270 5 468 212.36 9.113 1.099 0.349 9.368 1.126 0.271 6 134 66.04 15.883 1.788 0.374 10.849 1.299 0.526 7 167 61.64 4.480 0.591 0.544 4.086 0.543 0 .649 Population Density Group 1 168 81.22 9.469 1.140 0.620 8.843 1.078 0.859 2 429 184.28 6.319 0.789 0.150 6.230 0.778 0.169 3 1169 524.28 7.119 0.871 0.132 6.775 0.822 0.015 4 2825 1188.61 7.008 0.843 0.248 7.162 0.864 0.247 Rainfall Gro up 1 1180 493.64 6.373 0.766 0.246 6.523 0.789 0.473 2 1238 506.45 8.351 1.006 0.381 9.372 1.135 0.322 3 1465 634.65 6.748 0.829 0.087 6.002 0.739 0.062 4 708 343.65 7.856 0.950 0.155 7.520 0.904 0.151

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80 Table 5 8. Rural t wo l ane r oad MSE and v ariance of SE by SPF Estimation Data Set Validation Data Set Prediction Error Metric HSM State Calibration FL SPF State District Population Density Rainfall 2005 2007 2005 2007 Mean Square Error (MSE) 0.108 0.109 0.114 0.101 0.106 Variance o f SE 1.117 1.213 1.191 0.880 1.102 2005 2007 2008 2010 Mean Square Error (MSE) 0.074 0.075 0.073 0.072 0.074 Variance of SE 0.079 0.083 0.076 0.069 0.077 2008 2010 2005 2007 Mean Square Error (MSE) 0.108 0.109 0.110 0.100 0.101 Variance of SE 1.117 1.198 0.998 0.858 0.831 2008 2010 2008 2010 Mean Square Error (MSE) 0.074 0.075 0.073 0.072 0.073 Variance of SE 0.079 0.081 0.074 0.070 0.071 Table 5 9. Rural t wo l ane r oad MSE and v ariance of SE by SPF and AADT r ange Estimation Data Set Applicati on Data Set AADT Range MSE by Prediction Method Statewide Calibration Statewide SPF District SPF Population Density SPF Rainfall SPF 2005 2007 2005 2007 Low 0.030 0.031 0.034 0.032 0.031 Medium 0.075 0.075 0.076 0.075 0.075 High 0.313 0.320 0.34 0 0.273 0.305 2005 2007 2008 2010 Low 0.029 0.028 0.029 0.028 0.029 Medium 0.065 0.065 0.065 0.065 0.064 High 0.162 0.166 0.157 0.149 0.160 2008 2010 2005 2007 Low 0.030 0.031 0.034 0.032 0.032 Medium 0.075 0.076 0.076 0.075 0.077 High 0.303 0.319 0.321 0.271 0.270 2008 2010 2008 2010 Low 0.032 0.028 0.029 0.028 0.029 Medium 0.065 0.065 0.064 0.065 0.065 High 0.159 0.165 0.159 0.149 0.154

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81 Table 5 10. MSE r egression by SPF for r ural t wo l ane r oads Regression Parameter Coefficients Significance B Std. Error Constant 0.153 0.011 0.000 Length 0.205 0.008 0.000 AADT 3.104E 05 1.0600E 06 0.000 Statewide SPF 0.001 0.012 0.931 District SPF 0.002 0.012 0.891 Population Density SPF 0.005 0.012 0.697 Rainfall SPF 0.002 0.012 0.84 7 Temporal Change 0.001 0.008 0.915

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82 Figure 5 1 . Rural m ultilane h ighway 2005 2007 SPFs by d istrict . Figure 5 2 . Rural m ultilane h ighway 2005 2007 SPFs by p opulation d ensity g roup .

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83 Figure 5 3 . Rural m ultilane h ighway 2005 2007 SPFs by a vera ge a nnual r ainfall g roup . Figure 5 4 . Rural t wo l ane r oad 2005 2007 SPFs by d istrict .

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84 Figure 5 5 . Rural t wo l ane r oad 2005 2007 SPFs by p opulation d ensity g roup . Figure 5 6 . Rural t wo l ane r oad 2005 2007 SPFs by a verage a nnual r ainfall g roup .

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85 CHAPTER 6 TRANSFERABILITY THROUGH VARYING MODEL FORM This chapter examines the spatial and temporal transferability of crash estimation methods through the development of local crash prediction models with flexible functional forms. While the previous ch apter saw the potential for locally derived models under the same functional form as used in the HSM, models in this chapter incorporate additional local flexibility through the inclusion of a model coefficient on the segment length, non parametric models stratified by AADT, models segmented into high and low AADT categories, and models segmented by the number of bordering intersections. As in the previous chapters, temporal transferability is analyzed though comparing the performance of each of these mode l scenarios across application in four different temporal specifications. The four temporal specifications include two cases where the model estimation years are the same as the model application years, one case where the estimated model is forecasted to future years, and one case where the estimated model is backcasted to past years. Chapter 3 provides an explanation of the data collection and processing procedures used to construct the data sets used for this analysis on both rural two lane roads and ru ral multilane divided highways. Summary statistics for both facility types can also be seen in Chapter 3. This chapter includes an analysis framework, resulting crashing estimation models for each scenario, analysis of the error in predicted crashes for each crash estimation model, and summary and conclusions of the results from this chapter. Analysis Framework The crash estimation models developed in this chapter seek to address some of the critical questions raised through the examination of HSM calibra tion and locally developed SPFs in HSM analysis. These issues include the larger crash prediction error seen across sites with high

