Random Parameter Analysis of IIHS Vehicle Death Rate

Random Parameter Analysis of IIHS Vehicle Death Rate Factors and Their Contributions to Fixed Object and Non-Domestic Collision Severity

by

Wang Xi, M.S.

A Thesis

In

Civil Engineering

Submitted to the Graduate Faculty of Texas Tech University in

Partial Fulfillment of the Requirements for

the Degree of

MASTER OF SCIENCE

Approved

Dr. Venky Shankar Chair of the Committee

Dr. Raghu Betha

Mark Sheridan Dean of the Graduate School

August, 2021

Copyright 2021, Wang Xi

Texas Tech University, Wang Xi, August 2021

ii

ACKNOWLEDGMENTS Throughout the writing of this thesis I have received a great deal of support and

assistance.

I would first like to thank my academic advisor, Dr. Venky Shankar, whose

expertise was invaluable in formulating the research questions and methodology. Your

insightful feedback pushed me to sharpen my thinking and brought my work to a higher

level.

I would also like to thank my research team members, Taiwo Adebayo, Sharif

Arefin, and Nardos Feknssa, for their valuable guidance throughout my studies. You

provided me with the tools that I needed to choose the right direction and successfully

complete my thesis.

In addition, I would like to thank my parents for their wise counsel and

sympathetic ear. You are always there for me. Finally, I could not have completed this

thesis without the support of my friends, Youngha Oh and Yanni Chen, who created a

study group and we have been studying together through zoom online meeting to give

each other’s study motivation every night.


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TABLE OF CONTENTS ACKNOWLEDGMENTS ................................................................................. ii

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

CHAPTER II LITERATURE REVIEWS ........................................................ 2

CHAPTER III METHODOLOGY AND DATA ANALYSIS ......................... 7

CHAPTER IV RESULTS AND DISCUSSIONS .............................................. 9

BIBLIOGRAPHY ............................................................................................ 17


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CHAPTER I INTRODUCTION We study the severity of driver crashes involving fixed object and non-domestic

collisions on the SR5, SR82, SR90, SR182, SR205, SR405 and SR705 in the state of

Washington using a data set of 10871 for the years 2018 until 2019. We use a mixed

logit regression model with heterogeneity in variance to identify statistically relevant

factors explaining the severity of the most severe injury type, which is classified into

the four classes, which are non-apparent injury, possible injury, suspected minor injury

and suspected serious injury plus fatality, respectively. Furthermore, to account for

unobserved heterogeneity we use a mixed logit model with heterogeneity in variance.

We study the effect of a number of factors including time period, sobriety type,

vehicle count, work-zone information, first collision type, junction relationship, weather

conditions, pavement surface conditions, ambient light conditions, first impact location,

vehicle movement information, vehicle style, vehicle size, first vehicle action, vehicle

defects conditions, vehicle 1 demographics, driver 1 contributing causes, site-type

indicators, impairment & fault dummies and count, encroachment indicators, driver age

level indicators, wildlife indicator, posted speed limits, presence of traffic control

systems, age and gender of the driver and county locations of the crash.

The objective of this study was to determine the contributing factors to vehicle

driver crash severity involving fixed objects collisions. The results from this study need

to be evaluated with caution due to the lack of data about specified driver behaviors and

driver skills at the moment of crash related cases available in the WSDOT crash

database. Implications for identifying and improving the reporting of unobserved driver

behaviors, driver skills and other related factors are therefore discussed.


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CHAPTER II LITERATURE REVIEWS Seraneeprakarn et al (2017) and Mannering et al (2016) both mentioned that

unobserved heterogeneity had become a matter of considerable importance in the

analysis of crash data. In fact, numerous empirical studies have shown that unobserved

heterogeneity plays a key role in the analysis of crash data. They found that traditional

random parameters models estimated observation-specific parameters by assuming that

parameters were distributed across observations using an analyst-specified distribution.

There was always some concern about this required parametric assumption because

analysts were forced to consider a handful of distributions that may not necessarily track

the unobserved heterogeneity well. Seraneeprakarn et al (2017) and Mannering et al

(2016) discussed that allowing for heterogeneity in the means and variances of random

parameters empirically provided much more flexibility in tracking the unobserved

heterogeneity in the data with any given distributional assumption.

