Center for Accessibility and Safety for an Aging Population

Florida State University In Partnership with Florida A&M University and University of North Florida

RESEARCH FINAL REPORT

Micro-Analysis of Collisions in Crash Clusters: Creating Crash Patterns

Thobias Sando Eren Ozguven

Yassir Abdelrazig Ren Moses

Sai Saylesh Vemulapalli Michelle Angel

gainesville.com

utc.fsu.edu

Micro-Analysis of Collisions in Crash Clusters: Creating Crash Patterns

Dr. T. Sando Professor School of Engineering University of North Florida

Sai Saylesh Vemulapalli Graduate Student School of Engineering Florida State University

Dr. E. Ozguven Assistant Professor Civil and Environmental Engineering FAMU-FSU College of Engineering

Michelle Angel Research Associate School of Engineering University of North Florida

Dr. Y. Abdelrazig Associate Professor Civil and Environmental Engineering FAMU-FSU College of Engineering

Dr. R. Moses Professor Civil and Environmental Engineering FAMU-FSU College of Engineering

A Report on Research Sponsored by

Center for Accessibility and Safety for an Aging Population

Florida State University in Partnership with Florida A&M University and University of North Florida

August 2019

Technical Report Documentation Page 1. Report No.

2. Government Accession No.

3. Recipient's Catalog No.

4. Title and Subtitle Micro-Analysis of Collisions in Crash Clusters: Creating Crash Patterns

5. Report Date August 2019

6. Performing Organization Code

7. Author(s) Thobias Sando (PI), Eren Ozguven (Co-PI), Yassir Abdelrazig (Co-PI), Ren Moses (Co-PI), Sai Saylesh Vemulapalli (Research Assistant), and Michelle Angel (Research Associate)

8. Performing Organization Report No.

9. Performing Organization Name and Address Center for Accessibility and Safety for an Aging Population 2525 Pottsdamer St., Suite A 129, Tallahassee FL 32310

10. Work Unit No. 11. Contract or Grant No.

12. Sponsoring Agency Name and Address Research and Innovative Technology Administration 1200 New Jersey Ave., SE Washington, D.C. 20590

13. Type of Report and Period Covered

November 2018-August 2019

14. Sponsoring Agency Code

15. Supplementary Notes

16. Abstract The population in the United States is steadily aging. Consequently, a concentrated effort in recent years is being made to better understand the factors that affect elderly crash occurrence. The elderly are involved in different types of crashes depending on the roadway location. Intersections are locations of high crash risk for the elderly drivers. This study focuses on elderly drivers (age 65 and older) to better understand the types of crashes experienced at and near signalized intersections. The study examines if elements of intersection approaches, such as approach lane type, the number of turning lanes, and approach signal type, may be contributing factors to the likelihood of elderly driver crash involvement. Intersection crash data involving elderly drivers was obtained from crash cluster sites in ten urban counties in Florida. To estimate the likelihood of elderly drivers being involved in intersection crashes, crash data was evaluated using binary response regressions (logit, cauchit, and complimentary log-log) in a Bayesian framework. Leave-one-out cross validation was used to assess the predictive power of the estimated models. A model using cauchit link function was observed to have the best predictive accuracy. Results indicate that intersection type (2.976), travel street (-1.248), crash time (-2.311), number of right turning lanes (1.308), presence of a work zone (2.933), and age of driver not at-fault (0.465) , significantly contribute to elderly driver crash involvement. These findings can assist transportation agencies when developing countermeasures for intersection crashes involving elderly drivers. 17. Key Words Aged drivers, elderly drivers, intersection crashes

18. Distribution Statement

19. Security Classif. (of this report) Unclassified

20. Security Classif. (of this page) Unclassified

21. No. of Pages 32

22. Price

ii

Table of Contents

LIST OF FIGURES ...................................................................................................................... IV

LIST OF TABLES ........................................................................................................................ IV

LIST OF ABBREVIATIONS ........................................................................................................ V

ACKNOWLEDGMENTS ............................................................................................................ VI

DISCLAIMER ............................................................................................................................. VII

ABSTRACT ............................................................................................................................... VIII

CHAPTER 1 INTRODUCTION .................................................................................................... 1

1.1 BACKGROUND AND MOTIVATION .......................................................................................... 1 1.2 RESEARCH OBJECTIVE ........................................................................................................... 2

CHAPTER 2 LITERATURE REVIEW ......................................................................................... 3

CHAPTER 3 METHODOLOGY ................................................................................................... 5