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86 AADT or longer segment lengths, as well as the potential influence of intersection presence on segment crash frequency. To address these issues, four variations of model functional form are examined. First, a coefficient is added to the segment length parameter, second, a non parametric model using categorized AADTs is tested, next a model split into high and low AADTs is ex amined, and finally, a model split into categories based on the number of bordering intersections is examined. Considering both model estimation time periods and all of the segmented models estimated for each facility type, a total of 28 crash estimation models are estimated in this chapter. The predictive performance of the model specifications are compared to each other as well as to the two parameter statewide SPF through their performance on the application data set. Finally, an error regression mode l is developed to further examine the disaggregate predictive capabilities of each crash estimation model. The models developed in this chapter each allow for the inclusion of a model coefficient on the segment length parameter. The length coefficient all ows for a non linear relationship between segment length and predicted crash frequency. While length is previously accounted for by viewing crashes on a per mile basis, a model coefficient increases the model flexibility and treats segment length as an in fluential roadway characteristic. This additional coefficient results in a model form that is slightly different from the two parameter SPF equations discussed in the previous chapters. The three parameter model form is shown in Equation 6 1: (6 1) Where: N SPF = predicted average segment crash frequency for base conditions; = regression parameters; AADT = average annual daily traffic volume (vehicles per day);

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87 L = length of roadway segment (m iles). The non parametric AADT models were first developed with fourteen AADT bins in order to view the unconstrained relationship between AADT and crash frequency. The distribution of segments for the estimated models into their respective AADT bin is gi ven in Table 6 1 for rural multilane divided highways and Table 6 2 for rural two lane roads. Analysis of Rural Multilane Divided Highways Model Estimation The first model estimated in this chapter, the three parameter SPF, did not include intra model segm entation, so a single equation is all that is needed for each time period and facility type. Table 6 3 provides the crash estimation model parameters for both the 2005 2007 and 2008 2010 three parameter SPFs, as well as the statewide two parameter SPFs th at were discussed in the previous chapter and are included for comparison. The resulting coefficients on segment length for models from each time period are significantly less than 1.0. This shows that longer segments have a lower predicted crash frequen cy. Despite the introduction of the new significant coefficient on segment length, the AADT model coefficients are nearly unchanged. While the relationship between segment length and crash frequency is significant, its introduction does not impact the ba ckground relationship between AADT and crash frequency. The second model developed, the binned AADT model, also includes a coefficient on segment length, as well as separate model coefficients for each AADT category. The full set of model parameters is gi ven in Table 6 4 and is compared to the three parameter SPF in Figure 6 1 and Figure 6 2. The visual comparison between the binned AADT models and the three parameter SPFs illustrates the potential for improvement in modeling the relationship between cras h frequency and AADT. In both time periods, the SPF appears to overestimate crashes through the middle range of AADTs. Additionally, the slope of the binned AADT model varies

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88 significantly over different ranges of AADT, shallow at lower AADTs and becomin g noticeably greater after reaching AADTs greater than 22,500. As a result of this divide, 22,500 was selected as the separation point for the low and high AADT groups used in the next model. Based on the trends seen in the binned AADT model, the next mo del developed utilizes two AADT groups with separately modeled negative binomial models for each case. Table 6 5 gives the model parameters for low and high AADT groups through both study time periods. Figure 6 3 and Figure 6 4 illustrate how the low and high AADT groups compare to the three parameter SPF. The two figures show the substantial difference in the modeled relationship between AADT and crash frequency at the low and high AADT groups. While examining these models on the application data set i n the next section will show any potential predictive benefits, it is clear that the two AADT groups allow for increased flexibility in fitting the estimation data set. The final set of models developed is an alternative grouping method, with segments divi ded into three groups based on the number of bordering intersections. While segments can not contain an intersection, segments are split at all intersections and may be bounded by an intersection at either or both sides. Table 6 6 shows the distribution of segments with bordering intersections for the model estimation data set on both rural multilane divided highways and rural two lane roads. The coefficients for the intersection grouped crash estimation models are given in Table 6 7 and Table 6 8 for 20 05 2007 and 2008 2010 respectively. Figure 6 5 and Figure 6 6 provide a graphical comparison of the intersection grouped models for 2005 2007 and 2008 2010 respectively. From this comparison, it is evident that there does not appear to be a substantial d ifference in the modeled relationship between the number of bordering intersections and AADT over most of the range of segments. The 2005 2007 model does begin to show a

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89 difference between the intersection cases as the AADT increases above 25,000 vehicles per day, with increasing intersection count resulting in a lower estimation crash frequency. Model Validation and Comparison Analysis In order to validate and compare the accuracy of crash predictions provided by each crash estimation method, each model i s applied to the validation data set. To analyze the temporal transferability of the different model specifications, each estimation method is applied to four different estimation and application timeframe combinations, using the 2005 through 2007 and 200 8 through 2010 data sets. The mean square error (MSE) and the variance of the squared error for these applications are calculated . The results for the MSE and variance of the squared error are given in Table 6 9. The lowest prediction errors can be seen in the intersection group models for same year application scenarios and in the AADT binned models in the two different year application scenarios. The three parameter SPF, AADT binned model, and intersection grouped model all offer improvements compared to the two parameter SPF. These three methods have average decreased prediction errors of 6.5%, 9.4%, and 12%, respectively, and average improvements in reduction of the variance of the standard error of 29%, 33%, and 42%, respectively, across all four of the application scenarios. The aggregate metrics of MSE and variance of standard error show improvements for the more flexible model structures, and the next step is to introduce an error regression model to examine disaggregate effects of the crash estim ation models. Estimated model coefficients for the error regression are given in Table 6 10. Using this disaggregate analysis, none of the crash estimation methods offer a statistically significant improvement from the two parameter SPF; however, the err or reductions seen by the intersection grouped model and AADT binned model are the first to yield significant results with a confidence greater than 50%.

