Post on 01-Nov-2021
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
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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
Indicator Weather (Ambient/Pavement)
-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
Indicator Weather (Ambient/Pavement)
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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