3.1 STUDY AREA .......................................................................................................................... 5 3.2 DATA COLLECTION AND EXTRACTION .................................................................................... 6 3.3 BINARY REGRESSION MODELS ................................................................................................ 6 3.4 BAYESIAN INFERENCE SPECIFICATION ................................................................................... 8 3.5 MARKOV CHAIN MONTE CARLO (MCMC) ALGORITHM ....................................................... 9 3.6 MODEL PREDICTION ACCURACY ............................................................................................ 9

CHAPTER 4 CASE STUDY APPLICATION RESULTS .......................................................... 11

4.1 DESCRIPTIVE STATISTICS ..................................................................................................... 11 4.2 MODEL RESULTS .................................................................................................................. 13

CHAPTER 5 DISCUSSIONS ...................................................................................................... 16

5.1 INTERSECTION TYPE ............................................................................................................. 16 5.2 AT-FAULT LANE POSITION .................................................................................................... 16 5.3 NUMBER OF APPROACH RIGHT-TURN LANE .......................................................................... 16 5.4 TRAVEL STREET ................................................................................................................... 17 5.5 CRASH TIME ......................................................................................................................... 17 5.6 WORK ZONE ......................................................................................................................... 17 5.7 CRASH TYPE ......................................................................................................................... 18 5.8 NOT AT-FAULT DRIVER AGE ................................................................................................. 18 5.9 MODEL PREDICTION ACCURACY ........................................................................................... 18

CHAPTER 6 CONCLUSIONS & FUTURE RECOMMENDATIONS ...................................... 20

REFERENCES ............................................................................................................................. 22

iii

List of Figures

Figure 3. 1 Florida Counties included in the study ......................................................................... 5

Figure 4.1 Distribution of Elderly Driver Crashes per Florida County and Crash Type .............. 13

List of Tables

Table 4.1 Predictor Variables for the Binary Regression ............................................................. 11

Table 4.2 Model Results for all Link Functions ........................................................................... 15

Table 5.1 Cross validation of binary models ................................................................................ 19

iv

List of Abbreviations

ASAP Center for Accessibility and Safety for an Aging Population BCI Bayesian Credible Interval FAMU Florida A&M University FDOT Florida Department of Transportation FSU Florida State University LOOIC Leave-One-Out Information Criteria MCMC Markov Chain Monte Carlo NHTSA National Highway Traffic Safety Administration PSIS Pareto Smoothed Importance Sampling SMFL Safe Mobility for Life Coalition UNF University of North Florida USDOT United States Department of Transportation

v

Acknowledgments

This project was supported by the United States Department of Transportation (USDOT)

grant DTRT13-G-UTC42, and administered by the Center for Accessibility and Safety for an

Aging Population (ASAP) at the Florida State University (FSU), Florida A&M University

(FAMU), and University of North Florida (UNF). The authors also thank the Florida Department

of Transportation (FDOT) for providing the roadway data. The opinions, results, and findings

expressed in this manuscript are those of the authors and do not necessarily represent the views

of the USDOT, FDOT, the Center for Accessibility and Safety for an Aging Population, FSU,

FAMU, or UNF.

vi

Disclaimer

The contents of this report reflect the views of the authors, who are responsible for the

facts and the accuracy of the information presented herein. This document is disseminated under

the sponsorship of the U.S. Department of Transportation’s University Transportation Centers

Program, in the interest of information exchange. The U.S. Government assumes no liability for

the contents or use thereof.

vii

Abstract

The population in the United States is steadily aging. Consequently, a concentrated effort

in recent years is being made to better understand the factors that affect elderly crash occurrence.

The elderly are involved in different types of crashes depending on the roadway location.

Intersections are locations of high crash risk for the elderly drivers. This study focuses on elderly

drivers (age 65 and older) to better understand the types of crashes experienced at and near

signalized intersections. The study examines if elements of intersection approaches, such as

approach lane type, the number of turning lanes, and approach signal type, may be contributing

factors to the likelihood of elderly driver crash involvement. Intersection crash data involving

elderly drivers was obtained from crash cluster sites in ten urban counties in Florida. To estimate

the likelihood of elderly drivers being involved in intersection crashes, crash data was evaluated

using binary response regressions (logit, cauchit, and complimentary log-log) in a Bayesian

framework. Leave-one-out cross validation was used to assess the predictive power of the

estimated models. A model using cauchit link function was observed to have the best predictive

accuracy. Results indicate that intersection type (2.976), travel street (-1.248), crash time (-

2.311), number of right turning lanes (1.308), presence of a work zone (2.933), and age of driver

not at-fault (0.465) , significantly contribute to elderly driver crash involvement. These findings

can assist transportation agencies when developing countermeasures for intersection crashes

involving elderly drivers.

viii

Chapter 1 Introduction

1.1 Background and Motivation

People aged 65 years and above represent the fastest-growing segment of the population

in the United States (U.S.). In 2014, the number of people aged 65 and older represented 14.5%

of the U.S. population (about one in every seven Americans), and this number is expected to

become 21.7% of the population by 2040 (1). As the elderly population increases, so does their

proportion within the population of drivers. Records show that licensed elderly drivers

comprised 15% of the total driving population in 2006, compared to 18% in 2014 (2). The

increased number of elderly drivers presents traffic safety challenges for transportation agencies.