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90 Analysis of Rural Two Lane Roads Model Estimation Each of the models developed and analyzed for rural multilane divided highways were also examined for rural two lane road segments. The first of these models is the three parameter SPF, for which the model form is given in Equation 6 1. The coefficients derived for this model are given in Table 6 11, as well as the previously discussed two parameter SPF, which is included for comparison purposes. The resulting coefficients on segment length for models from each time period are significantly less than 1.0. This shows that longer segments have a lower pre dicted crash frequency. Despite the introduction of the new significant coefficient on segment length, the AADT model coefficients are nearly unchanged. While the relationship between segment length and crash frequency is significant, its introduction do es not impact the background relationship between AADT and crash frequency. The second model developed, the binned AADT model, also includes a coefficient on segment length. Additionally, rather than treating AADT as a variable with a continuous and force d distribution, each of the AADT bins has a separate model coefficients. The full set of model parameters is given in Table 6 12 and is compared to the three parameter SPF in Figure 6 7 and Figure 6 8. Based on the visual comparison between the binned AA DT models and the three parameter SPFs, it is evident that the SPF fits the relationship between AADT and crash frequency very well, especially at low AADT values. As the AADT increases, the binned model does begin to show some fluctuation. As a result, 12,500 was selected as the separation point for the low and high AADT groups used in the next model. Based on the trends seen in the binned AADT model, the next model developed utilizes two AADT groups with separately estimated negative binomial models for each case. Table 6 13 gives the model parameters for low and high AADT groups through both study periods.

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91 Figure 6 9 and Figure 6 10 illustrate how the low and high AADT groups compare to the three parameter SPF. The two figures show that the low AADT group is nearly identical to the lower range of the three parameter SPF. At higher AADT values, the grouped model allows for a shallower slope in the relationship between crash frequency and AADT. The final set of models developed for rural two lane roa ds is an alternative grouping method, with segments divided into three groups based on the number of bordering intersections. While segments are split such that they do not contain any intersections, they can be bounded by an intersection at either or bot h sides. Table 6 6 shows the distribution of segments with bordering intersections for the model estimation data set. The coefficients for the intersection grouped crash estimation models are given in Table 6 14 and Table 6 15 for 2005 2007 and 2008 2010 respectively. Figure 6 11 and Figure 6 12 provide a graphical comparison of the intersection grouped models for 2005 2007 and 2008 2010 respectively. While there does not appear to be any substantial differences between the three intersection groups, th e pattern is consistent across both time periods, with the zero intersection group estimating a lower crash frequency than the segments with bordering intersections. Model Validation and Comparison Analysis In order to validate and compare the accuracy o f crash predictions provided by each crash estimation method, each model is applied to the validation data set. To analyze the temporal transferability of the different model specifications, each estimation method is applied to four different estimation a nd application timeframe combinations, using the 2005 through 2007 and 2008 through 2010 data sets. The mean square error (MSE) and the variance of the squared error for these applications are calculated . The results for the MSE and variance of the square d error are given in Table 6 16. By these aggregate error metrics, there are no noticeable prediction improvements made from any of

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92 the models with modified functional forms. The two parameter SPF shows the smallest MSE in most cases, with results only o ne to two percent lower than the alternative models. Across all models, the MSE was lower when applied to 2008 2010 than 2005 2007 (regardless of the estimation time period). It is only when results are viewed by categorized AADT groups, that differences begin to be seen between the two parameter SPF and the other models. When separated into two AADT groups, less than 5,000 and greater than or equal to 5,000, the two parameter SPF performs better in the high AADT group, while all of the alternate models show reduced errors on the low AADT segments. In both cases, the improved crash estimations are only by a difference of five to six percent. The MSE error regression model performed for rural two lane roads is given in Table 6 17. As expected based on th e previous results, none of the crash estimation models show a significant improvement or difference from the two parameter SPF. Using an error regression performed on the group of low AADT segments, the previously discussed prediction improvements seen i n the alternate model forms are not statistically significant, as each models shows improvement with a confidence near 50%. As seen throughout the model comparisons and error regression models, the temporal difference in the models is not significant, as there is no difference between models estimated and applied to different years or to the same year. Summary and Conclusions of Varying Model Form This chapter examined several modifications to the standard functional form used to estimate crash frequency o n rural multilane divided highways and rural two lane roads in Florida. The four modified functional forms included a three parameter SPF (with an additional coefficient for segment length), a non parametric model using binned AADTs, a two category model split into high and low AADT, and a three category model split by the number of bordering intersections. Models were compared and analyzed through estimation and application

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93 across four different temporal specifications through the calculation of MSE, var iance of the SE, and error regression models. Beyond the shared temporal conclusion that there is no significant difference between models applied to the same or different years from when they were developed, results differed significantly by facility type . For rural multilane divided highways, there was a clear divide evident in the slope of the relationship between AADT and crash frequency. This divide was seen through the implementation of the binned AADT model and was used to set the border of 22,500 between low and high AADT groups. The crash estimation error analysis showed substantial crash prediction improvements using the three parameter SPF, AADT binned model, and the intersection categorized model. These three alternative functional forms saw aggregate MSE reductions from 6.5% to 12% and average variance of squared error improvements between 29% and 42%. Despite these improvements, the error regression model found that none of the new models showed a significant disaggregate improvement compar ed to the two parameter SPF. On rural two lane roads, all four of the new model functional forms did not offer improved crash prediction methods as compared to the two parameter SPF.

