Injury Severity Analysis of Rear-End Crashes at Signalized Intersections

Abstract

Signalized intersections are common hotspots for rear-end crashes, causing severe injuries and property damage. Despite recent attempts to determine the contributing causes to injury severity in this crash type, the frequency of severe rear-end crashes is still significant. Therefore, exploring commonly omitted potential risk factors is essential to proper detection of contributing factors to these crashes and planning appropriate countermeasures. This research incorporated the examination of intersection crash data in Wyoming to examine injury severity risk factors in this crash type. The study examined a set of potential roadway, driver, crash, and environmental risk factors, including pavement surface friction, which is a commonly omitted factor in relevant studies. A random-parameters ordinal probit model was developed for the analysis. The findings demonstrated that two crash attributes (motorcycle involvement and improper seat belt use), three driver’s attributes (driver’s condition, age, and gender), and two environmental and roadway characteristics (road condition and pavement friction) impacted the injury severity of rear-end crashes at signalized intersections.

1. Introduction

Road traffic develops negative impacts on society and represents one of the main challenges in sustainable transportation. Road transportation has severe negative effects on road users’ safety and overall health as well as the environment. Traffic crashes claim approximately 1.3 million lives worldwide and are considered the primary cause of death for children and young adults [1]. In 2021, almost 43,000 people died in traffic crashes in the US. Traffic crashes have a direct negative impact on the environment through gas leaks and spillage, car repairs and disposal, road repairs, excessive emissions because of crash-related congestion and detours, and more [2,3,4].

Due to high crash rates and injury severity levels, intersections are commonly identified as crash-prone spots on road networks. Crashes occurring at intersections are responsible for over 20% of crash fatalities and over 40% of total traffic-related injuries in the US. Intersections are considered high-risk crash locations for all road users due to the complex traffic movements of different transportation modes [5,6,7,8].

Rear-end crashes are one of the most observed crash types in the US, comprising over 30% of total traffic crashes, and they are the predominant crash type at intersections [7,9]. As for injury severity, rear-end crashes are responsible for 7% and 30% of total crash fatalities and injuries at intersections, respectively [2]. Rear-end crashes account for 40% of crashes at signalized intersections in the state of Wyoming. Increased rear-end crashes are observed at signalized intersections because of the high diversity of drivers’ actions in accordance with signal indication changes. The risk of rear-end crashes increases significantly with improper driving behavior, such as distracted driving and tailgating (following vehicles too closely). Sustaining proper space between vehicles that follow one another is critical to allow for adequate reaction time and prevent potential collision with a vehicle ahead that may abruptly brake [10,11,12,13,14,15,16].

The risk of crash occurrence and crash injury is influenced by various roadway, environmental, driver, and crash-related attributes. While crash analysis studies typically incorporate roadway characteristics, pavement surface friction number is a commonly neglected variable in these studies. Pavement friction is likely to influence rear-end crashes at signalized intersections, as it directly impacts the required stopping distance. In addition, pavement friction was reported to be a significant factor impacting the occurrence of this crash type [17,18].

Since rear-end crashes are highly frequent at intersections, special attention should be directed to this type of crash. This study’s objective was to investigate the risk factors influencing the injury severity of rear-end crashes at signalized intersections. The examined risk factors in this study included driver, crash, roadway, and environmental factors. Since pavement friction was a major factor that influenced rear-end crashes observed at signalized intersections [17], further investigation was needed to examine the impact of pavement friction on injury severity for this crash type. To the best of the authors’ knowledge, this is the first study to examine the effect of pavement friction on injury severity in rear-end crashes at signalized intersections. The study explored the role of pavement friction, among other potential risk factors, in crash injury severity. A random-parameters ordinal probit model was developed to examine the impact of these variables on the crash injury severity.

2. Literature Review

Pavement surface friction is the resisting force that eliminates the relative motion between vehicle tires and pavement surface [19,20]. Traffic movements induce aggregate polishing in the pavement surface, which eventually reduces the pavement friction supply. Therefore, transportation agencies need to regularly monitor friction levels. A recent survey comprised a review of current friction management programs across state Departments of Transportation (DOTs). The study indicated that only 11 among the surveyed 32 DOTs evaluated pavement friction on specific roadway locations (intersections, curves, and ramps) when safety-issue evaluation was demanded. The increase of wet-pavement crashes was usually the safety concern that prompted friction data collection [21].