The National Highway Traffic Safety Administration (NHTSA) (3) observed an 8.8% increase in

fatalities for drivers aged 65 years and above from the year 2014 to 2015. This percentage

increase was more than a 7.2% average increase for all age groups. Surprisingly, most of these

crashes occurred at intersections (4). For example, from 2005 to 2007, intersection crashes

comprised 53.9% of crashes involving elderly drivers in the U.S. (5).

Many driving maneuvers that are performed instinctively by younger drivers become

difficult to perform with age (6). Most of these maneuvers involve intersections, such as

negotiating left turns across traffic and traversing intersections. As a result, elderly drivers can be

vulnerable at intersections and have greater potential to be involved in intersection crashes. In

these type of crashes, the elderly are more likely to be at-fault, i.e., fail to yield the right of way,

disregard the traffic signal, or turning left (7). About 66% of elderly drivers’ inadequate

surveillance errors and 77% of their gap or speed misjudgment are made when initiating a left

turn at an intersection (8). It is approximated that for each year increase in age among seniors,

the likelihood of being involved in a left turn crash at an intersection increases by 8% (9).

1

Moreover, elderly drivers are overinvolved in turning collisions, especially those related to

initiating left turn maneuvers (4).

Therefore, to protect elderly drivers and all road users, it is critical to understand

intersection characteristics that may influence crash occurrence. More specifically, it is useful to

understand the characteristics that may have a direct impact on the behavior of an approaching

elderly driver. These characteristics are features that a can be seen by a driver when approaching

or traversing an intersection, such as intersection type, approach signal type, and number of turn

lanes. In addition, the study includes other driver attributes and environmental aspects that can

amplify the effect of intersection approach characteristics on elderly driver crash involvement.

Considering the scarcity of studies specific to aged driver safety on explicit roadway sections,

this study offers useful information for transportation agencies when developing

countermeasures for lowering the risk of elderly driver intersection crashes.

1.2 Research Objective

Many studies (4, 11, 12, 14, 15) on traffic safety involving elderly drivers have focused

on drivers’ traits, crash characteristics, environmental attributes, and corresponding effects on

occurrence and severity of crashes. Few studies have investigated the relationship between such

attributes, specifically, approach characteristics at signalized intersections, and their impact on

the likelihood of elderly drivers being at-fault or not at-fault in a crash. This study investigates

factors that influence the involvement of aged drivers in intersection crashes by including

intersection approach characteristics. Results from the analysis of these variables will help traffic

safety agencies in devising countermeasures to decrease elderly driver crash involvement on a

specific section of a roadway.

2

Chapter 2 Literature Review

Elderly drivers are more involved in crashes per mile driven compared to younger

drivers, with the exception of drivers under the age of 24 (10). Cicchino and McCartt (8)

observed that a critical reason for 97% of crashes involving elderly drivers was the result of

driver error. The same study (8) suggested that among elderly drivers who made critical errors,

33% made inadequate surveillance errors, and 6% made gap or speed misjudgment errors. Other

common errors made by elderly drivers involved in crashes include illegal maneuvers,

daydreaming, and errors due to medical events. A study by Oxley et al.(11) suggested that failure

to yield the right of way, search and detection errors, and evaluation errors are the most common

errors made by elderly drivers. Although terminologies used to describe errors are different, both

studies suggested similar errors as a reason behind elderly driver vulnerability. In addition,

Oxley et al. (11) specifically identified inappropriate gap selection and task complexity as main

factors influencing elderly driver crashes.

A few studies have investigated the role of the complexity of intersections on increasing

crash risk for elderly drivers (12). Research findings have identified that elderly drivers are more

likely to encounter crashes at intersections than younger drivers (4). A study by NHTSA (13)

observed that elderly drivers have an increased risk of being at-fault in a crash occurring at

locations, such as driveways, alleys, and intersections, and specifically intersections controlled

by stop or yield signs. There is an increase in the proportion of crashes at crossroads and T-

junctions as age increases when considering drivers aged 60 years or older only (14). Generally,

intersections are dangerous locations for drivers, pedestrians, and bicyclists, regardless of road

user age. This is due to the complexity and higher number of traffic conflicts associated with

individual intersections. Road geometry, lane configurations, presence and nature of traffic

3

devices, and volume of other road users are main attributes that add to the complexity of

intersections. Therefore, to safely use intersections, elderly drivers must be observant of all of

the complex features at the intersections. This includes other drivers in their own and adjacent

lanes, other road users, signage, and other information (12).