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94 Table 6 1. Rural m ultilane d ivided h ighway AADT b ins Bin Nu mber Lower Bound AADT Upper Bound AADT Number of Segments 2005 2007 2008 2010 1 0 4700 74 92 2 4700 6700 151 107 3 6700 8700 239 217 4 8700 10700 103 145 5 10700 12700 193 159 6 12700 14700 97 135 7 14700 16700 115 113 8 16700 18700 124 80 9 1 8700 20700 75 80 10 20700 22700 27 54 11 22700 24700 69 54 12 24700 26700 70 71 13 26700 28700 18 57 14 28700 N/A 86 77 Table 6 2. Rural t wo l ane r oad AADT b ins Bin Number Lower Bound AADT Upper Bound AADT Number of Segments 2005 2007 2008 2010 1 0 1750 525 563 2 1750 3000 831 905 3 3000 4250 897 911 4 4250 5500 773 838 5 5500 6750 501 418 6 6750 8000 359 327 7 8000 9250 199 161 8 9250 10500 129 102 9 10500 11750 123 117 10 11750 13000 44 39 11 13000 14250 44 44 12 14250 15500 36 47 13 15500 16750 28 28 14 16750 N/A 102 91

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95 Table 6 3. Rural m ultilane d ivided h ighway t wo p arameter and t hree p arameter SPF s Regression Coefficient 2005 2007 Three Parameter 2005 2007 Two Parameter 2008 2010 Three Parameter 2008 2010 Two Parameter Parameter Value Std. Error Parameter Value Std. Error Parameter Value Std. Error Parameter Value Std. Error Constant 8.630 0.529 8.689 0.535 8.171 0.502 8.033 0.540 AADT 1.016 0.055 1.031 0.055 0.957 0.052 0.956 0.056 Length 0.912 0.039 N/A N/A 0.86 4 0.034 N/A N/A Table 6 4. Rural m ultilane d ivided h ighway b inned AADT m odel Regression Coefficient 2005 2007 2008 2010 Parameter Value Std. Error Parameter Value Std. Error Constant 2.233 0.081 1.942 0.080 Length 0.869 0.035 0.827 0.034 Bin 1 2.0 86 0.198 1.811 0.215 Bin 2 1.795 0.152 1.683 0.139 Bin 3 1.826 0.126 1.570 0.124 Bin 4 1.556 0.135 1.567 0.160 Bin 5 1.579 0.131 1.212 0.122 Bin 6 1.452 0.137 1.173 0.153 Bin 7 1.056 0.130 0.919 0.131 Bin 8 1.124 0.164 1.125 0.143 Bi n 9 1.086 0.146 0.715 0.156 Bin 10 0.756 0.172 1.057 0.268 Bin 11 0.819 0.177 0.448 0.143 Bin 12 0.567 0.127 0.240 0.127 Bin 13 0.194 0.126 0.113 0.175 Table 6 5. Rural m ultilane d ivided h ighway l ow and h igh AADT g rouped m odel Regression C oefficient 2005 2007 Low AADT 2005 2007 High AADT 2008 2010 Low AADT 2008 2010 High AADT Parameter Value Std. Error Parameter Value Std. Error Parameter Value Std. Error Parameter Value Std. Error Constant 5.465 0.791 10.100 2.445 5.496 0.776 10.350 2.773 AADT 0.667 0.085 1.171 0.237 0.662 0.084 1.175 0.269 Length 0.872 0.044 0.925 0.073 0.828 0.045 0.855 0.074

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96 Table 6 6. Bordering intersection d istributions Rural Multilane Divided Highways Rural Two Lane Roads Number of Bordering Intersect ions Number of Segments Percentage of Segments Number of Segments Percentage of Segments 0 388 26.9 1061 23.1 1 584 40.5 1976 43.0 2 469 32.5 1554 33.8 Table 6 7. Rural m ultilane d ivided h ighway 2005 2007 i ntersection g rouped m odels Regression Coeffi cient 0 Intersections 1 Intersection 2 Intersections Parameter Value Std. Error Parameter Value Std. Error Parameter Value Std. Error Constant 9.643 0.882 9.535 0.952 5.486 1.051 AADT 1.123 0.089 1.098 0.100 0.689 0.112 Length 0.951 0.066 0.792 0.0 63 0.999 0.074 Table 6 8. Rural m ultilane d ivided h ighway 2008 2010 i ntersection g rouped m odels Regression Coefficient 0 Intersections 1 Intersection 2 Intersections Parameter Value Std. Error Parameter Value Std. Error Parameter Value Std. Error Con stant 8.337 0.837 7.484 0.946 8.164 0.963 AADT 0.973 0.084 0.887 0.100 0.954 0.101 Length 0.886 0.054 0.802 0.070 0.944 0.061

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97 Table 6 9. Rural m ultilane d ivided h ighways MSE and v ariance of SE by c rash e stimation m ethod Estimation Data Set Valid ation Data Set Prediction Error Two Parameter SPF Three Parameter SPF AADT Bins AADT Split Intersection Split 2005 2007 2005 2007 Mean Square Error (MSE) 0.289 0.261 0.272 0.281 0.240 Variance of SE 2.257 1.728 2.317 2.062 1.310 2005 2007 2008 2010 Me an Square Error (MSE) 0.252 0.212 0.197 0.260 0.199 Variance of SE 2.222 0.925 0.520 3.179 0.588 2008 2010 2005 2007 Mean Square Error (MSE) 0.258 0.261 0.249 0.260 0.250 Variance of SE 1.931 2.000 1.716 1.795 1.884 2008 2010 2008 2010 Mean Square Error (MSE) 0.212 0.208 0.199 0.218 0.197 Variance of SE 0.986 0.599 0.517 0.915 0.487 Table 6 10. Rural m ultilane d ivided h ighway MSE r egression Regression Parameter Coefficients Significance B Std. Error Constant 0.427 0.031 0.000 Length 0.67 5 0.022 0.000 AADT 2.869E 05 1.1079E 06 0.000 Three Parameter SPF 0.017 0.033 0.601 Binned AADT 0.024 0.033 0.470 High/Low AADT 0.002 0.033 0.951 Grouped Intersection 0.031 0.033 0.340 Temporal Change 0.002 0.021 0.926

