Exploring the Factors Affecting the Injury Severity of Crashes on Mountainous Freeways with High Proportions of Heavy Vehicles Considering Their Heterogeneous and Interactive Effects

Abstract

Freeway transportation safety issues have attracted public concern in China for decades. This study aims to identify the factors influencing the injury severity of freeway crashes and to quantify their effects on the likelihood of various crash severity levels, with consideration of heterogeneity and interactions. The empirical analysis is based on three years of crash data from two mountainous freeways in Guangdong, China, covering the years of 2021 to 2023. A random parameters logit model with interaction terms is developed for the analysis. Goodness-of-fit indicators reveal that accommodating the interactive effects can significantly improve model fit performance. The estimation results of the parameters and marginal effects indicate that the factors related to vehicle type, time of day, crash season and cause, 3D curvature, and traffic volume have significant effects on crash severity. Notably, interactive effects are revealed between spring and evening, autumn and fixed objects, and non-local vehicles and improper driving. According to the findings, some countermeasures on safety education, traffic management, and freeway design are provided for preventing freeway crash injury, which is helpful for the development of sustainable transportation systems.

1. Introduction

From the perspectives of energy consumption and greenhouse gas emission, other transport modes (e.g., rail, air, or sea transport) may be more sustainable than roadway transport [1]. In China, however, most passengers and cargo are transported by roadways, of which freeways are the primary type. The total length of freeways in China has ranked the first worldwide for over ten years. As an important aspect of sustainability in freeway transportation, traffic safety issues have raised the concerns of freeway designers, operation managers, and safety scholars for a long time. While the design and construction standards for freeways are higher than those for other types of roadways, freeway traffic crashes are more likely to result in severe casualties [2], given that the vehicle speeds on freeways are usually higher. The safety situation of mountainous freeways may be more serious, since poor roadway geometry alignments (e.g., small curve radius, great grades, and combinations of horizontal and vertical curves) on certain sections can lead to limited sight distances and driver misperception [3,4]. In addition, the high proportion of heavy vehicles is also expected to increase the risk and injury severity of freeway crashes, due to their lower speeds relative to passenger cars (leading to greater speed variance) and greater crash aggressivity (that imposes more hazards on other vehicles) [5].

In the literature, a large number of studies have analyzed the factors influencing freeway crash frequency [6,7], real-time crash risk [8,9], and crash injury severity [2,10], which aim to design effective countermeasures for improving freeway safety performance. With regard to freeway crash severity analysis, researchers in the U.S. [10,11,12,13,14,15,16,17,18,19], China [2,20,21,22,23,24,25,26,27,28,29,30,31], and other countries [32] have investigated the effects of the observed factors pertaining to human factors (e.g., driver age and gender, airbag deployment, and driving behavior), vehicle (e.g., vehicle type and year), roadway (e.g., pavement condition, horizontal curvature, vertical grade, number and width of lanes, and speed limit), environment (e.g., weather conditions, lighting conditions, and traffic volume), emergency medical service (e.g., its response time, on-scene time, and transport time), and crash configuration (e.g., crash type, number of vehicles involved, and crash time, day, and season) on the injury severity of freeway crashes, freeway tunnel crashes, or certain types of freeway crashes (e.g., single-vehicle crashes, rear-end crashes, truck crashes, median crashes, tire failure-related crashes, and secondary crashes). Parametric methods, including Bayesian logistic regression, ordered logit models, generalized ordered logit models, spatial generalized ordered logit/probit models, and random parameters logit models, and non-parametric or machine learning methods, including random forest, support vector machine, and classification regression trees, have been adopted in the above research. The parametric models (especially random parameters models) are more prevalent, because of their strong abilities of interpretation and addressing certain issues (e.g., unobserved heterogeneity) of crash data [33]. Nonetheless, these models assume that the effects of factors are mutually independent. The interactions between various factors are omitted, which may not comprehensively or precisely reveal the contributing factors to freeway crash severity and quantify their effects on the probabilities of each severity level.