4

Chapter 3 Methodology

3.1 Study area

Ten (10) Florida counties were selected for the study to analyze the characteristics of

crashes experienced by aging road users at signalized intersections. These counties include

Alachua, Bay, Broward, Duval, Escambia, Hillsborough, Leon, Miami-Dade, Monroe, and

Pinellas County. Figure 1 shows the Florida counties included in the study. These counties were

slated as the top 10 urban priority counties in 2014 (16), based on the average rate of crashes

involving persons age 65 and older compared to the population of that age group, by the Safe

Mobility for Life Coalition (SMFL), a partnership of the Florida Department of Transportation

(FDOT) State Traffic Engineering Operations Office and 26 member organizations (17).

Figure 3. 1 Florida Counties included in the study

5

3.2 Data collection and extraction

Crash reports were obtained from the FDOT database for each county involved in the

study for a period of three years (2008-2010). A combined total of 1467 crashes involving

individuals age 65 and above occurred during this period. Since the focus of this study was to

investigate crashes involving elderly drivers at signalized intersections, crash events that

occurred outside a radius of 250 ft of an intersection were not included in the analysis. A driver

was coded as At-fault if an elderly driver was recorded responsible for the collision, or Not At-

fault if records did not specify responsibility. Additionally, for collisions where the attending

officer could not determine responsibility, both drivers were included in the Not At-fault

category. Elderly drivers that were exposed to hit-and-run crashes were also included in the Not

At-fault category. Collisions with pedestrians and bicyclists accounted for less than 3% of total

crash events and therefore, were removed from the dataset because crash responsibility was not

defined. The reduced data set contained 1041 crash occurrences involving drivers age 65 and

older.

3.3 Binary regression models

To identify crash patterns involving elderly drivers in each Florida County, models for

binary response were developed. Various models can be used for data that have a binary

response; however, logistic/logit, probit, and complimentary log-log are the notable examples

(18). Other models suitable for binary response modeling are log-log and cauchit. It is difficult to

differentiate between the logit and probit functions in terms of goodness-of-fit because they are

both symmetrical and are linearly related. Apart from the similarity between logit and probit

models, other models, such as complimentary log-log and cauchit, have equivalent predictive

power (19). The logit function is commonly used in studies due to its simpler interpretation, and

6

its results can be estimated as the odds ratio for the model predictors (18, 19). On the other hand,

complimentary log-log is suitable for studies whose data expresses skewness characteristics,

such as pedestrian crash injury severity. This is due to the nature of complementary log-log,

where by its results tend to approach infinity more slowly than either the logit or probit functions

(20). Cauchit link is considered the most appropriate for the high level of sparseness in the

analyzed data (19). Therefore, in these models, the probability of occurrence of one event rather

than the other, with respect to covariates xi , is expressed as shown in Equation 3.1.

𝑔𝑔(𝑣𝑣) = 𝑥𝑥𝑖𝑖𝑇𝑇𝛽𝛽 (3.1)

where,

𝑔𝑔(𝑣𝑣): a function that links the linear predictors to the response variable

β: the estimates.

The link of linear predictor into the response variable can be as logit, cloglog, or cauchit

as shown in Equations 3.2, 3.3, and 3.4, respectively.

𝑔𝑔(𝑣𝑣) = log (𝑣𝑣/(1 − 𝑣𝑣)) (3.2)

𝑔𝑔(𝑣𝑣) = log (−𝑙𝑙𝑙𝑙𝑔𝑔(1 − 𝑣𝑣)) (3.3)

𝑔𝑔(𝑣𝑣) = Tan (𝜋𝜋𝑣𝑣 − (𝜋𝜋/2)) (3.4)

7

3.4 Bayesian Inference Specification

Model parameter estimates are deduced using Bayesian framework due to the reliability

of results compared to maximum likelihood estimates (21). This method estimates the

distribution of a targeted parameter by considering the Bayes rule which suggests that the

posterior distribution can be expressed as shown in Equation 3.5. In this equation f(ϴ|y)

represents the posterior distribution of the parameter ϴ , given the observed data y and prior

distribution of the data 𝑓𝑓(𝑦𝑦|𝛳𝛳) (22).