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98 Table 6 11. Rural t wo l ane r oad t wo p arameter and t hree p arameter SPF s Regression Coefficient 2005 2007 Three Parameter 2005 2007 Two Parameter 2008 2010 Three Parameter 2008 2010 Two Parameter Parameter Value Std. Error Parameter Value Std. Error Parameter Value Std. Error P arameter Value Std. Error Constant 7.415 0.282 7.577 0.275 7.297 0.277 7.496 0.282 AADT 0.887 0.033 0.917 0.032 0.873 0.033 0.910 0.033 Length 0.837 0.025 N/A N/A 0.838 0.025 N/A N/A Table 6 12. Rural t wo l ane r oads b inned AADT m odel Regression C oefficient 2005 2007 2008 2010 Parameter Value Std. Error Parameter Value Std. Error Constant 1.292 0.093 1.259 0.101 Length 0.831 0.025 0.838 0.025 Bin 1 2.324 0.130 2.315 0.135 Bin 2 1.763 0.110 1.882 0.117 Bin 3 1.435 0.104 1.328 0.110 Bin 4 1.295 0.105 1.226 0.111 Bin 5 0.982 0.108 0.953 0.118 Bin 6 0.836 0.112 0.799 0.121 Bin 7 0.691 0.122 0.681 0.136 Bin 8 0.626 0.137 0.665 0.152 Bin 9 0.436 0.132 0.225 0.137 Bin 10 0.701 0.206 0.250 0.194 Bin 11 0.107 0.171 0.422 0.185 Bin 12 0.158 0.185 0.055 0.172 Bin 13 0.172 0.196 0.139 0.205 Table 6 13. Rural t wo l ane r oad l ow and h igh AADT g rouped m odel Regression Coefficient 2005 2007 Low AADT 2005 2007 High AADT 2008 2010 Low AADT 2008 2010 High AADT Parameter Value Std. Error Parameter Value Std. Error Parameter Value Std. Error Parameter Value Std. Error Constant 7.021 0.335 0.065 5.859 7.325 0.333 0.970 5.253 AADT 0.839 0.040 0.139 0.603 0.876 0.040 0.213 0.542 Length 0.835 0.025 0.823 0.095 0.845 0.026 0.76 4 0.105

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99 Table 6 14. Rural t wo l ane r oads 2005 2007 i ntersection g rouped m odels Regression Coefficient 0 Intersections 1 Intersection 2 Intersections Parameter Value Std. Error Parameter Value Std. Error Parameter Value Std. Error Constant 7.038 0. 565 7.717 0.434 7.291 0.498 AADT 0.840 0.066 0.925 0.051 0.872 0.058 Length 0.772 0.050 0.885 0.038 0.825 0.043 Table 6 15. Rural t wo l ane r oads 2008 2010 i ntersection g rouped m odels Regression Coefficient 0 Intersections 1 Intersection 2 Intersecti ons Parameter Value Std. Error Parameter Value Std. Error Parameter Value Std. Error Constant 7.075 0.558 7.484 0.403 7.395 0.520 AADT 0.840 0.065 0.902 0.047 0.880 0.062 Length 0.889 0.051 0.845 0.036 0.808 0.047 Table 6 16. Rural t wo l ane MSE and v ariance of SE by c rash e stimation m ethod Estimation Data Set Validation Data Set Prediction Error Two Parameter SPF Three Parameter SPF AADT Bins AADT Split Intersection Split 2005 2007 2005 2007 Mean Square Error (MSE) 0.109 0.110 0.108 0.108 0.112 Variance of SE 1.213 1.399 1.361 1.363 1.365 2005 2007 2008 2010 Mean Square Error (MSE) 0.075 0.077 0.076 0.077 0.078 Variance of SE 0.083 0.106 0.095 0.099 0.124 2008 2010 2005 2007 Mean Square Error (MSE) 0.109 0.110 0.109 0.112 0.110 Varianc e of SE 1.198 1.421 1.396 1.594 1.342 2008 2010 2008 2010 Mean Square Error (MSE) 0.075 0.077 0.077 0.077 0.078 Variance of SE 0.081 0.108 0.101 0.107 0.113

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100 Table 6 17. Rural t wo l ane r oads MSE r egression Regression Parameter Coefficients Signific ance B Std. Error Constant 0.183 0.013 0.000 Length 0.225 0.009 0.000 AADT 3.535E 05 1.2104E 06 0.000 Three Parameter SPF 0.002 0.014 0.912 Binned AADT 0.000 0.014 0.971 High/Low AADT 0.002 0.014 0.906 Grouped Intersection 0.002 0.014 0.858 Tem poral Change 0.000 0.009 0.976

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101 Figure 6 1 . Rural m ultilane d ivided h ighway 2005 2007 b inned AADT c omparison . Figure 6 2 . Rural m ultilane d ivided h ighway 2008 2010 b inned AADT c omparison .

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102 Figure 6 3 . Rural m ultilane d ivided h ighway 2005 200 7 l ow and h igh AADT g rouped m odel . Figure 6 4 . Rural m ultilane d ivided h ighway 2008 2010 l ow and h igh AADT g rouped m odel .

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103 Figure 6 5 . Rural m ultilane d ivided h ighway 2005 2007 i ntersection g rouped m odel . Figure 6 6 . Rural m ultilane d ivided i ig hway 2008 2010 i ntersection g rouped m odel .

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104 Figure 6 7 . Rural t wo l ane r oad 2005 2007 b inned AADT c omparison . Figure 6 8 . Rural t wo l ane r oad 2008 2010 b inned AADT c omparison .

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105 Figure 6 9 . Rural t wo l ane r oad 2005 2007 l ow and h igh AADT g roupe d m odel . Figure 6 10 . Rural t wo l ane r oad 2008 2010 l ow and h igh AADT g rouped m odel .

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106 Figure 6 11 . Rural t wo l ane r oads 2005 2007 i ntersection g rouped m odel . Figure 6 12 . Rural t wo l ane r oads 2008 2010 i ntersection g rouped m odel .