Crashes that occur on wet pavements are commonly linked to insufficient skid resistance, as wet surfaces can considerably reduce frictional force. Deteriorated friction supply may lead to the same issue on dry pavement surfaces [22,23,24]. The State of Wyoming receives significant snowfall and commonly experiences non-dry pavement conditions across its road network. Therefore, more than 30% of crashes in Wyoming occur on non-dry road surfaces, which include snowy, wet, slushy, and icy road surfaces [25,26]. Pavement surface treatments are responsible for providing sufficient friction levels across the roadway network. Various surface treatments are commonly implemented as location-specific applications to enhance friction levels at spots with higher friction demand, including intersections, curves, and ramps. These treatments include chip seals, hot-mix asphalt (HMA) overlays, high-friction surface treatments (HFST), micro-milling, and open-graded friction course (OGFC) [22,27,28].

This section provides a review of multiple studies relevant to the severity of rear-end crashes and skid resistance. The reviewed studies’ limitations are identified and this research’s contribution to the road safety literature is discussed.

Yu et al. [29] examined data from work zones to examine temporal stability of contributing factors to injury severity in rear-end crashes. The research team utilized a random-parameters logit approach with heterogeneity in means and variances. The authors concluded that driver’s condition and access control were significant contributing factors with temporal stability. Even though the authors accounted for the pavement surface type, paved or unpaved, the pavement skid resistance measure was not incorporated in the modeling.

Ahmadi et al. [30] examined the influencing factors of rear-end crashes using support vector machine (SVM), random-parameters multinomial logit, and multinomial logit frameworks. The study aimed to ascertain the influence of risk factors on injury severity. The SVM model demonstrated a superior performance by marginally exceeding that of the other models. The results demonstrated that crashes involving older drivers, driving under the influence, motorcycles, or poor lighting were more likely to be severe. Although the authors incorporated multiple attributes, including the driver’s characteristics, vehicle characteristics, and roadway design features, pavement surface friction was omitted from the analyses.

Chen et al. [31] utilized a random-parameters bivariate ordered probit model to study the injury severity of drivers in rear-end crashes where both colliding vehicles were passenger cars. The authors employed this model to address the unobserved heterogeneity and possible correlation in injury levels between two cars in the same crash. The results demonstrated that driver’s age and gender, vehicle year, and seat belt use affected injury severity in this crash type. However, the authors did not consider any pavement surface characteristics in that study.

Lee et al. [32] employed Bayesian ordinal logistic regression frameworks to examine the influence of the pavement surface condition on crash injury severity. The authors conducted their analysis on data from Florida. According to the authors’ findings, poor pavement surface conditions increased the severity of crashes involving multiple vehicles on roads with both high and low speed limits. However, single-vehicle crashes demonstrated a different trend. The authors incorporated only the pavement condition factor and not the skid resistance in their analyses.

Chen et al. [33] selected a random-parameters, seemingly unrelated negative binomial regression structure to investigate the impact of the pavement roughness on multi-lane and two-lane highway safety. The model captured correlations among the various crash severity categories and unobserved heterogeneity effects. The authors concluded that poor pavement surfaces were associated with higher crash count on multi-lane highways as opposed to two-lane highways. That is, lower pavement roughness translated to fewer injury and non-injury crashes on multilane highways. However, the research team did not investigate the influence of pavement friction on crash severity.

Wang et al. [34] developed multiple generalized estimating equation (GEE) models to investigate the injury severity of rear-end crashes at roadway segments. The results showed that vehicle type, rainy and foggy weather, crash time, traffic volume, and season of the year were all significant contributing factors. The findings also emphasized the significance of addressing the unobserved heterogeneity that could have improved the model performance. However, that study did not consider intersection crashes or include pavement friction in the analysis.