Interactive effects are defined as the cumulative effects of two or more explanatory variables on the response variable. In the realm of traffic safety, a limited number of studies [34,35,36,37,38,39,40] have taken factor interactions into consideration. In particular, Jung et al. [34] investigated the injury severity of two-vehicle crashes in rainy weather and found that it is significantly affected by the interactions of upgrade class with left shoulder width and lane number. Based on a binary logit analysis of wrong-way driving crashes, Ponnaluri [35] found that the interactions between facility type and lighting condition, and between facility type and urban/rural location, have significant effects on fatality likelihood. Ahmed et al. [36] adopted a Bayesian logistic model for analyzing the injury severity of rural highway crashes in Wyoming State. The results suggested that there were various interactive effects (e.g., speeding and horizontal curves, truck involvement and vertical grade) on crash severity. In an analysis of pedestrian crash severity in Hong Kong, significant interactive effects of weather conditions (including rain and temperature) and driver/pedestrian behaviors (e.g., driver inattention, pedestrian jaywalking, pedestrians running onto the road) were uncovered [38]. Sun et al. [39] proposed a hybrid method of using random forest and random parameters logit models for analyzing the injury severity of crashes involving vulnerable road users and found that the likelihood of fatality was increased by primary roads and rural areas, while it was decreased by their interaction. These works all concluded that accounting for the interactions between the observed factors provided deeper insights into the mechanisms of crash injuries. To our knowledge, there is no reported research which investigates the interactive effects on freeway crash injury severity in the parametric modeling paradigm.

To this end, the current research aims to reveal the factors influencing the injury severity of freeway crashes with consideration of their interactive and heterogeneous effects, using a random parameters logit model incorporating interaction terms between various factors. The three-year (2021–2023) crash data from two mountainous freeways with high proportions of heavy vehicles in Guangdong Province, China, is employed for the empirical analysis. To demonstrate the benefits of capturing the interactive effects, the random parameters models with and without interaction terms are compared.

The rest of the article is structured as follows: Section 2 describes the collected crash data. Section 3 introduces the formulation of the random parameters logit model and the methods for model comparison. The model results are summarized and analyzed in Section 4. The conclusions and practical implications are provided in Section 5.

2. Data

In this study, a three-year (2021–2023) crash dataset from two mountainous freeways in Guangdong Province, China: Shantou–Kunming Freeway (from the kilometer marker K45 to K114) and Meizhou–Shanwei Freeway (from the kilometer marker K0 to K28) is employed for the crash injury severity analysis. Figure 1 illustrates the locations of the freeway sections under investigation. The two freeway sections are spatially adjacent and are operated and managed by the same agency—the Luda Constituent Company of Guangdong Road and Bridge Construction Development Co. Ltd. The dataset was assembled with information from four different data sources: (i) crash records, (ii) roadway designs, (iii) traffic flow, and (iv) meteorological conditions. Given that the data were sourced from a third party and do not contain the private information of the involved persons, ethical review was not required in the present study.

2.1. Crash Record

The traffic crash data were retrieved from the Freeway Maintenance and Administration Management System, which is maintained by the freeway management agency. According to the system, 664 crashes occurred on the selected sections of the two freeways from 2021 to 2023. By removing the crash records with incomplete information, the data of 617 crashes were extracted and processed for the study. In the raw crash records, crash injury severity is categorized into four levels: no injury, slight injury, severe injury, and fatality, in accordance with the rules of the Ministry of Public Security. Among the extracted data, only one and nine crashes resulted in severe injuries and fatalities, respectively. Due to this sparseness, the two severity levels were combined to constitute the “fatal and severe injury (FSI)” category.

In addition to crash injury severity, the system also provides information on the types and license numbers of the involved vehicles, and the dates, time, types, and causes of crashes. These vehicle and crash attributes are categorized based on the original definitions in the system and their classifications in similar works [2,29].

2.2. Roadway Design

The profiles of the two freeway sections which are designed by the Guangdong Provincial Highway Survey, Planning and Design Institute were also obtained from the management agency. The quantities of roadway attributes (e.g., the number and width of lanes, the type and width of shoulders, speed limit) are constant along the two freeway sections. Although it is fixed, noticeably, the speed limit is only 80 km/h, which is significantly lower than the counterparts (100 or 120 km/h) on other freeways in China. Three geometric design attributes of crash locations, including vertical grade, three-dimensional (3D) curvature, and 3D torsion, were extracted from the freeway profiles. The two 3D highway attributes were selected because they determine the geometric morphology of freeways, whose alignments are 3D in nature. The 3D curvature measures the bending of a freeway, and the 3D torsion measures its twisting. Please refer to Wang et al. [41] for more detailed descriptions and computing formulas of the attributes. While Wang et al. [41] found that freeway crash rate is significantly associated with 3D attributes, their effects on freeway crash severity have not been investigated. In addition, in the two mountainous freeway sections, the minimum grade of down-slopes reaches −4.67%, and the maximum grade of up-slopes reaches 4.8%.