Shankar et al (2000) studied the impacts of the bridge rail on vehicular accident

severity, particularly, concrete balusters and metal rails underperformed in comparison

with the average bridge rail type, whereas thrie-beam guardrails and safety shape

barriers had superior performance. Shankar et al (2000)’s study presented a statistical

framework that was particularly suitable for capturing real-world, unobserved effects

that impacted reported accident severity distribution. Meanwhile, his study mentioned

that policy sensitivities showed systemwide savings through upgrading the

underperforming rails to provide substantial performance. The combination of insights

from the relative performance of bridge rails and the associated policy sensitivities

provided direction for national policy on roadside design.

Shankar et al (2004) developed a multivariate model that incorporated the effects

of design, traffic, weather, and related interactions with design variables on reported

roadside crashes. Their study provided a framework that accounted for all measurable

effects, and the provided model minimized the impact of omitted variable effects.

Furthermore, the presented framework accounted for partial observability effects that

stemed from fluctuations in environmental conditions as well as unobserved effects that


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contribute to heterogeneity in the traffic safety network. Shankar et al (2004)

represented the state highway network in the state of Washington on the basis of

environmental and road classification factors and therefore were used for the collection

of detailed precipitation, snowfall, and temperature data in addition to roadway and

roadside design and traffic parameters. The resulting model suggested that the marginal

impact of weather was both in main effects and interactive form, and that even after

controlling for unobserved heterogeneity and partial observability, weather effects

played a statistically significant role in roadside crash occurrence.

Al-Bdairi et al (2020) investigated the determinants of driver injury severity in

animal-vehicle collisions while systematically accounting for unobserved heterogeneity

in the data by using three methodological approaches: mixed logit model, mixed logit

model with heterogeneity in means, and mixed logit model with heterogeneity in means

and variances. In their study, the temporal stability and transferability of the models

were investigated through a series of likelihood ratio tests. Marginal effects were also

used to study the temporal stability of the explanatory variables. Model estimation

results showed that many parameters can potentially increase the likelihood of severe

injuries in Animal-vehicle crashes including freeways/expressways, daylight crashes,

early morning crashes, dry road surface and clear weather condition. Moreover, the

model estimation results showed that accounting for the heterogeneity in the means (and

variances) of the random parameters can improve the overall fit of the model. Some

variables showed relatively similar marginal effects among different methodological

approaches while some others showed different marginal effects upon the application

of different methods.

Koppel et al (2018) used medico-legal data to investigate fatal older road user

(aged 65 years and older) crash circumstances and risk factors relating to four key

components of the Safe System approach (e.g., roads and roadsides, vehicles, road users

and speeds) to identify areas of priority for targeted prevention activity.

Lambert et al (2003) used benefit-cost analysis to address the need for allocation

of resources to run-off-road and fixed-object hazards on immense secondary road


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systems. A decision aid was developed to assist the planner in guardrail resource

allocation by accounting for the potential crash severities, traffic exposures, costs of

treatment, and other factors. A premise is that no single benefit–cost ratio or selection

criterion applies across all localities. They described (1) archiving and comparison of

protected and unprotected hazards; (2) regional screening of hazardous corridors and

(3) multi-criteria benefit–cost analyses of guardrail sites.

Li et al (2018) developed a finite mixture random parameters approach to

interpret both within-class and between-class unobserved heterogeneity among crash

data. In their study, a two-class finite mixture random parameter model with normal

distribution assumptions was selected as the final model. Estimation results showed that

three variables, including young (specific to injury), male (specific to serious injury and

fatality), and large truck (specific to serious injury and fatality), are found to be normally

distributed and have significant impacts on driver injury severities. Variables with fixed

effects including rural, wet, 60 mph or higher, no statutory limit, dark, Sunday, curve,

rollover, light truck, old, and drug/alcohol impaired also have significant influences on

driver injury severities.

Li et al (2019) made use of a two-year crash dataset including all single-vehicle

crashes in New Mexico and they adopted to analyze the impact of contributing factors

on driver injury severity. In order to capture the across-class heterogeneous effects, a

latent class approach was designed to classify the whole dataset by maximizing the

homogeneous effects within each cluster. The mixed logit model was subsequently

developed on each cluster to account for the within-class unobserved heterogeneity and

to further analyze the dataset. According to their estimation results, several variables

including overturn, fixed object, and snowing, were found to be normally distributed in

the observations in the overall sample, indicating there exist some heterogeneous effects

in the dataset. Some fixed parameters, including rural, wet, overtaking, seatbelt used,

65 years old or older, etc., were also found to significantly influence driver injury

severity. Their study provided an insightful understanding of the impacts of these

variables on driver injury severity in single-vehicle crashes, and a beneficial reference


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for developing effective countermeasures and strategies for mitigating driver injury

severity.