Chen et al. [35] investigated driver injury severities in rear-end crashes via a joint approach combining multinomial logit modeling and the Bayesian network structure. The data belonged to New Mexico. The authors examined the impact of various crash attributes on driver injury severity, including roadway geometric, driver, crash, and traffic control characteristics, among others. The authors concluded that involvement of trucks, poor lighting, strong winds, and count of crashing vehicles may raise the risk of drivers becoming severely injured in rear-end crashes. The authors considered road surface condition (dry, wet, etc.), and pavement type (paved or not); however, pavement friction was not included in the modeling.

Yuan et al. [36] examined the injury severity of rear-end crashes that involved trucks as the vehicles in front. The authors concluded that driver’s age, visibility, number of lanes, and weight difference between crashing vehicles significantly influenced crash severity. Even though the study considered the effect of roadway surface conditions (wet/dry), pavement friction was omitted from the modeling.

Chen et al. [37] explored the factors that influenced the severity of intersection rear-end crashes in Victoria, Australia by means of a logistic regression approach. The research team considered variables from a multitude of attributes. As per the results, driver’s age, driver’s gender, locations with posted speed limits of 100 kilometers/hour (~60 miles/hour), traffic control type, time of crash (morning, afternoon, etc.), type of crash, and seat belt use all impacted rear-end crash severity. However, the authors neglected pavement surface characteristics altogether.

Haleem and Abdel-Aty [38] investigated the factors that impacted the severity of crashes at unsignalized intersections in Florida. The authors employed ordinal probit, binary probit, and nested logit structures. The authors considered the intersection’s features, driver’s characteristics, pavement surface type (asphalt, concrete, etc.), and surface condition (dry, wet, etc.), among other factors. Multiple factors were found to affect crash injury severity risk, such as traffic pattern and number of turning lanes on the major approach. However, the authors did not account for pavement surface skid resistance.

Hussein et al. [39] performed a before–after safety study to examine the impact of pavement maintenance on the safety of signalized intersections. The authors incorporated pavement condition factors such as roughness, rutting, and skid resistance, along with other variables including traffic volume, posted speed limit, lighting condition, time of day, and road surface condition (dry or wet). As per the study’s results, pavement surface maintenance had a significant positive effect on reducing crash frequency and injury severity. However, the study did not consider manner of collision or differentiate between crash types.

Sharafeldin [17] examined the risk factors that contributed to rear-end crash observation compared to other crash types at signalized intersections. The study examined crash records from the state of Wyoming. The investigated variables included intersection, driver, crash, and environmental risk factors. The authors concluded that driver’s age, speed, vehicle type, lighting and weather conditions, urbanization, and pavement surface friction were significant contributing factors to rear-end crash occurrences at signalized intersections. Even though the study considered pavement friction as a risk factor for rear-end crash observation, crash injury severity was not considered.

Generally, there is an increasing interest in the relationship between road safety and pavement surface friction. However, to the best of the authors’ knowledge, no study has examined the impact of pavement friction on the injury severity of rear-end crashes at signalized intersections. In this research, the injury severity of rear-end crashes at intersections is modeled as a function of potential risk factors including pavement surface friction.

3. Data Preparation

Crash information was obtained from the Critical Analysis Reporting Environment (CARE) package provided by the Wyoming Department of Transportation (WYDOT). The crash data were collected from police reports and maintained in the WYDOT database. The crash information was prepared in such a way that each data point represented a crash record with the friction number at the intersection measured at the year of crash. Note that pavement friction numbers varied by year.

The data included records of 3156 rear-end crashes at 240 signalized intersections for the years 2007 to 2017, except 2010 and 2011. Intersection crashes were classified as those that took place within 250 feet (76.2 m) of the intersection’s center, as per the American Association of State Highway and Transportation Officials [40]. The crash data comprised information on roadway, environmental, crash, and driver’s characteristics. Pavement surface friction was one of the major roadway attributes examined in this study.