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107 CHAPTER 7 SUM MARY AND CONCLUSIONS The publication of the HSM in 2010 and corresponding adoption of its crash estimation methods in the following years has led to the importance of examining the most effective methods of transferring the HSM crash methods for applicatio n to local conditions. The HSM provides a detailed procedure for the development of a single statewide calibration factor, but leaves an inconclusive suggestion that the accuracy of crash estimation models can be improved through localized calibration fac tors or recalculation of model coefficients through local SPF development. This research examined the spatial transferability of HSM crash estimation models through statewide calibration, intra state localized calibration (FDOT districts, population densi ty groups, and average annual rainfall groups), state SPF calculation, and SPF calculation for the three intra state groups. The temporal aspects of crash estimation model transferability were also examined in order to determine the effects of different t ime periods on the accuracy of crash predictions. This chapter includes a summary of the work completed and results in data collection and preparation, HSM calibration, and SPF development. This is followed by overall conclusions and recommendations from this project and possibilities for future extensions of research on this topic. Summary of Research Data Summary For the investigation of the spatial and temporal transferability of crash estimation models, data were collected related to three primary are as; (1) roadway attributes, (2) historical crash data, and (3) segment location. Roadway attribute data included both geometric and operational characteristics and were collected from yearly end of year archives of the FDOT

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108 RCI. Yearly historical crash d ata, consisting of all fatal and injury crashes, were collected from the FDOT CARS database. Segment location attributes were recorded from census data (for population density groups) and historical state weather databases (for average annual rainfall gro ups). All data attributes were collected for 2005 through 2010 for both rural multilane divided highways and rural two lane roads. Using the FDOT RCI data, homogeneous segments were created inspected for data consistency and completeness. The segmentatio n and data validation process resulted in analysis sample sets of 790.56 miles across 2,056 segments for rural multilane divided highways and 2,769.06 miles across 6,499 segments for rural two lane roads. Seventy percent of these segments for each facilit y type were used for model development, while the remaining thirty percent were used for model application. HSM Calibration Summary Chapter 4 described the calibration of HSM crash estimation models, as performed for both facility types under the statewide case as well as the three intra state localized groups. Calibration factors were developed and applied for two different time periods, 2005 through 2007 and 2008 through 2010, resulting in four temporal application scenarios. Across all spatial and temp oral specifications, a total of 64 calibration factors were developed and analyzed for their predictive accuracy. For both facility types, statewide calibration proved to yield substantially lower MSE values across all segments and, through the development of error regression models, showed significantly smaller errors than seen with the application of the uncalibrated HSM models. Compared to statewide calibration, the three localized calibration alternatives (FDOT district, population density group, and a verage annual rainfall group) did not show a significant difference in crash estimation accuracy. Aggregate MSE analysis resulted in higher errors within

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109 the subset of segments with higher AADTs. The error regression models also illustrated that increasi ng AADT, as well as increasing length, contribute to a statistically significant increase in MSE. Analysis of the MSEs and the error regression models showed that there was not a significant difference across the two time frames. Models calibrated on ei ther time frame performed similarly, both in aggregate terms and in the error regression models, performed similarly across the same validation data set. This downplays the importance of frequent updates to calibration factors, as small changes in the cal ibration factor did not offer significantly improved accuracy of crash estimations. The results of the error analysis with regards to spatial and temporal calibration transferability emphasize the significance of statewide calibration, as recommended by t he HSM, while also providing states with the information that it is not necessary to invest in detailed localized calibration factors or update calibration factors on a yearly basis. SPF Development Summary Chapter 5 introduced locally developed SPFs as an alternative to calibration. As locally developed SPFs consist of the recalculation of crash estimation model coefficients, these SPFs allow for flexibility in modeling the relationship between AADT and estimated crash frequency. The development of local SPFs was performed on both facility types for the statewide case as well as the three intra state localized groups. Similarly to calibration factors, SPFs were developed and applied for two different time periods, 2005 through 2007 and 2008 through 2010, resulting in four temporal application scenarios. Across all spatial and temporal specifications, a total of 62 SPFs were developed and analyzed for their predictive accuracy. SPF results for rural multilane divided highways showed that prediction models using district based SPFs and population density based SPFs performed slightly better than statewide

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110 calibration (reduced MSEs for 10 out of 12 and 9 out of 12 AADT categories, respectively). Crash estimations using district SPFs also had the benefit of consistently showing substantially lower variance of the squared errors. A lower variance of crash estimation errors is significant in decreasing the propensity for large estimation errors. Error regression models did not show any improvement in crash es timation using statewide or locally derived SPFs as compared statewide calibration. Aggregate analysis results for rural two lane roads showed that crash estimation with population density based SPFs had improved accuracy compared to statewide calibrated HSM models, seen across 9 out of the 12 AADT categories. The error regression models for rural two lane roads also showed a possible improvement through crash estimation with population density based SPFs; however, this result was only significant at a 30 % confidence level. The analysis results of temporal transferability using locally developed SPFs mirrored those seen in Chapter 4, showing no significant difference in errors for any of the temporal estimation and application specifications. This lack o f temporal effects, in combination with the potential for improved accuracy through locally developed SPFs, point towards future resources being more efficiently spent at one time to develop local SPFs rather than spread out for frequent calibration of pre existing crash estimation models. Summary of Alternate Model Forms Chapter 6 examined several modifications to the standard functional form used to estimate crash frequency on rural multilane divided highways and rural two lane roads in Florida. The fou r modified functional forms included a three parameter SPF (with an additional coefficient for segment length), a non parametric model using binned AADTs, a two category model split into high and low AADT, and a three category model split by the number of bordering intersections. Models were compared and analyzed through estimation and application