2.3. Traffic Flow and Meteorological Condition

The monthly traffic data recorded by the Electronic Toll Collection (ETC) units along the two freeway sections from 2021 to 2023 were also collected. According to the data, the number of truck vehicles accounts for over 60% in the mixed traffic flow. Each crash was matched to the nearest upstream ETC unit. The monthly traffic volume from the nearest ETC unit was used as an explanatory variable for the analysis of freeway crash severity.

The meteorological observation data at a municipal-level weather station near the two freeway sections were obtained from the National Oceanic and Atmospheric Administration, which is an official website of the United States government. Information on the temperature, wind speed, and precipitation on the day of each crash are available.

The definitions/categorizations of the above variables and their descriptive statistics in the prepared dataset are summarized in

Table 1. Definitions and descriptive statistics of the variables for modeling freeway crash injury severity.

Scope of Work	Variable	Definition	Mean	S.D.	Min.	Max.	Proportion
Crash injury severity	No injury a	No one is injured	—	—	—	—	0.849
	Slight injury	The most severe injury level of involved occupants is slight injury	—	—	—	—	0.134
	Fatal and severe injury	The most severe injury level of involved occupants is severe injury or fatality	—	—	—	—	0.017
Vehicle involved	Car a	Only cars involved = 1; else = 0	—	—	—	—	0.509
	Bus	At least one bus involved = 1; else = 0	—	—	—	—	0.013
	Truck	At least one truck involved = 1; else = 0	—	—	—	—	0.389
	Heavy trailer	At least one heavy trailer involved = 1; else = 0	—	—	—	—	0.387
	Other vehicle	At least one other vehicle (such as road sweeper) involved = 1; else = 0	—	—	—	—	0.011
	Non-local vehicle	At least one non-local vehicle (i.e., not registered in Guangdong Province) involved = 1; else = 0	—	—	—	—	0.454
Time of the day	Before dawn	Crash time is within [12:00 am, 5:59 am] = 1; else = 0	—	—	—	—	0.183
	Morning	Crash time is within [6:00 am, 11:59 am] = 1; else = 0	—	—	—	—	0.222
	Afternoon a	Crash time is within [12:00 pm, 5:59 pm] = 1; else = 0	—	—	—	—	0.361
	Evening	Crash time is within [6:00 pm, 11:59 pm] = 1; else = 0	—	—	—	—	0.233
Day of the week	Weekday	Crash occurred on weekday = 1; crash occurred on weekend = 0	—	—	—	—	0.679
Crash season	Spring	Crash occurred in February, March, or April = 1; else = 0	—	—	—	—	0.253
	Summer a	Crash occurred in May, June, or July = 1; else = 0	—	—	—	—	0.263
	Autumn	Crash occurred in August, September, or October = 1; else = 0	—	—	—	—	0.266
	Winter	Crash occurred in November, December, or January = 1; else = 0	—	—	—	—	0.218
Crash type	Rollover	A rollover crash = 1; else = 0	—	—	—	—	0.071
	Fixed object	A collision with a fixed object = 1; else = 0	—	—	—	—	0.295
	Rear-end a	A rear-end crash = 1; else = 0	—	—	—	—	0.554
	Angle	An angled crash = 1; else = 0	—	—	—	—	0.060
	Others	An crash of other types = 1; else = 0	—	—	—	—	0.024
Crash cause	Improper driving	Crash cause is improper driving (e.g., speeding and illegal overtaking) = 1; else = 0	—	—	—	—	0.437
	Insufficient safety distance a	Crash cause is insufficient safety distance = 1; else = 0	—	—	—	—	0.521
	Other causes	Other crash causes (e.g., tire failure) = 1; else = 0	—	—	—	—	0.042
Road design	Grade	Vertical grade of crash location (%)	1.8	1.2	0.0	4.8	—
	Curvature	3D curvature of crash location (1/km)	0.2	0.3	0.0	3.2	—
	Torsion	3D torsion of crash location (1/km)	−0.7	6.8	−60.7	22.5	—
Traffic volume	Traffic	Normalized monthly traffic volume at the crash location (105 passenger car unit, PCU)	5.92	1.08	2.51	9.12	—
Meteorology	Temperature	Average temperature on the crash day (°C)	23.4	5.9	7.8	32.8	—
	Wind speed	Average wind speed on the crash day (m/s)	2.2	0.7	0.7	5.0	—
	Precipitation	Precipitation on the crash day (mm)	10.7	27.1	0.0	233.0	—

^a Reference category.