Pavement friction measurements were collected by WYDOT personnel using a locked-wheel tester. The locked-wheel device is a trailer with two wheels fitted with two tires. One or both wheels are locked to test the friction in the longitudinal direction. The tires may be either smooth or ribbed standard tires [19]. A locked-wheel tester measures pavement friction by fully locking the testing wheel(s) and reporting the average sliding force after achieving the fully locked state. Therefore, the locked-wheel tester can only measure the friction periodically due to the full-lock requirement [41]. The Federal Highway Administration (FHWA) recommends using continuous pavement friction measurement (CPFM) to collect friction data continuously along road networks including special road locations, such as curves, tangent sections, and intersections [42].

The data calibration was conducted by the WYDOT at the designated regional calibration center. When friction was not measured directly at the intersection milepost, the nearest two measurements (before and after the intersection) along the major route of the intersection were averaged to estimate friction at the intersection point. Furthermore, for years when no friction testing was performed, friction numbers were calculated through averaging of the measurements from previous and subsequent years. This approach was only applied in locations where no maintenance work was performed (decreasing friction numbers) and the difference in friction numbers (FN40R) between the previous and subsequent years was less than 10. This procedure assumed that pavement friction was deteriorating at a steady rate over three years. The friction measurements were allocated to the crash records of their years.

Table 1. Data summary statistics.

Categorical Variables
Response		Count	Percent
No injury (property damage only, PDO, or O)		2433	77.1
Possible injury or suspected minor injury (BC)		703	22.3
Fatal injury or suspected serious injury (KA)		20	0.6
Roadway and Environmental Characteristics
Type: four legs or more (1 if yes or 0 otherwise)		2732	86.6
Location: urban (1 if yes or 0 otherwise)		3063	97.1
Grade: uphill (1 if yes or 0 otherwise)		61	1.9
Grade: downhill (1 if yes or 0 otherwise)		194	6.1
Lighting: non-daylight (1 if yes or 0 otherwise)		540	17.1
Road condition: non-dry surface (1 if yes or 0 otherwise)		871	27.6
Adverse weather (1 if yes or 0 otherwise)		578	18.3
Crash Characteristics
Weekend crash (1 if yes or 0 otherwise)		1079	34.2
Hit-and-run crash (1 if yes or 0 otherwise)		210	6.7
Motorcycle involvement (1 if yes or 0 otherwise)		35	1.1
Improper or non-use of safety restraints (1 if yes or 0 otherwise)		457	14.5
Vehicle 1: large (1 if yes or 0 otherwise)		50	1.6
Vehicle 2: large (1 if yes or 0 otherwise)		53	1.7
Driver’s Characteristics
Driver 1: female (1 if yes or 0 otherwise)		1296	41.1
Driver 1: not normal condition (1 if yes or 0 otherwise)		180	5.7
Driver 2: female (1 if yes or 0 otherwise)		1441	45.7
Driver 2: not normal condition (1 if yes or 0 otherwise)		49	1.6
Continuous Variable
	Mean	Minimum	Maximum
Pavement friction	39.0	19	66
Driver 1’s age	36.8	10	102
Driver 2’s age	39.7	14	102

presents the summary statistics of the data.

The response variable (crash injury severity) was categorized as O (property damage only [PDO] or non-injury crashes), BC (possible or suspected minor injury), or KA (fatal or suspected serious injury). The injury severity was considered for each crash as a unit, not for individual occupants or individual vehicles. PDO crashes accounted for the majority (77.1%) of the crash records. Possible and suspected minor-injury crashes represented 22.3% while fatal and suspected serious-injury crashes represented 0.6% of the crash records. The examined roadway characteristics were intersection location, intersection type, grade (uphill, downhill, and level), and pavement friction. The range of pavement friction values (FN40R) was 19 to 66, with an average of 39. Figure 1 demonstrates the friction number distribution for the data.

As for the other roadway attributes, the majority of the crashes occurred at intersections with four or more legs and intersections in urban areas. The intersections were defined as urban or rural as reported by the US Census Bureau [43]. Concerning the roadway grade, the proportions of crashes at uphill and downhill intersections were low compared to crashes at level intersections.