𝑓𝑓(𝛳𝛳|𝑦𝑦) = 𝑓𝑓�𝑦𝑦�𝛳𝛳�𝑓𝑓(𝛳𝛳)𝑓𝑓(𝑦𝑦)

𝛼𝛼𝑓𝑓(𝑦𝑦|𝛳𝛳)𝑓𝑓(𝛳𝛳) (3.5)

The main advantage of the Bayesian inference method, compared to a conventional

frequentist approach, is that extra knowledge and experience related to the data is introduced in

the analysis as prior information (23). Normally detailed prior information on the data is

unavailable in such a way that estimated prior information is defined, but ensured not to

influence posterior distribution. Low information priors for proper prior distribution with large

variance is sometimes considered as one of the options. Such priors contribute negligible

information to the posterior distribution (22). In the case of lack of informative priors, non-

informative priors were defined for the unknown parameters by referring to previous studies

involving traffic crashes. Consistent with Helai et al. (24) non-informative priors were defined

for all coefficients with normal distributions (0,1000) and the variance of the normal distributed

random effects with an inverse gamma distribution (0.001,0.001). The 95% Bayesian Credible

Interval (BCI) was provided to detect the significance of the variables. In order to ensure validity

and practicality of model results, experience on traffic crash issues and engineering judgment

was involved in the interpretation procedure (21, 24). In this study, the Bayesian inference was

8

done by considering non-informative prior distribution and using the Monte Carlo Markov Chain

(MCMC) algorithm, specifically Gibbs sampler in R Studio software.

3.5 Markov Chain Monte Carlo (MCMC) Algorithm

This method is used to estimate the marginal likelihood integrals using computer

simulation. The main idea behind this method is that properties of a distribution that are not easy

to understand can be learned by continuously sampling from the distribution and estimating the

properties of the samples. Enough number of sampling with respective distribution of samples

will ensure that distribution properties are learnt within acceptable accuracy (25). The Markov

concept is applied when producing a chain that eventually converges to the posterior distribution.

In order to monitor convergence of MCMC algorithm, the MC error is calculated, where a small

value of this error implies calculations have been done precisely. Monte Carlo error measures the

variability of each estimate due to the simulation. It is proportional to the inverse of the

generated sample size that can be controlled by the user. This means a sufficient number of total

iterations ensures the quantity of interest is estimated precisely. Observed autocorrelations is

another measure for convergence where by low or high values indicate fast or slow convergence,

respectively (22).

3.6 Model Prediction Accuracy

Cross-validation is one of the approaches (the other being information criteria) for

estimating out-of-sample predictive accuracy using within sample fits. There are various

methods for comparing predictive accuracy of models but leave-one-out cross validation shows

the predictive accuracy of the estimated Bayesian model by comparing the predictive power of

two or more models. This method has various advantages over Akaike information criteria and

Bayesian information criteria; however, it is rarely used due to more computational procedures.

9

An efficient method for estimating Leave-One-Out Information Criteria (LOOIC) is

Pareto-Smoothed Importance Sampling (PSIS), which is considered robust in case the Bayesian

framework has used weak priors. Leave-one-out cross validation method was applied in this

study to measure the predictive performance of each model, comparing and selecting a model

with the best fit. LOOIC was computed from the existing posterior simulations using PSIS, a

new procedure for regularizing importance weights. The advantage of the PSIS method over the

conventional importance sampling method is that it provides a more accurate and reliable

estimate using importance weights that are smoothed by fitting a generalized Pareto distribution

to the upper tail of the distribution of the importance weight (26).

10

Chapter 4 Case Study Application Results

4.1 Descriptive statistics

Table 4.1 gives a summary of the data and predictor variables that were used in the statistical modeling. The response variable is a binary, suggesting whether an elderly driver is at-fault or not at-fault.

Table 4.1 Predictor Variables for the Binary Regression

Variable name Description At-fault Not at-fault Total

Count Percent Count Percent Count Percent At-fault driver gender

Female 148 18 240 29 388 47 Male 176 21 270 32 446 53

Not at-fault driver injury

No injuries 248 30 405 49 653 78

Injuries 76 9 105 13 181 22

Driver turning

No driver turned 251 30 326 39 577 69 One or more driver turned 73 9 184 22 257 31

Intersection type

4-leg standard 189 23 302 36 491 59 4-leg staggered/skewed 41 5 61 7 102 12

3-leg, T-type 77 9 128 15 205 25 Interchanges 17 2 19 2 36 4

At-fault lane position

Through lane 202 24 269 32 471 56 Left-turn lane 77 9 146 18 223 27 Right-turn lane 45 5 95 11 140 17