.

3. Method

3.1. Random Parameters Logit Model

Unobserved heterogeneity is one of the most important characteristics of traffic crash data [33]. A random parameters logit model (also called a “mixed logit model”) is a very prevalent method of analyzing crash injury severity with three or more levels while accommodating for the heterogeneity in it. In our random parameters logit model, to measure the propensity of the injury severity level $j$ for crash $i$, a latent variable $S_{i,j}$ is defined as follows [42]:

$$S_{i,j}={\beta }_{i,j}{X}_{i,j}+{\epsilon }_{i,j},$$

(1)

where $X_{i,j}$ is a vector of observed factors specific to crash $i$ that may affect injury severity $j$, and ${\beta }_{i,j}$ is a vector of random parameters which correspond to the vector of observed factors and are allowed to vary across the observations. ${\epsilon }_{i,j}$ is a residual term which is assumed to follow an extreme value Type I distribution that is independent and identical across the observed crashes and divided severity levels.

To reveal the interactive effects of the observed factors on crash injury severity, noticeably, the interaction terms of the factors in Table 1 are also incorporated into the vector $X_{i,j}$. While the interactions among three or more factors is possible, only those between two factors (i.e., their products, such as rollover × grade) are considered in the analysis, which is consistent with previous studies [34,35,36,37,38,39].

The vector of random parameters ${\beta }_{i,j}$ is structured as follows:

$${\mathbf{\beta }}_{i,j}={\mathbf{b}}_j+{\mathbf{\delta }}_{i,j},$$

(2)

where ${\mathbf{b}}_j$ is a vector of fixed parameters corresponding to the means of the random parameters specific to the injury severity $j$. ${\mathbf{\delta }}_{i,j}$ represents the random components unique to each crash and severity level, which are assumed to follow a distribution, such as normal distribution.

The probability of a crash $i$ leading to a particular injury severity level $j$ is thus formulated as:

$$P_{i,j}=\int {\displaystyle \frac{\exp \left({\mathit{\beta }}_{i,j}{\mathit{X}}_{i,j}\right)}{\sum \exp \left({\mathit{\beta }}_{i,j}{\mathit{X}}_{i,j}\right)}}f({\beta }_{i,j}|{\mathbf{b}}_j,\theta )d{\beta }_{i,j},$$

(3)

where $f({\beta }_{i,j}|{\mathbf{b}}_j,\theta )$ is the density function of ${\beta }_{i,j}$ and $\theta$ is a vector of parameters describing the density function of distribution for ${\mathbf{\delta }}_{i,j}$.

To estimate the random parameters logit models with and without interactions, a simulation-based maximum likelihood approach with Halton draws was adopted [43]. A total of 500 Halton draws was set, as some previous research [44,45] has shown that this is appropriate for the estimation of random parameters models. The model estimation was conducted via programming in the econometric software NLOGIT 6.0. Additionally, to quantify the effects of significant factors on each crash injury severity, their marginal effects were also estimated. For a continuous variable $x_k$, its marginal effect on $P_{i,j}$ is computed by its first-order derivative with respect to $x_k$. For a dummy variable $x_k$, the marginal effect on $P_{i,j}$ is calculated as:

$$E_{i,j,k}=p_{i,j}\left(x_k=1\right)-p_{i,j}\left(x_k=0\right),$$

(4)

Since the marginal effect of a certain variable may vary across the observations, its average for the entire dataset is quantified and reported.

3.2. Model Comparison Criteria

To compare the random parameters logit models with and without interactions in terms of goodness-of-fit, the widely used Akaike Information Criterion (AIC), McFadden Pseudo R², and the likelihood ratio test are adopted. According to the likelihood performance of a model and its number of parameters, the AIC provides a measure of the information loss amount in it. The AIC is defined as [46]:

$$AIC=2\left(K-LL\left(\beta \right)\right),$$

(5)

where $K$ is the number of estimable parameters in the model, and $LL\left(\beta \right)$ is its log-likelihood at convergence. Generally, a model with a lower AIC is preferred.