When it came to environmental conditions, crashes mainly occurred during daylight while a small proportion occurred at nighttime, dusk, or dawn, which are referred to as ‘non-daylight’. There was a considerable proportion of crashes that occurred during adverse weather conditions. Adverse weather categories included snow, rain, hail, fog, blizzard, and any other inclement weather conditions. As for road surface condition, 27.6% of the crashes occurred under non-dry road conditions such as snowy, icy, wet, slushy, frosty, or any other non-dry conditions.

In terms of crash characteristics, over a third of the reported crashes occurred on the weekend (Friday, Saturday, or Sunday). Hit-and-run and crashes involving motorcycles represented low proportions. A considerable number of crashes involved improper or non-use of safety restraints. A low proportion of vehicles involved in crashes was considered large vehicles. This category included large and medium-sized trucks, construction vehicles, buses, and motor homes [10].

Regarding the driver’s characteristics, the age, gender, and condition for each of the two involved drivers was considered separately. Driver’s age was included as a continuous variable, with drivers reported as older than 99 considered 102 years old. It should be noted that for crashes involving three or more vehicles, the drivers’ attributes of the two foremost vehicles involved in the crash were included. Male drivers represented the majority of the drivers involved in rear-end crashes at signalized intersections. Low percentages of crashes involved drivers in non-normal conditions. The non-normal condition encompassed drivers under the influence of drugs, alcohol, or medications and drivers who had fainted, were asleep, or were ill. All independent variables were checked for multicollinearity and no variables were highly correlated.

4. Research Methodology

The ordinal nature of the injury severity scale encouraged the extensive use of ordered response models to examine the risk factors of the crash injury severity. Ordered probit and logit models were broadly utilized to examine the influence of different factors on crash injury severity [44,45,46,47,48]. Several studies evaluated the performance of injury severity analysis frameworks by comparing ordered models to multinomial and nested modeling approaches. Multiple studies confirmed the superiority of ordered modeling frameworks due to its simplicity and better reported results [49,50]. However, all these models suffered from the drawbacks of underreported data [51,52]. A recent study [51] reported that ordered models do not allow both the highest and lowest severity levels to vary. Therefore, an increase in the probability of the fatality level is accompanied by a decease in the PDO level and vice versa. As this might be an issue for safety studies involving predictive analysis, this should not impact studies investigating the risk factors of injury-related crashes.

One of the main drawbacks of non-random-parameters models is related to omitting the systematic variations, namely the unobserved heterogeneity effects. This limitation can generate biased and faulty conclusions [45]. Random parameters were incorporated to account for these effects throughout the dataset. Traffic safety studies utilized random-parameters (mixed) ordinal logit and probit models to investigate the influencing risk factors in crash injury severity [44,45,46,47,53].

In this study, a random-parameters probit model was developed to investigate factors affecting the injury severity of rear-end crashes at signalized intersections. As reported by Eluru et al. [54], the ordinal probit structure describes the latent propensity (y_i*) for each crash record, i, as follows:

$${\mathit{y}}_{\mathit{i}}^{*}={\mathit{\beta }}_{\mathbf{0}}+{\mathit{\beta }}_{\mathbf{1}}{\mathit{X}}_{\mathbf{1}\mathit{i}}+{\mathit{\beta }}_{\mathbf{2}}{\mathit{X}}_{\mathbf{2}\mathit{i}}+\dots +{\mathit{\beta }}_{\mathit{P}}{\mathit{X}}_{\mathit{P}\mathit{i}}+{\mathit{\epsilon }}_{\mathit{i}}$$

(1)

The injury risk factors are defined by Xs while their regression coefficients, which are derived via the maximum likelihood estimation (MLE) method, are defined by β’s. The random error term is represented by ɛ_i and assumed to be normally distributed. As reported by Eluru et al. [55], the following equation was implemented to compute the outcome probabilities—P(.)s—where F(.) represents the function of the cumulative standard normal distribution:

$$\mathit{P}\left({\mathit{y}}_{\mathit{i}}=\mathrm{O}\right)=\mathit{F}\mathbf{(}-\mathbf{(}{\mathit{\beta }}_{\mathbf{0}}+\sum _{\mathit{p}=\mathbf{1}}^{\mathit{P}}{\mathit{\beta }}_{\mathit{p}}{\mathit{X}}_{\mathit{p}\mathit{i}}\mathbf{\left)}\mathbf{\right)}$$