Meng et al (2020) collected dataset from the National Automotive Sampling

System-Crashworthiness Data System to investigate common damage patterns of

guardrail end terminals by using post-crash pictures. Conditions of in-service end

terminals mounted along roads in portions of six U.S. states were examined by using a

sample from the second Strategic Highway Research Program-Roadway Information

Database. They used finite element models of two minor and three severely damaged

ET-Plus systems, a commonly used energy absorbing guardrail end terminal along U.S.

roads, were developed. The findings of their study pointed out the need for in-service

performance evaluations and proper maintenance and repair practices of end terminals.

They also supplemented the simulation model to do crash tests to certify new hardware

designs.

Ryb et al (2013) categorized three different newer occupant protection

technology as 1994–1997, 1998–2004, or 2005–2010 model years. Logistic regression

was used to calculate odds ratios and 95% confidence intervals for the association

between AI and model year independent of possible confounders. Analysis was

repeated, stratified by frontal and near lateral impacts. Ryb et al (2013) found that AIs

were associated with advanced age, male gender, high BMI, near-side impact, rollover,

ejection, collision against a fixed object, high ΔV, vehicle mismatch, unrestrained

status, and forward track position.

Neyens & Boyle (2007) tried to determine how different distraction factors

impact the crash types that are common among teenage drivers. A multinomial logit

model was developed to predict the likelihood that a driver will be involved in one of

three common crash types: an angular collision with a moving vehicle, a rear-end

collision with a moving lead vehicle, and a collision with a fixed object. These crashes

were evaluated in terms of four driver distraction categories: cognitive, cell phone

related, in-vehicle, and passenger-related distractions. Neyens & Boyle (2007) found

that different driver distractions have varying effects on teenage drivers’ crash


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involvement. Teenage drivers that were distracted at an intersection by passengers or

cognitively were more likely to be involved in rear-end and angular collisions when

compared to fixed-object collisions. In-vehicle distractions resulted in a greater

likelihood of a collision with a fixed object when compared to angular collisions. Cell

phone distractions resulted in a higher likelihood of rear-end collision.


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CHAPTER III METHODOLOGY AND DATA ANALYSIS The mixed logit model, also called the random parameters logit model, has been

used in many recent traffic studies (Neyens & Boyle, 2007; Manner & Wünsch-Ziegler,

2013). The mixed logit model is an extension of the ordinary logit model. The ordinary

logit model assumes that the unobserved variables are uncorrelated over the response

outcomes, which is called the independence from irrelevant alternative (IIA)

assumption. The IIA assumption can be viewed as a model restriction or as a reasonable

assumption for a well-specified model that captures all sources of correlation over the

alternatives (Rezapour et al., 2019).

However, crashes can be complex events involving a variety of factors that are

accident-specific that might not be adequately modeled under the IIA assumption. In

such cases, the mixed logit model is used to account for heterogeneity across crashes by

allowing the influence of predictors to vary by crash.

Thus, for this analysis, there are four category contrasts for each of the vehicle

driver severity types: (1) no apparent injury, (2) possible injury, and (3) suspected minor

injury 9 also called evident injury), and (4) suspected serious injury plus fatality. The

output of a mixed logit regression model with heterogeneity in variance typically reveals

all but one of the relationship contrasts, and this is typically how the results of such

analyses are reported.

In the standard mixed logit model, the means and variances of the random

parameters are assumed to be fixed across the observations. Having this assumption, the

analyst will be unable to check whether the unobserved heterogeneity is a function of

explanatory variables or not. Following the previous studies (Al-Bdairi et al., 2020), this

research aims to use mixed logit model with heterogeneity in variance in analyzing the

vehicle driver crash injury severities.

Heterogeneity of variance refers to the violation of the homogeneity of variance

assumption, one of the main assumptions underlying the analysis of grouped data in the

univariate and multivariate contexts (i.e., independent samples t-test, analysis of

variance, and multivariate analysis of variance). Broadly speaking, heterogeneity of


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variance means that the population variances of the groups or cells being compared are

not homogenous or equal. Because variances are averaged in the calculation of standard

error and error terms, under the assumption they are roughly equal, heterogeneity will

create bias and inconsistencies in significance tests and confidence intervals for the

model under consideration. Therefore, generally, the impact of heterogeneous variance

will depend on the ratio of largest to smallest variance between groups, and on whether

the sample sizes for the groups being compared are equal or not.