The McFadden Pseudo R² is calculated as:

$${\mathrm{McFadden} \mathrm{Pseudo} \mathrm{R}}^2=1-{\displaystyle \frac{LL\left(\beta \right)}{LL\left(\mathbf{0}\right)}},$$

(6)

where $LL\left(\mathbf{0}\right)$ is the log-likelihood of the null model (i.e., the model with constant only). A greater value of McFadden Pseudo R² indicates better fit performance.

Based on the definition in [43], the likelihood ratio test statistic for models A and B is computed as:

$${\chi }^2=-2\left(LL\left({\beta }_A\right)-LL\left({\beta }_B\right)\right),$$

(7)

where $LL\left({\beta }_A\right)$ and $LL\left({\beta }_B\right)$ represents the log-likelihood at convergence of models A and B, respectively. The statistic ${\chi }^2$ is assumed to follow a chi-square distribution, whose degree of freedom is the difference in the number of estimable parameters between the two models.

4. Result Analysis

4.1. Model Comparison

The estimation and comparison results of the random parameters logit models with and without interactions are shown in

Table 2. The estimation and comparison results of the random parameters logit models with and without interactions.

Variable	Random Parameters Logit Model		Random Parameters Logit Model with Interactions
	Coef.	z-Stat.	Coef.	z-Stat.
Constant [MI]	−2.90 ***	−10.49	−3.47 ***	−9.67
Constant [FSI]	−4.36 ***	−4.06	−4.42 ***	−4.11
Bus [MI]	0.67 **	2.20	0.67 **	2.04
Truck [MI]	0.22	0.28	0.14	0.17
S.D. of truck	1.88 *	1.66	2.30 **	2.00
Heavy trailer [MI]	1.96 ***	2.93	2.26 ***	3.12
Before dawn [MI]	0.60 *	1.65	0.76 *	1.88
Curvature [MI]	0.35 **	2.06	0.39 **	2.22
Traffic [MI]	0.25 **	2.26	0.26 **	2.20
Bus [FSI]	1.45 *	1.91	1.44 *	1.90
Heavy trailer [FSI]	4.27 ***	3.87	4.26 ***	3.87
Other vehicle [FSI]	−2.16 **	−2.20	−2.14 **	−2.17
Before dawn [FSI]	2.51 ***	2.72	2.51 ***	2.72
Evening [FSI]	1.89 **	2.12	1.93 **	2.18
Improper driving [FSI]	−2.58 **	−2.57	−2.49 **	−2.48
Spring × evening [MI]	-	-	1.46 ***	2.73
Fixed object × autumn [MI]	-	-	0.97 **	2.32
Non-local vehicle × improper driving [MI]	-	-	0.68 **	2.03
$K$	15		18
$LL\left(\beta \right)$	−261		−252
$AIC$	552		540
McFadden Pseudo R2	0.61		0.63
${\chi }^2$	$12 > {\chi }_{3, 0.05}^2=7.81$

MI: minor injury; FSI: fatal and severe injury; ***: significant at 0.01 level; **: significant at 0.05 level; *: significant at 0.1 level.

, where only those factors with significant effects (i.e., the corresponding parameters different from zero at least at the 0.1 significance level) on crash injury severity are included. According to the results, the AIC value (=540) of the random parameters logit model with interactions is smaller than that (=552) of the random parameters logit model (without interactions), which indicates the better fit performance of the former model. It is also demonstrated by the higher value of the McFadden Pseudo R² for the model with interactions. The findings are reasonable, because there are three pairs of factors (i.e., spring × evening, fixed object × autumn, and non-local vehicle × improper driving) with significant interactive effects on crash injury severity. They are also consistent with the conclusions in previous studies [34,36,37,38]: capturing the interactions among the observed factors is able to improve the goodness-of-fit of models. The findings can be further validated by the results of the likelihood ratio test. Specifically, the likelihood ratio test statistic between the two models equals 12, which is bigger than the chi-squared critical value at the 0.05 significance level (=7.81). That is, the two models are significantly different from each other.

4.2. Interpretation of Model Estimation and Marginal Effects

Due to the superiority of the random parameters logit model with interactions, the effects (including the main effects and interactive effects) of significant factors on the injury severity of freeway crashes are interpreted according to the results of its parameter estimation (shown in Table 2) and the corresponding marginal effects (shown in

Table 3. The marginal effects of significant factors on freeway crash severity.