(2)

$$\mathit{P}\left({\mathit{y}}_{\mathit{i}}=\mathrm{BC}\right)=\mathit{F}\mathbf{(}{\mathit{\psi }}_1-\mathbf{(}{\mathit{\beta }}_{\mathbf{0}}+\sum _{\mathit{p}=\mathbf{1}}^{\mathit{P}}{\mathit{\beta }}_{\mathit{p}}{\mathit{X}}_{\mathit{p}\mathit{i}}\mathbf{\left)}\mathbf{\right)}-\mathit{F}\mathbf{(}-\mathbf{(}{\mathit{\beta }}_{\mathbf{0}}+\sum _{\mathit{p}=\mathbf{1}}^{\mathit{P}}{\mathit{\beta }}_{\mathit{p}}{\mathit{X}}_{\mathit{p}\mathit{i}}\mathbf{\left)}\mathbf{\right)}$$

(3)

$$\mathit{P}\left({\mathit{y}}_{\mathit{i}}=\mathrm{KA}\right)=\mathbf{1}-\mathit{F}\mathbf{(}{\mathit{\psi }}_{\mathbf{1}}-\mathbf{(}{\mathit{\beta }}_{\mathbf{0}}+\sum _{\mathit{p}=\mathbf{1}}^{\mathit{P}}{\mathit{\beta }}_{\mathit{p}}{\mathit{X}}_{\mathit{p}\mathit{i}}\mathbf{\left)}\mathbf{\right)}$$

(4)

The structure of the random-parameters ordinal probit model had at least one parameter assigned as random. The random parameters’ coefficients were permitted to vary across the dataset. The model was adjusted as follows to accommodate the random parameters, where j defines the injury severity level [56]:

$${\mathit{P}}^{\mathit{m}}\left({\mathit{y}}_{\mathit{i}}=j\right)=\int \left(\mathit{P}\left(\mathit{j}\right)\times \mathit{f}\left(\beta |\phi \right)\right)\mathit{d}\beta$$

(5)

The coefficients’ vector, β, is defined as β + ω_i, where ω_i is a variable with normal distribution. φ represents the vector of the means and variances for distributions. The random parameters’ density function is defined by the term f(β|φ). Outcome probabilities (P_i^m’s) could not be calculated directly because the integral was high-dimensional. Therefore, the density function was simulated and samples were drawn from the coefficients’ vector, β. Then probabilities (P_i^ms) were computed for each sample. The final estimated probability was the average of the estimated probabilities. The Halton draws method, which determines a sequence of non-random draws, was employed for this study. The Halton draws technique is shown to achieve more accurate estimates of the probability distributions for random parameters as compared to techniques that utilize fully random draws. One thousand Halton draws were sampled for this analysis, since this number of draws was reported to lead to accurate estimates of random parameters [46,57,58].

Marginal effects were calculated to determine the influences of the risk factors on crash injury severity. A marginal effect is an average variation in probability of sustaining injury severity j, ΔP(y = j), due to a variable’s effect, given that all other variables are controlled [55].

5. Empirical Analysis

The study developed an ordinal probit model to conduct the preliminary analysis of the crash data. The model included the full set of predictors, which included crash, driver, environmental, and roadway characteristics parameters as presented in Table 1. The 90th percentile confidence level was employed in this analysis. The log–likelihood ratio test was performed to test for model significance. The analysis results are provided in

Table 2. Ordinal probit model results.

Parameter	Estimate	Standard Error	p-Value
Constant	−1.131	0.070	<0.001
Motorcycle involvement	0.700	0.204	0.001
Improper or non-use of safety restraints	0.378	0.067	<0.001
Non-dry road surface	−0.178	0.057	0.002
Driver 1: not normal condition	0.472	0.097	<0.001
Driver 2’s age	0.006	0.001	<0.001
Driver 2: female	0.178	0.050	<0.001
Driver 2: not normal condition	0.439	0.177	0.013
ψ	1.830	0.083	<0.001
Model Fit Summary
Log–likelihood	−1727
Log–likelihood of constant-only model	−1790
Log–likelihood ratio χ2	126
Degrees of freedom	7
p-Value	<0.001

.