Approach through lanes

None 20 2 38 5 58 7 Not Shared 431 52 283 34 714 86 Single Shared 21 3 41 5 62 7

Approach left-turn lanes

None 54 6 79 9 133 16 Single 182 22 268 32 450 54

Multiple 88 11 163 20 251 30

Approach right-turn lanes

None 166 20 256 31 422 51 Single 144 17 228 27 372 45

Double 14 2 26 3 40 5

Approach signal type

None 34 4 56 7 90 11 Permitted 190 23 257 31 447 54 Protected/Permitted 48 6 90 11 138 17 Protected 52 6 107 13 159 19

Median type

Flat 257 31 399 48 656 79 Raised 67 8 111 13 178 21

Travel Street

Major 247 30 368 44 615 74 Minor 77 9 142 17 219 26

Crash day

Weekday 273 33 412 49 685 82 Weekend 51 6 98 12 149 18

11

Table 4.1 Predictor Variables for the Binary Regression (continued)

Variable name Description At-fault Not at-fault Total Count Percent Count Percent Count Percent Crash time Peak Hours 144 17 110 13 254 30 Non Peak Hours 214 26 366 44 580 70 Weather Condition

Clear 236 28 379 45 615 74 Other 131 16 88 11 219 26

Lighting Condition

Daylight 282 34 443 53 725 87 Dark 42 5 67 8 109 13

Work zone

No 306 37 498 60 804 96 Yes 18 2 12 1 30 4

Crash type

Rear-end 200 24 211 25 411 49 Sideswipe 43 5 127 15 170 20 Collision at angle 81 10 172 21 253 30

Season

Spring 117 14 176 21 293 35 Summer 207 25 334 40 541 65

Not at-fault driver age Continuous data 834 100

For the study period (2008-2010), the majority of traffic crashes that involved elderly

drivers (65+ years) occurred along the study segment in Miami-Dade County (33.7%). This was

the expected result considering that this county contains the largest population of elderly drivers

among the 10 counties studied. Broward and Alachua County segments represented the next

highest percentage of crashes, 12.3% and 10.1%, respectively. Figure 4.1(a) shows the

distribution of crashes involving elderly drivers (65+ years) among the counties studied. When

considering the type of collision, it was found that rear-end collisions comprised nearly 40% of

crashes in each study year. Left-turn collisions accounted for approximately 20% of total crashes

each year, followed by sideswipe collisions, with the least percentage in 2008 (16%). Right angle

and right-turn collisions represented the fewest type of crashes involving drivers age 65+ during

the study period. Figure 4.2(b) depicts a summary of the crash types involving elderly drivers

from 2008 to 2010.

12

(a) Florida County

(b) Crash Type

Figure 4.1 Distribution of Elderly Driver Crashes per Florida County and Crash Type

4.2 Model Results

In developing binary models, summary statistics for the posterior samples of response

variables were tested at 95% BCI. Model estimation results for the Bayesian inference of binary

models that used different link functions are shown in Table 4.2. The table describes variables

020406080

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Num

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s Age

65+

County2008 2009 2010

86 79 9

11

22 21 1916

2319

45 42 43

0

10

20

30

40

50

2008 2009 2010

Perc

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Type

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YearRight Angle Right Turn Left Turn Sideswipe Rear End

13

with significant posterior distributions and a sign for the mean of the distributions. A number of

variables were found to be significant depending on the link function used to model the data.

Some of the variables were significant in all link functions used in the analysis. Influence of

interchanges, compared to the standard 4-legged intersection, was significant in all models and

had a positive mean for its posterior distribution. Crash time had a significant impact in all

models with an estimated mean of the distribution with a positive sign suggesting that elderly

drivers are more at-fault in crashes occurring during off-peak hours. Sideswipe collisions and

collisions at angles are more profound when elderly drivers are at-fault, compared to rear end

collisions. Age of the driver who is not at-fault had a significant effect on an elderly driver with a

higher probability of being at-fault in a crash. Other variables that were not found significant in

all models, but significant in at least one of the models include: at-fault lane position, number of

right turn lanes, type of roadway, and presence or absence of a work zone. A discussion on the

significant variables is given in Chapter 5.