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111 across four different temporal specifications through the calculation of MSE, variance of the SE, and error regression models. Beyond the shared temporal conclus ion that there is no significant difference between models applied to the same or different years from when they were developed, results differed significantly by facility type. For rural multilane divided highways, there was a clear divide evident in the slope of the relationship between AADT and crash frequency. This divide was seen through the implementation of the binned AADT model and was used to set the border of 22,500 between low and high AADT groups. The crash estimation error analysis showed su bstantial crash prediction improvements using the three parameter SPF, AADT binned model, and the intersection categorized model. These three alternative functional forms saw aggregate MSE reductions from 6.5% to 12% and average variance of squared error improvements between 29% and 42%. However, the error regression model found that these models only showed a significant disaggregate improvement compared to the two parameter SPF at a 50% confidence level. On rural two lane roads, all four of the new mod el functional forms did not offer improved crash prediction methods as compared to the two parameter SPF. Conclusions and Future Expansion As a result of this research, there are both broad conclusions that can be drawn across any crash estimation method a nd specific conclusions within a given facility type. Applicable to both facility types and for both HSM calibration and local SPF development, results for the analysis of temporal transferability showed that there is not a significant difference between the crash estimation accuracy of models developed from a different time period than when they are applied. In this case, models estimated or calibrated based on the three years before or after the application time period were just as suitable as those bas ed on the same application time period. This creates a six year time frame with equal temporal transferability. This result can be used to

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112 support increased duration between model updates (calibration or SPF estimation), that will yield a more effective use of time and money. Also evident across both facility types, were the trends of increasing MSE with increasing segment AADT and length. Finally, statewide model calibration resulted in improved crash estimation accuracy when compared to the uncalibrat ed model, showing the significance of statewide HSM calibration. Further improvements were not found through calibration by FDOT district, population density group, or average annual rainfall group, despite substantial variation between the statewide cali bration factor and the intra state group calibration factors. Using the locally developed SPFs in Chapter 5, aggregate error results showed the potential for modeling improvements across both facility types. Rural multilane divided highways experienced lo wer MSE values, especially on high AADT sites, using FDOT district based SPFs and population density group SPFs. Rural two lane road SPFs displayed crash estimation accuracy improvements using the population density SPFs. These locally developed SPFs for both facility types are recommended for statewide implementation for crash frequency estimation. The observed reduction in the MSE and variance of the SE offer immediate improvement in crash prediction, especially across segments with high AADTs, which a re often considered high priority segments. There is the opportunity for future work branching from the conclusions developed here, for both spatial and temporal transferability. Analysis across additional facility types, such as urban road segments (curr ently limited by roadway attribute availability), would allow for the possible expansion of the ideas presented in this research. Expansion of the temporal investigation into additional years, would allow for testing beyond the current six year time frame , potentially leading to crash estimation models that can be confidently applied over a

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113 wider time period. Finally, with a larger and more diverse pool of segment attributes, it would be possible to consider additional alternative functional forms that ut ilize roadway characteristics directly in the model. These models would be able to examine the spatial transferability of multiple roadway attribute relationships and allow for local ly specific relationships rather than relying on externally developed CMF s. The modeled interaction of AADT with these additional roadway characteristics may also allow for a better understanding of the relationship between AADT and crash frequency, as well as more accurate crash predictions.

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114 APPENDIX COUNTY CALIBRATION GROUPS Appendix A provides the complete list of county groups used in the alternative calibration analysis. The groups include FDOT districts, county population density, and county average annual rainfall. Table A 1. List of c ounty c alibration g roups C ounty County Number Population Density FDOT District Population Density Group Average Annual Rainfall Group Alachua 26 283 2 3 3 Baker 27 46 2 4 2 Bay 46 223 3 3 1 Bradford 28 97 2 4 3 Brevard 70 535 5 2 3 Broward 86 1445 4 1 2 Calhoun 47 26 3 4 1 Charlotte 1 235 1 3 4 Citrus 2 243 7 3 3 Clay 71 316 2 3 3 Collier 3 161 1 3 3 Columbia 29 85 2 4 2 De Soto 4 55 1 4 4 Dixie 30 23 2 4 2 Duval 72 1134 2 1 3 Escambia 48 453 3 2 1 Flagler 73 197 5 3 3 Franklin 49 22 3 4 1 Gadsden 50 90 3 4 2 Gil christ 31 48 2 4 2 Glades 5 16 1 4 4 Gulf 51 28 3 4 1 Hamilton 32 29 2 4 3 Hardee 6 43 1 4 4 Hendry 7 34 1 4 4 Hernando 8 366 7 3 3 Highlands 9 97 1 4 4 Hillsborough 10 1205 7 1 3 Holmes 52 42 3 4 1 Indian River 88 274 4 3 3 Jackson 53 54 3 4 2 Jefferson 54 25 3 4 2 Lafayette 33 16 2 4 2 Lake 11 317 5 3 4 Lee 12 789 1 2 3 Leon 55 413 3 2 1 Levy 34 36 2 4 2

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115 Table A 1 Continued. List of c ounty c alibration g roups County County Number Population Density FDOT District Population Density Group Average Annual Rainfall Group Liberty 56 10 3 4 1 Madison 35 28 2 4 3 Manatee 13 435 1 2 3 Marion 36 209 5 3 3 Martin 89 269 4 3 3 Miami Dade 87 1315 6 1 2 Monroe 90 74 6 4 4 Nassau 74 113 2 4 3 Okaloosa 57 194 3 3 1 Okeechobee 91 52 1 4 4 Oran ge 75 1268 5 1 4 Osceola 92 202 5 3 4 Palm Beach 93 670 4 2 2 Pasco 14 622 7 2 3 Pinellas 15 3347 7 1 4 Polk 16 335 1 3 4 Putnam 76 102 2 4 3 Santa Rosa 58 150 3 3 1 Sarasota 17 683 1 2 2 Seminole 77 1367 5 1 4 St. Johns 78 316 2 3 3 St. Lucie 9 4 486 4 2 3 Sumter 18 171 5 3 3 Suwannee 37 60 2 4 2 Taylor 38 22 2 4 2 Union 39 64 2 4 3 Volusia 79 449 5 2 3 Wakulla 59 51 3 4 1 Walton 60 53 3 4 1 Washington 61 43 3 4 1