The results of the ordinal probit model indicated that a select number of explanatory variables were insignificant at the 90th percentile confidence level (Table 2). In further modeling trials, these variables were assigned as random parameters using the ‘Rchoice’ package [59] of statistical data analysis software R. After a test of whether the predictors were random, a random-parameters ordered probit model was developed including one random parameter and seven non-random parameters. The modeling results are presented in

Table 3. Random-parameters ordered probit model results.

Parameter	Estimate	Standard Error	p-Value
Constant	−1.195	0.170	<0.001
Motorcycle involvement	0.869	0.293	0.003
Improper or non-use of safety restraints	0.481	0.120	<0.001
Non-dry road surface	−0.227	0.083	0.006
Driver 1: not normal condition	0.585	0.158	<0.001
Driver 2′s age	0.007	0.002	<0.001
Driver 2: female	0.216	0.072	0.003
Driver 2: not normal condition	0.557	0.251	0.026
Mean pavement surface friction *	−0.006	0.008	0.487
Standard deviation of the random parameter	0.020	0.010	0.050
ψ	2.346	0.471	<0.001
Model Fit Summary
Log–likelihood	−1725
Log–likelihood of constant-only model	−1790
Log–likelihood ratio χ2	130
Degrees of freedom	9
p-Value	<0.001

* Factor identified as a random parameter.

.

The results of the modeling demonstrated that pavement surface friction was a random parameter with higher friction numbers that were more likely to be linked with lower-severity crashes. With a mean of −0.006 and a standard deviation of 0.020, 62.5% of crashes had a negative coefficient for pavement surface friction, since they had a lower injury severity with increased friction numbers.

The marginal effects of the explanatory variables are presented in

Table 4. Marginal effects of rear-end crash severity factors.

Variable	Marginal Effects (%)
	ΔP(y = O)	ΔP(y = BC)	ΔP(y = KA)
Motorcycle involvement	−26.87	26.44	0.44
Improper or non-use of safety restraints	−12.92	12.81	0.11
Non-dry road surface	4.21	−4.19	−0.02
Driver 1: not normal condition	−16.42	16.25	0.17
Driver 2’s age	−8.52	8.47	0.05
Driver 2: female	−5.12	5.09	0.03
Driver 2: not normal condition	−15.45	15.30	0.15
Mean pavement friction	2.53	−2.52	−0.01

Notes: ΔP(y = O) = change in the likelihood of incurring no injuries, ΔP(y = BC) = change in the likelihood of sustaining possible or suspected minor injury, ΔP(y = KA) = change in the likelihood of sustaining fatal or suspected serious injury.

. In Table 4, ΔP(.)s indicate the changes in the risks of observing crash injury severity j, whether KA, BC, or O. The effect of each variable on the response was calculated assuming the control of all other variables and considering the continuous variables at their average values.

The crash characteristics had a significant effect on risk of severe crashes. Crashes involving motorcycles were found to be severe relative to those not involving motorcycles. It was estimated that, on average, crashes involving motorcycles would have 26.44% and 0.44% higher chances of causing BC and KA injuries, respectively, relative to non-motorcycle-related crashes. Motorcyclists are among vulnerable road users due to their lack of protection, which may give rise to severe injuries in crashes. Multiple researchers reported that higher injury severity was associated with crashes involving motorcycles [60,61]. Crashes involving improper or non-use of safety restraints had higher injury severity levels, with marginal effects of 12.81% and 0.11% for BC and KA injuries, respectively. This finding emphasized the major role of seat belt use in reducing crash injuries [62,63].

As for the environmental variables, only road surface condition was a significant factor. Crashes on non-dry road surfaces were less likely to cause severe injuries. It was estimated that crashes on non-dry road surfaces would have 4.19% and 0.02% lower chances of resulting in BC and KA injuries, respectively, compared to crashes that occurred on dry road surfaces. This finding could be linked to cautious driving and lower travel speeds under those conditions [64].