A severity function determining the proportion of injury severities on a roadway

segment is defined as (Rezapour et al., 2019).

Snj = xnjβnj + εnj, (1)

Where j indexes the injury severity category (j = 1, 2, …, J), n denotes the crash

( n= 1, 2,…, N), Snj is a severity function, xnj is a vector of observed predictors, βnj is a

vector of unknown parameters, and εnj is the error term that is assumed to be independent

and identically distributed with an extreme value distribution. Conditional on βn, the

probability for alternative i is

"ni(βni) = #$%('()*())

∑ #$%(-./0 '()*()) (2)

The unconditional probability for alternative i is given by

Pni = ∫3ni (βni) f(βni φi) d βni (3)

Where f(βni | φi) is the probability density function (PDF) of βni with φi denoting

a vector of parameters characterizing the PDF of βni (Rezapour et al., 2019).


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CHAPTER IV RESULTS AND DISCUSSIONS Table 4.1 shows the variable name, variable description, group affiliation,

coefficients, t-statistics, and p-value for mixed logit regression model with

heterogeneity in variance. As the baseline is the vehicle driver suspected serious injury

plus fatal severity level, on the contrary, the coefficient for County Franklin is positively

correlated with the expected vehicle driver non-apparent injury severity level. The

coefficient estimate of 0.8612 is based on dummy indicator coded as 1 if crash occurred

at County Franklin. Coefficient restriction was evaluated using likelihood ration tests.

The significance of the constrained coefficient has a t-statistic of -2.384 indicating

98.29% confidence level. This indicates that for one unit of increase in County Franklin,

we can expect a 0.8612 unit increase in expected vehicle driver non-apparent injury

severity level.

The coefficient for sobriety type is positively correlated with the expected

vehicle driver non-apparent injury severity level instead. The coefficient estimate of

1.5798 is based on dummy indicator coded as 1 if the vehicle driver had been drinking

and ability impaired at the time of crash. Coefficient restriction was evaluated using

likelihood ration tests. The significance of the constrained coefficient is high, with a t-

statistic of -7.785 indicating almost 100.00% confidence level. This indicates that for

one unit of increase in ability impaired indicator, we can expect a 1.5798 unit increase

in expected vehicle driver non-apparent injury severity level.

The coefficient for Earth Bank or Ledge Indicator is positively correlated with

the expected vehicle driver non-apparent injury severity level. The coefficient estimate

of 0.5903 is based on dummy indicator coded as 1 if vehicle crashed into earth bank or

ledge. Coefficient restriction was evaluated using likelihood ration tests. The

significance of the constrained coefficient has a t-statistic of -1.918 indicating 94.49%

confidence level. This indicates that for one unit of increase happened in earth bank or

ledge, we can expect a 0.5903 unit increase in expected vehicle driver non-apparent

injury severity level.


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Table 4.1: Mixed Logit Regression Model with Heterogeneity in Variance Result Summary Variable Name Variable Description Variable Type Group Coeff. T-Stat P-Value

Constant 1 5.2813 17.928 0.0000 Constant 2 2.0897 7.803 0.0000 Vehicle Driver No Apparent Injury Category County Franklin County Indicator (1 if crash

occurred at County Franklin; 0 otherwise)

Indicator Counties -0.8612 -2.384 0.0171

Sobriety Type Indicator

Ability impaired indicator (1 if driver had been drinking and ability impaired at the time of crash; 0 otherwise)

Indicator Sobriety -1.5798 -7.785 0.0000

Earth Bank or Ledge Indicator

1 if vehicle had impact with earth bank or ledge in crash; 0 otherwise

Indicator First Collision Type

-0.5903 -1.918 0.0551

Vehicle Overturned Crash Indicator

1 if vehicle overturned in crash; 0 otherwise

Indicator First Collision Type

-1.7747 -7.073 0.0000

Changing Lanes Indicator

First vehicle action indicator (1 if vehicle was changing lanes at the time of the crash; 0 otherwise)

Indicator First Vehicle Action

-0.9237 -3.916 0.0001

Driver Age minimum is 15, maximum is 96 Count Vehicle 1 Demographics

-0.0124 -2.642 0.0082 Gender Indicator Male Indicator (1 if driver is male;

0 otherwise) Indicator 0.3550 2.540 0.0111

Apparently Asleep or Fatigued Crash Related Indicator

1 if driver was apparently asleep or fatigued at the time of crash; 0 otherwise

Indicator Driver 1 Contributing

Cause

-0.7660 -2.674 0.0075


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Table 4.1 (continued): Mixed Logit Regression Model with Heterogeneity in Variance Result Summary