14

Table 4.2 Model Results for all Link Functions Link function Cauchit Logit Cloglog

Variable name Description Mean MC Error Mean MC

Error Mean MC Error At-fault driver gender Female Male 0.133 0.009 -0.013 0.004 0.020 0.002 Not at-fault driver injury No injuries Injuries -0.130 0.010 0.020 0.005 0.112 0.003 Driver Turning No driver turned One or more driver turned -1.139 0.013 -0.375 0.007 -0.089 0.004 Intersection type 4-leg standard 4-leg staggered/skewed 0.306 0.012 -0.074 0.006 -0.120 0.004 3-leg, T-type 0.205 0.011 0.006 0.006 -0.140 0.003 Interchanges 2.976 0.030 1.504 0.011 0.902 0.006 At-fault lane position Through lane Left-turn lane 0.423 0.017 0.067 0.009 -0.455 0.005 Right-turn lane -1.025 0.017 -0.719 0.007 -0.650 0.004 Approach through lanes None Not Shared -0.102 0.025 -0.127 0.013 -0.080 0.007 Single Shared 1.245 0.022 -0.006 0.012 -0.451 0.007 Approach left-turn lanes None Single -1.151 0.018 -0.389 0.008 -0.068 0.004 Multiple -1.676 0.019 -0.973 0.008 -0.402 0.004 Approach right-turn lanes None Single -1.248 0.011 -0.220 0.005 0.016 0.003 Double 0.863 0.021 1.110 0.011 0.715 0.006 Approach signal type None Permitted 0.129 0.019 -0.255 0.009 -0.420 0.005 Protected/Permitted 1.133 0.025 -0.016 0.011 -0.096 0.006 Protected 0.529 0.021 0.016 0.012 0.122 0.007 Median type Flat Raised -0.687 0.009 -0.265 0.005 -0.022 0.003 Travel Street Major -2.311 0.019 -0.942 0.008 -0.255 0.004 Minor Crash day Weekday Weekend 0.282 0.010 0.250 0.005 0.181 0.003 Crash time Peak Hours Non Peak Hours 1.308 0.010 0.721 0.004 0.364 0.002 Weather Condition Clear Other 0.457 0.010 0.284 0.004 0.226 0.003 Lighting Condition Daylight Dark 1.437 0.016 0.544 0.006 0.293 0.003 Work zone No Yes 2.933 0.029 1.534 0.010 0.379 0.005 Crash type Rear-end Sideswipe -1.642 0.012 -1.242 0.006 -0.830 0.003 Collision at angle -1.769 0.013 -1.134 0.007 -0.616 0.004 Season Spring Summer -0.473 0.010 -0.078 0.004 -0.102 0.002 Not at-fault driver age Continuous data 0.465 0.002 0.211 0.000 0.109 0.000

Constant -27.74 0.107 -12.14 -

0.021 -6.501 0.011 NOTES: All significant variables are at 95% Bayesian Credible Interval (BIC)

15

Chapter 5 Discussions

5.1 Intersection type

Results from Table 4.2 (2.976, 1.504, and 0.902) suggest that elderly drivers are more

susceptible at interchange crossings compared to standard 4-legged intersections. A study by

Stutts et al. (15) suggested that the crash risk of elderly drivers at interchange crossings is equal

to or more than at standard intersections. This can be attributed to the complexity of interchange

intersections. Interchanges have geometric variability, such as position of traffic signals. Due to

reduced driving ability, elderly drivers are not expected to easily cope with complexities and a

lot of variabilities on the roadway.

5.2 At-fault lane position

Results from the cloglog model suggest that elderly drivers are less likely to be at-fault

drivers in crashes where the at-fault vehicle was in the right turning lane (Table 4.2). Moreover,

it suggests that elderly drivers are more involved in crashes where the at-fault driver is on a

through lane compared to a right turn lane. Even though elderly drivers are associated with many

errors when performing turning maneuvers, their less involvement in these crashes can be

attributed to the defensive nature of their way of driving, especially when undergoing turning

maneuvers at protected or unprotected intersections.

5.3 Number of approach right-turn lane

Table 4.2 indicates that the probability of an older driver being at-fault in a crash at an

intersection where there is a single right turn lane is less, compared to when there is no right turn

lane. The presence of a dedicated right turn lane offers protection to the driver turning right, with

or without signal protection. Commuters using conflicting approaches are potentially more aware

of turning vehicles when a dedicated right turn lane exists. Moreover, dedicated right turn lanes

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are fairly common at heavily traveled intersections, suggesting that driver familiarity may reduce

the likelihood of crash involvement due to decision and gap misjudgment errors.

5.4 Travel Street

The probability of elderly drivers being at-fault in a crash diminishes when the travel

street is a major thoroughfare, compared to a minor street (Table 4.2). This observation reflects

on the tendency of elderly drivers to avoid major streets and freeways for their travels. Avoiding

heavy traffic, high travel speeds, trucks, difficulties with merging or changing lanes, and

preference for more scenic routes are common reasons elderly drivers appear to prefer minor

streets. A previous study by Mayhew et al. (4) observed that elderly drivers have less exposure to

freeway crashes.