Variable	No Injury	Minor Injury	Fatal and Severe Injury
Bus	−3.68%	2.35%	1.32%
Truck	−4.64%	4.71%	−0.08%
Heavy trailer	−1.38%	0.61%	0.79%
Other vehicle	1.05%	0.16%	−1.22%
Before dawn	−2.59%	1.25%	1.34%
Evening	−0.89%	−0.16%	1.05%
Improper driving	1.14%	0.32%	−1.45%
Curvature	−0.50%	0.52%	−0.03%
Traffic	−0.84%	0.85%	−0.01%
Spring × evening	−1.29%	1.32%	−0.03%
Autumn × fixed object	−1.89%	1.92%	−0.03%
Non-local vehicle × improper driving	−2.15%	2.20%	−0.06%

).

Vehicle type is an important characteristic of the involved vehicles with significant influence on crash injury severity. Specifically, the parameters of buses and heavy trailers for minor injury and FSI are all significantly positive, which indicate that the involvement of buses and heavy trailers in freeway traffic crashes increases the injury severity level of freeway crashes. According to the estimated marginal effects, compared to passenger car-only crashes (the reference category), the involvement of buses and heavy trailers would increase the probability of minor injury by 2.35% and 0.61%, respectively, and increase the probability of FSI by 1.32% and 0.79%, respectively. These results are anticipated because the crash aggressivity of these vehicles is stronger (given their bigger sizes and masses and higher stiffness) than passenger cars [2,5,29], which would result in greater damage to the other vehicles colliding to them. The coefficient of trucks for minor injury is a random parameter with a mean of 0.14 and a standard deviation of 2.30, which suggests that the involvement of trucks would increase the probability of minor injury for 52.4% of freeway crashes and decrease the probability of minor injury for the remaining 47.6%. On average, the involvement of trucks would decrease the probability of no injury by 4.64% and increase the probability of minor injury by 4.71%, as revealed by the estimated marginal effects. It is interesting to find that the coefficient of other vehicles for FSI are significantly negative, which suggests that the involvement of other types of vehicles would decrease the probability of FSI. This is possibly due to the vehicles mostly being specialized, such as road sweepers, which are usually driven at very low speeds.

With regard to the time of day, the time being before dawn had positive effects on both minor injury and FSI. According to the marginal effects, the probabilities of minor injury and FSI crashes occurring before dawn are 1.25% and 1.34% higher, respectively, relative to those occurring in the afternoon (the reference category). Evening also has a significantly positive effect on KSI, which indicates that freeway crashes in the evening are more likely to result in severe outcomes. The results are generally in line with the previous findings [30,47], which argued that they may be attributed to the limited visual field and lower mental alertness of vehicle drivers in the evening and before dawn.

While the main effects of the seasonal variables are not statistically significant, the interactive effects between some of them and other factors are significant. Specifically, the interaction between spring and evening was found to be positively associated with minor injury. There is a sharp rise in freeway traffic volume during the Spring Festival, which is the most important festival in China, and many people will return to their hometown from big cities by driving cars along freeways, because freeways are free of charge during the festival. This increased traffic volume usually results in traffic congestion on freeways, while the limited visual field in the evening might bring about vehicle collisions. The interactive effects between autumn and fixed objects on minor injury is also significantly positive, which means that fixed-object crashes are more likely to result in minor injuries in autumn.

Curvature was the only roadway factor found to have a significant effect on freeway crash injury severity. According to its marginal effects, a one-unit increase in the 3D curvature would increase the probability of minor injury by 0.52% and decrease the probabilities of no injury and FSI by 0.50% and 0.02%, respectively. This finding is generally consistent with [41], in which the authors concluded that 3D curvature is significantly associated with the safety performance of freeways. It is also similar to the effect of horizontal curvature on freeway crash severity: a greater curvature requires stronger force for vehicles negotiating the curve, and therefore reduces vehicle control [29,47].

The parameter of traffic for minor injuries is positive at the 0.05 significance level, which indicates that freeway sections with higher traffic volumes are more likely to experience minor injury crashes. Specifically, a 10⁵ PCU increase in the monthly traffic volume is expected to increase the probability of minor injuries by 0.85% and decrease the probabilities of no injury and FSI by 0.84% and 0.01%, respectively. This conforms to transportation intuitions and the extant literature [2,47]: a higher traffic volume would bring about severer traffic congestion and lower vehicle speed. The traffic congestion may make some aggressive drivers change lanes frequently and thus increase traffic conflicts. The lower vehicle speed would decrease the probability of severe outcomes.