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116 LIST OF REFERENCES American Association of State Highway and Transporta tion Officials (AASHTO) . 2010. Highway Safety Manual. AASHTO, Washington, D.C. Banihashemi, M. Highway Safety Manual, New Model Parameters vs. Calibration of Crash Prediction Models. 2011. Presented at the 90th Annual Meeting of the Transportation Researc h Board, Washington, D.C. Benac, J., L. Nelson Taullie, L. A. Spell, C. Wright, and J. J. Zogby. State of Florida Traffic Records Assessment. 2006. Florida Departmen t of Transportation. Bonneson, J. and P. McCoy. 1997. Effect of Median Treatment on Urban Arterial Safety: An Accident Prediction Model . Transportation Research Record 1581 , pp. 27 3 6. Transportation Researc h Board, Washington, D.C. Bornheimer, C., S. D. Schrock, M. H. Wang, and H. Lubliner. 2012. Developing a Regional Safety Performance Func tion for Rural Two Lane Highways. Presented at the 91st Annual Meeting of the Transportation Re search Board, Washington, D.C. Bowman, B., R. Vecellio, and J. Miao. 1995. Vehicle and Pedestrian Accident Models for Median Locations. Journal of Transportatio n Engineering , Novem ber/December, pp. 531 537. Brimley, B. K., M. Saito, and G. G. Schultz. 2012. Calibration of the Highway Safety Manual Safety Performance Function and Development of New Models for Rural Two Lane Two Way Highways. Presented at the 91st Annual Meeting of the Transportation Researc h Board, Washington, D.C. Council, F., E. Zaloshnja, T. Miller, and B. Persaud. 2005. Crash Cost Estimates by Maximum Police Reported Injury Severity Within Selected Crash Geometries. Publication FHWA HRT 05 05 1. Federal Highway Administration, US Depart ment of Transportation, Washington, D.C. Federal Highway Administration (FHWA). 2012. Toward Zero Deaths: A National Strategy on Highway Safety . US Department of Transportation, Washington D . C. http://safety.fhwa.dot.gov/tzd/ . Accessed April 12, 2012. Florida Department of Transportation (FDOT). 2013. District Map. FDOT Public Information Office, Tallahassee, F lorida . http://www.dot.state.fl.us/publicinformationoffice/images/District%20Map%20 %20Lg.jpg . Accessed December 20, 2013. Florida Highway Patrol. 2011. FHP Policy on Crash Reports. Florida Department of Highway Safety and Motor Vehicles. http://www.flhsmv.gov/fhp/misc/Floridalaw/ReportForm.htm . Accessed July 25, 2011.

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117 Garber, N. and A. Ehrhart. 2000. The Effect of Speed, Flow, and Geometric Characteristics on Crash Rates for Different Types of Virginia Highways. VTRC Report. Charlottesville , Virginia. Garber, N. J., P. R. Haas, and C. Goose. 2010. Development of Safety Performance Functions for Two Lane Roads Maintained by the Virginia Depar tment of Transportation . FHWA/VTRC 10 R25. Virginia Department of Transportation, Richmond, VA. Greibe, P. Accident Prediction Models for Urban Roads. 2003. Accident Analysis and Prevention 35(2) , pp. 273 285. Griffin, L. I. and K. K. Mak. 1987. The Be nefits to Be Achieved from Widening Rural, Two Lane Farm to Market Roads in Texas . Report No. IAC (86 86) 1039. Texas Transportation Institute, College Station, T exas . Hadayeghi, A., A. S. Shalaby, and B. N. Persaud. 2010. Development of Planning Level T ransportation Safety Tools Using Geographically Weighted Poisson Regression. Accident Analysi s and Prevention 42 , pp. 676 688. Hadi, M. A., J. Aruldhas, L. F. Chow, and J. A. Wattleworth. 1995. Estimating Safety Effects of Cross Section Design for Various Highway Types Using Negative Binomial Regression. Transportation Research Record 1500 , pp. 169 177. Transportation Researc h Board, Washington, D.C. Hamidi, A., M. D. Fontaine, and M. J. Demetksy. 2010. A Planning Level Methodology for Identifying High Cr . FHWA/VTRC 11 R4 . Virginia Department of Transportation, Richmond, VA. Harwood, D. W. 1986. Multilane Design Alternatives for Improving Suburban Arterials . NCHRP 282. Transportation Research Board, Washington , D . C. Harwood, D. W., K. M. Bauer, K. R. Richard, D. K. Gilmore, J. L. Graham, I.B. Potts, D. J. Torbic, and E. Hauer. 2007. Methodology to Predict the Safety Performance of Urban and Suburban Arterials, NCHRP Web Only Document 129, Phases I and II. National Cooperative Highway Research Program, Transportation Re search Board, Washington, D. C . http://onlinepubs.trb.org/onlinepubs/nchrp/nchrp_w129p1&2.pdf . Accessed July 25, 2011. Harw ood, D.W., F. M. Council, E. Hauer, W. E. Hughes, and A. Vogt. 2000. Prediction of the Expected Safety Performance of Rural Two Lane Highways. McLean, Virginia: Federal Highway Administration, Turner Fairbank Highway Research Center, and Midwest Research I nstitute. Harwood, D. W., E. R. Kohlman Rabbani, K. R. Richard, H. W. McGee, and G. L. Gittings. 2003. Systemwide Impact of Safety and Traffic Operations Design Decisions for 3R Projects . NCHRP 486. Transportation Research Board, Washington , D . C.

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122 BIOGRAPHICAL SKETCH Phillip Haas earned his Bachelor of Science degree in c ivil e ngineering from the University of Virginia in 2007. He received his Master of Science degree in c ivil e ngineering in 2009 from the University of Virginia. He will receive his Doctorate of Philosophy d egree in c ivil e ngineering in 2015 from the University of Florida.