5.5 Crash time

Elderly drivers have an increased probability of being at-fault during off-peak hours

compared to peak hours. This can be attributed to elderly driver preference to avoid heavily

congested periods and conflicts associated with peak hours. Additionally, NHTSA (6) found that

elderly drivers have an elevated crash risk during daylight hours and at intersections. Daytime

hours are often preferred by elderly drivers due to diminished sight or difficulties seeing at night.

5.6 Work zone

In this study, the work zone variable was categorized based on its presence (yes) or

absence (no) for all intersections where the crash has occurred. According to the results

summarized in Table 4.2, the likelihood of an elderly driver being at-fault at intersections within

a work zone is lower than at intersections outside of a work zones. Normally, work zones are

characterized with lower speed limits, shifting lanes, curbs, and other attributes, which require

drivers to drive more carefully and pay closer attention to the road. It is a common observation

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that elderly drivers are more defensive compared to younger drivers (drivers age less than 65).

Therefore, elderly drivers are more likely to adhere to traffic regulations when navigating work

zones.

5.7 Crash type

The likelihood of an elderly driver being at-fault in sideswipe and collisions at an angle is

higher than that for rear end collisions. Angle collisions represent most of the crashes that occur

while performing turning maneuvers and crashes between vehicles at a right angle. A study by

NHTSA (6) suggested that drivers who are 60 years and older are more likely to be involved in

angle crashes. Braitman et al. (12) suggested that elderly drivers are less involved in rear end

collisions rather other collision types due to different errors made by elderly drivers when trying

to perform intersection maneuvers, such as left turns or right turns. Common errors that are

associated with elderly drivers involved in angle crashes and sideswipe crashes are surveillance

errors and gap or speed misjudgment errors, respectively.

5.8 Not at-fault driver age

It is more likely that as the age of a driver (not at-fault in a crash) increases, the

likelihood the driver will be elderly and at-fault. Intuitively, younger drivers can recognize

hazards and quickly respond to avoid a crash from happening, while elderly drivers are slower at

recognizing and avoiding hazards. This observation related to the perception reaction time to

avoid a crash was also reported in the NHTSA study (6).

5.9 Model prediction accuracy

Table 5.1 shows analysis results for the determination of prediction accuracy of the link function

used for the models. A model that has the lower LOOIC value, in comparison to other models, is

considered to have better prediction accuracy than others. The cauchit model indicated that it has

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the highest prediction accuracy (LOOIC=509), compared to other models (logit and cloglog).

The logit model (LOOIC=523) has less predictive accuracy than the cauchit model, but better

predictive power than the cloglog model (LOOIC=596). The expected log predictive density

(ELPD_LOO) shows a similar trend to that is expressed by LOOIC.

Table 5.1 Cross validation of binary models

Model LOOIC SE_LOOIC ELPD_LOO SE_ELPD_LOO Cauchit 509 39 -254 19 Logit 523 37 -261 18

Cloglog 596 39 -297 19

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Chapter 6 Conclusions & Future Recommendations

The reduced driving ability of elderly drivers contributes to an increased risk of being at-

fault in certain types of crashes. As observed, elderly drivers experience more challenges in

navigating intersections compared to other roadway segments, due to the complexity and

increased number of conflicts at intersections. There is a need to better understand the

relationship between crashes involving elderly drivers at intersections and related predictor

factors that increase their risk of involvement. This may assist transportation agencies with

developing effective countermeasures to reduce intersection crashes among elderly drivers,

especially at-fault crashes.

Findings from the Bayesian regression analysis revealed that at 95% BCI, four predictor

variables significantly affect the odds of an elderly driver being/not being at-fault in an

intersection crash. These variables include: intersection type, crash time, age of a driver not at-

fault, and crash type. Other factors were significant in at least one of the models: at-fault lane

position, number of right turn lanes, type of travel street, and work zones.

Although age is generally considered as a factor in decreased driving ability, it does not

provide sufficient information to determine driving ability, since the onset and degree of physical

impairments that may affect driving skills differ among individuals. Further research can be done

to investigate the effects of unobserved attributes of elderly drivers involved in intersection

crashes. Given the increased crash risk of elderly drivers and the greater tendency of being at-

fault in some crashes, there is a need to develop countermeasures that will help improve the

safety and mobility status of elderly drivers. Driving is an important and often essential activity

for elderly persons, since it provides them with mobility, independence, and opportunities to be

involved in the community. While intimidating at times, driving can also improve the quality life

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for an older individual. Thus, findings from this study can assist transportation agencies in

developing strategies to improve the safety of elderly drivers, particularly in areas where

alternative transportation options that favor the needs of the aged population are limited.

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