Regarding the causes of crashes, the negative coefficient of improper driving for FSI suggests that improper driving is less likely to result in FSI than insufficient safety distance (the reference category). Its marginal effects reveal that the probability of FSI caused by improper driving is 1.45% lower than that caused by insufficient safety distance. Additionally, the interactive effect between improper driving and non-local vehicles on the propensity of minor injury is positive at the 0.05 significance level, which means that the improper driving behavior of non-local vehicle drivers is more likely to result in minor injury. This may be attributed to the drivers of non-local vehicles being unfamiliar with mountainous freeways [29]. When encountering an upcoming crash, they may not take proper actions to avoid crash injury.

While interaction and heterogeneity were found in the effects of the observed factors, there are some limitations in this research. First, information related to human factors (e.g., the age and gender of drivers involved) and emergency medical services (e.g., its response time and on-scene time) was not recorded in the crash data. Therefore, their main and interactive effects on freeway crash injury severity were not investigated. Second, the crash data were from two freeways in Guangdong Province, China. The transferability of the analysis results to freeways in other regions or countries is not verified. Third, the random parameters logit model was formulated in the standard form. More complicated versions, such as a model with heterogeneity in means and variances, may further reveal heterogeneous effects, although they were not found in the random parameters used in the current research.

5. Conclusions and Future Research

This research investigates the heterogeneous and interactive effects of vehicle characteristics (i.e., vehicle type and registration location), roadway design attributes (i.e., vertical grade, 3D curvature and torsion), traffic volume, meteorological conditions (i.e., temperature, wind speed, and precipitation), crash time (i.e., time of day, day of week, and season), type, and causes on the injury severity of freeway crashes, using a three-year (2021–2023) crash dataset from Shantou–Kunming Freeway and Meizhou–Shanwei Freeway in China, which are featured by mountainous terrain and high proportions of heavy vehicles. A random parameters logit model with interaction terms was developed for the empirical investigation.

The results of the model estimation indicate that there is unobserved heterogeneity in the effect of trucks on crash injury severity. Three pairs of explanatory variables, including spring and evening, autumn and fixed objects, and non-local vehicles and improper driving, significantly increase the likelihood of minor injury. It is also increased by traffic volume and the 3D curvature of freeway sections. Compared with passenger car-only crashes, the involvement of buses and heavy trailers would increase the likelihoods of minor injury and FSI, and the involvement of other vehicles (e.g., road sweepers) would decrease the likelihood of FSI. Freeway crashes in the evening and before dawn, and those caused by insufficient safety distance, are more likely to result in severe outcomes. The marginal effects of these significant variables on the probabilities of each injury severity level are quantified. In addition, the results of DIC, McFadden Pseudo R², and the likelihood ratio test suggest that the random parameters logit model with interactions outperforms the counterpart without interactions. The findings justify the necessity and advantage of capturing the heterogeneity and interaction in crash data.

The analysis results provide some suggestions for designing countermeasures for the prevention of freeway traffic injury (especially severe injuries and fatalities), which is a key goal of developing a safe and sustainable freeway transportation system. For example, more safety education/campaigns and more frequent police patrols during the evening (especially in spring) and before dawn are suggested to regulate drivers to obey the traffic rules, especially those for intercity buses, heavy vehicles, and hazardous material vehicles; (1) the drivers of these vehicle types are prohibited from continuously driving for over 4 h during daytime (6:00 a.m. to 10:00 p.m.) or over 2 h during nighttime (10:00 p.m. to 6:00 a.m.), and the rest time of each vehicle stop should be not less than 20 min; (2) the cumulative driving time of bus drivers within 24 h should be no more than 8 h; and (3) the driving speed of intercity buses during nighttime should be under 80% of the posted speed limit. Adding vehicle distance confirmation markers to the hotspots of crashes attributed to insufficient safety distance is helpful for reducing crashes of this type and mitigate their crash injury severity. Setting solid lines in freeway sections with high traffic volume is expected to reduce lane-changing behaviors and the potential traffic crashes and injuries caused by them. Reducing the 3D curvature of freeway geometry alignments is encouraged during their reconstruction projects to improve safety performance.

Due to the limitations in the crash data collection and methodology, some directions for future research are provided. The effects of human factors, emergency medical services, and their interactions with other factors on crash injury severity should be examined, and the spatial transferability and temporal stability of the findings should be validated if more crash data are available. In addition, extending the random parameters logit model to further account for heterogeneity in means and variances is also worth exploration.