Variable Name Variable Description Variable

Type Group Coeff. T-Stat P-Value Vehicle Driver Possible Injury Category County King County Indicator (1 if crash occurred at

County King; 0 otherwise) Indicator Counties 1.0089 4.440 0.0000

Sobriety Type Indicator

Ability Impaired Indicator (1 if driver had been drinking and ability impaired at the time of crash; 0 otherwise)

Indicator Sobriety -1.2618 -3.809 0.0001

Snowing Indicator

1 if crash occurred in snowing weather; 0 otherwise

Indicator Weather (Ambient/Pavement)

-0.9779 -2.177 0.0295

Change Lanes to Left Indicator

1 if vehicle was changing lanes to the left at the time of the crash; 0 otherwise

Indicator Vehicle Movement -1.3744 -1.956 0.0505

Vehicle Driver Suspected Minor Injury (Evident Injury) Category County Spokane County Indicator (1 if crash occurred at

County Spokane; 0 otherwise) Indicator Counties 0.6597 1.944 0.0519

March Indicator Month of March Indicator (1 if crash occurred in the month of March; 0 otherwise)

Indicator Crash Time Period -1.2487 -1.991 0.0465

Slush Indicator 1 if crash occurred on slushy pavement; 0 otherwise


-1.1900 -2.237 0.0253

Station Wagons/Minivan Indicator

1 if vehicle style is station wagons or minivan in crash; 0 otherwise

Indicator Vehicle Style -0.8637 -2.167 0.0302

Vehicle Size 1 if vehicle size is small or midsize in crash; 0 otherwise

Indicator Vehicle Size -0.5758 -2.711 0.0067

Baseline: Vehicle Driver Suspected Serious Injury + Fatality Category


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Table 4.1 (continued): Mixed Logit Regression Model with Heterogeneity in Variance Result Summary Variable Name Variable Description Variable Type Group Coeff. T-Stat P-Value

Random Parameter Posted Speed Limit

10 mph, 15 mph, 20 mph, 25 mph, 30 mph, 35 mph, 40 mph, 45 mph, 50 mph, 55 mph, 60 mph, 70 mph

Count Posted Vehicle Speed Limit for

Vehicle 1

0.0469 2.509 0.0121

Heterogeneity in Variance Pickups Indicator 1 if vehicle style is pickups in

crash; 0 otherwise Indicator Vehicle Style -0.4600 -1.799 0.0721

Coefficient of Variation of Crash Death Rate Continuous Indicator

Coefficient of variation (standard deviation over mean), if coefficient of variation of rollover death rate in vehicle size is greater than 1.146, or if coefficient of variation of multi-vehicle death rate in vehicle style is greater than 0.591 and less than 0.700; 0 otherwise

Continuous IIHS Crash Death Rates

-0.1714 -1.323 0.1860

Wet Indicator 1 if crash occurred on wet pavement; 0 otherwise


0.1780 -1.591 0.1116

Minimum Multiple Vehicle Death Rate of Vehicle Style Continuous Indicator

Minimum multi-vehicle death rate of vehicle style (minimum is 0; maximum is 4)

Continuous IIHS Crash Death Rates Vehicle Style

-0.1132 -1.205 0.2284


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Table 4.1 (continued): Mixed Logit Regression Model with Heterogeneity in Variance Result Summary Mean Single Vehicle Death Rate of Vehicle Style Continuous Indicator

Mean single vehicle death rate of vehicle style (minimum is 6.273; maximum is 52.172)

Continuous 0.0059 0.816 0.4144

Goodness of Fit Measures

Based on 2689 Observations, 26

Parameters

Convergent Log-Likelihood -1522.417 AIC1 of Mixed Logistic Regression Model

1.15167

BIC2 of Mixed Logistic Regression Model

1.20868

HQIC3 of Mixed Logistic Regression Model

1.17229

1 Akaike Information Criterion (AIC) is computed as an observation-level value given by: !"#$ = (2( − 2*+,)// where k is the number of parameters estimated, lnL is the log-likelihood at convergence, and N is the number of observations 2 Bayesian Information Criterion (BIC) is computed as an observation-level value given by: 0"#$ = ((*+[/] − 2*+,)// 3 Hannan-Quinn Information Criterion (HQIC) is computed as an observation-level value given by: 34"#$ = (2(*+[*+[/]] − 2*+,)//


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The coefficient for Vehicle Overturned Crash Indicator is positively correlated

with the expected vehicle driver non-apparent injury severity level. The coefficient

estimate of 1.7747 is based on dummy indicator coded as 1 if crash type was vehicle

overturned. Coefficient restriction was evaluated using likelihood ration tests. The

significance of the constrained coefficient is high, with a t-statistic of -7.073 indicating

almost 100.00% confidence level. This indicates that for one unit of increase in vehicle

overturned, we can expect a 1.7747 unit increase in expected vehicle driver non-

apparent injury severity level.