Driver’s characteristics were found to significantly influence rear-end crash injury severity. Driver’s condition was found to play a major role in impacting injury severity risk. Crashes involving a driver in non-normal condition had higher chances of a BC injury by an estimated 16.25% (Driver 1) or 15.30% (Driver 2). This also increased the chances of incurring a KA injury by an estimated 0.17% (Driver 2) or 0.15% (Driver 1). Driver’s age was also found to influence the crash severity risk. Older drivers were more likely to be associated with severe injury-related crashes. It was estimated that, on average, crashes involving a driver aged 75 would have 8.47% and 0.05% higher chances of resulting in BC and KA injuries, respectively, relative to a driver aged 25. The higher injury severity risk could be related to the vulnerability and deteriorated medical conditions of older drivers involved in the crashes. Lombardi et al. [65] arrived at a similar conclusion. Driver’s gender was another factor that was found to influence the injury severity risk; that is, female drivers were more likely to be involved in severe injury-related crashes compared to male drivers. The marginal effects were estimated as 5.09% and 0.03% for BC and KA injuries, respectively. Gong et al. [53] reported similar conclusions.

As for roadway attributes, pavement friction was the only variable that influenced crash severity. It was estimated that increasing pavement friction numbers (FN40R) from 25 to 45 would reduce the risk of incurring injuries for 62.5% of crashes. The average marginal effect of this factor was computed as −2.52% and −0.01% for sustaining BC and KA injuries, respectively, while assuming control of all other variables. A recent study demonstrated that low pavement friction levels were associated with observed rear-end crashes at signalized intersections [17]. Najafi et al. [66] reported that insufficient friction levels increased the likelihood of crash occurrence and incurring of severe injuries. Sharafeldin [63,67] reported that lower pavement friction contributed to higher crash severity levels at intersections. The findings of this study and [17] emphasized the key role of pavement friction in occurrence and severity of rear-end crashes at signalized intersections. The significant influence of pavement friction on this crash type could be related to the direct correlation between friction and stopping distance, which is crucial to allow reaction time to avoid collision with a vehicle ahead at a signalized intersection. This result highlighted the importance of maintaining adequate friction levels of roadway networks, especially at high-risk crash locations such as intersections, to mitigate crash injury severity.

6. Conclusions and Recommendations

This study explored the factors that contribute to severe injuries in rear-end crashes at signalized intersections. The study examined roadway, environmental, crash, and driver potential risk factors. The random-parameters ordinal probit model was developed to study those factors. The findings identified significant risk factors for injury severity in this crash type. Pavement friction was found to be a random parameter, with higher friction numbers more likely to be associated with lower injury severity levels. Motorcycle crashes were found to have significantly higher injury severity. In addition, improper or non-use of seat belts was associated with severe crashes. Female and older drivers were more likely to be involved in severe injury-related crashes compared to male drivers and young drivers, respectively. The chances of observed non-injury crashes were higher on non-dry road surface conditions. Finally, crashes that involved drivers in non-normal conditions were found to be at risk of resulting in severe injuries.

The findings highlighted the role of pavement friction in crash injury mitigation. It is recommended to provide sufficient friction levels in the roadway network, especially at high-risk locations with higher friction demands, such as intersections. This can reduce severe crash injury risk: specifically, that incurred by rear-end crashes. The study showed that several driver attributes have a significant influence on crash injury severity. Therefore, significant efforts are essential to alleviation of driver behavior concerns. Traffic safety campaigns are recommended to target the most at-risk groups of drivers. This study identified those groups as motorcycle riders, females, and elderly drivers. This study’s findings may provide a better knowledge of the influencing factors of severe injury resulting from rear-end crashes and help in the planning of practical countermeasures.

7. Study Limitations and Future Research

A study limitation was the identification of the at-fault drivers, since no at-fault driver was perceivable in the data. This identification would help better identify the at-fault driver’s attributes influencing the crash injury severity. The same limitation applied to identifying leading and following vehicles.