The coefficient for changing lanes indicator is positively correlated with the

expected vehicle driver non-apparent injury severity level. The coefficient estimate of

0.9237 is based on dummy indicator coded as 1 if the first action of vehicle was

changing lanes at the time of crash. Coefficient restriction was evaluated using

likelihood ration tests. The significance of the constrained coefficient is high, with a t-

statistic of -3.916 indicating 99.99% confidence level. This indicates that for one unit

of increase in vehicle changing lanes, we can expect a 0.9237 unit increase in expected

vehicle driver non-apparent injury severity level.

The coefficient for driver age is positively correlated with the expected vehicle

driver non-apparent injury severity level. The coefficient estimate of 0.0124 is based on

driver age count number. Coefficient restriction was evaluated using likelihood ration

tests. The significance of the constrained coefficient has a t-statistic of -2.642 indicating

99.18% confidence level. This indicates that for one unit of increase in age, we can

expect a 0.0124 unit increase in expected vehicle driver non-apparent injury severity

level.

The coefficient for apparently asleep or fatigued crash related indicator is

positively correlated with the expected vehicle driver non-apparent injury severity level.

The coefficient estimate of 0.7660 is based on dummy indicator coded as 1 if driver was

apparently asleep or fatigued at the time of crash. Coefficient restriction was evaluated

using likelihood ration tests. The significance of the constrained coefficient has a t-

statistic of -2.674 indicating 99.25% confidence level. This indicates that for one unit


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of increase in apparently asleep or fatigued crash related indicator, we can expect a

0.7660 unit increase in expected vehicle driver non-apparent injury severity level.

On the contrary, the coefficient for driver gender is negatively correlated with

the expected vehicle driver non-apparent injury severity level. The coefficient estimate

of 0.3550 is based on dummy indicator coded as 1 if driver gender is male. Coefficient

restriction was evaluated using likelihood ration tests. The significance of the

constrained coefficient has a t-statistic of -2.540 indicating 98.89% confidence level.

This indicates that for one unit of increase in driver gender indicator, we can expect a

0.3550 unit decrease in expected vehicle driver non-apparent injury severity level,

which indicates that male drivers have a higher chance to survive in vehicle crashes.

On the other hand, regarding non-apparent driver injury severity category, we

have counties group, sobriety group, first collision type group, first vehicle action group,

vehicle 1 demographics group and driver 1 contributing cause group contributing to

fixed object and non-domestic collisions. Regarding possible driver injury severity

category, we have counties group, sobriety group, weather (ambient/pavement) and

vehicle movement group contributing to fixed object and non-domestic collisions.

Lastly, regarding driver evident injury severity category, we have counties group, crash

time period group, weather (ambient/pavement), vehicle style group and vehicle size

group contributing to fixed object and non-domestic collisions. All driver injury severity

categories have counties group, indicating that our model can define specific county

location in different driver injury severity levels. In terms of two minor driver crash

injury severity levels, which are non-apparent severity and possible severity,

respectively, we both have sobriety group, indicating that driving ability impaired can

cause minor driver injuries, but not necessary indicator in serious driver injuries. In

terms of two evident driver crash injury severity levels, which are possible severity and

minor severity, respectively, we both have weather (ambient/pavement) group,

indicating that ambient weather or pavement surface can lead to relatively higher chance

to get serious driver injuries.


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Last but not least, as shown in Table 4.1, the random parameter is posted speed

limit, ranging from 10 mph to 70 mph, which is indicated that vehicle driver crash

severity level is not impacted by the posted speed limit along the roadways.

Furthermore, wet indicator was found in the heterogeneity in variance category. The

significance of the constrained coefficient has a t-statistic of -1.591 indicating only

around 88.84% confidence level. It gives us a light of how different vehicle models

interact with wet pavement. Due to unobserved pavement maintenance, unobserved

pavement surface condition, unknown driver skills, unobserved different vehicle tire

quality with different control speed, unknown vehicle speed on wet pavement at the

crash time, different vehicle models may contribute to different driver crash severity

level.


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