Evaluate Weather Conditions The Condition

Int J Environ Res Public Wellness. 2020 Apr; 17(8): 2768.

Investigating the Impacts of Real-Fourth dimension Weather Conditions on Freeway Crash Severity: A Bayesian Spatial Analysis

Qiang Zeng

^aneSchoolhouse of Civil Technology and Transportation, South China University of Technology, Guangzhou 510641, China; nc.ude.tucs@gnaiqgnez

²Jiangsu Province Collaborative Innovation Centre of Mod Urban Traffic Technologies, Nanjing 211189, China

Wei Hao

³Schoolhouse of Traffic and Transportation, Changsha University of Scientific discipline and Technology, Changsha 410114, China; nc.ude.tsusc@iewoah

Jaeyoung Lee

⁴School of Traffic and Transportation Engineering, Central South University, Changsha 410075, China; ude.fcu.sthgink@gnuoyeaj

Feng Chen

^vKey Laboratory of Road & Traffic Engineering of the Ministry building of Education, Tongji University, Shanghai 201804, China

Received 2020 Feb twenty; Accepted 2020 Apr 14.

Abstract

This study presents an empirical investigation of the impacts of existent-time weather weather on the freeway crash severity. A Bayesian spatial generalized ordered logit model was developed for modeling the crash severity using the hourly air current speed, air temperature, precipitation, visibility, and humidity, equally well every bit other observed factors. A total of 1424 crash records from Kaiyang Thruway, Prc in 2014 and 2015 were nerveless for the investigation. The proposed model can simultaneously accommodate the ordered nature in severity levels and spatial correlation beyond side by side crashes. Its force is demonstrated by the being of significant spatial correlation and its better model fit and more than reasonable interpretation results than the counterparts of a generalized ordered logit model. The estimation results show that an increment in the precipitation is associated with decreases in the probabilities of lite and severe crashes, and an increase in the probability of medium crashes. Additionally, driver type, vehicle type, vehicle registered province, crash fourth dimension, crash type, response time of emergency medical service, and horizontal curvature and vertical grade of the crash location, were also found to have significant furnishings on the crash severity. To alleviate the severity levels of crashes on rainy days, some engineering countermeasures are suggested, in addition to the implemented strategies.

Keywords: crash severity, conditions condition, generalized ordered logit model, spatial correlation, conditional autoregressive prior, Bayesian inference

1. Introduction

Weather conditions have been found to bear upon traffic crash take chances and severity (e.thousand., [1,ii,3,iv,5]). Especially, agin weather weather condition (eastward.k., typhoon, rainstorm, and heavy fog) may consequence in astringent crashes on rural freeways, which are characterized with a high vehicle speed and a large proportion of heavy vehicles [6]. Quantifying the furnishings of weather conditions on the crash severity has a potential to provide directions for developing countermeasures and policies aimed at decreasing the amount of property harm and mitigating the level of injury severity sustained past involved route users, and thus improving the prophylactic performance of freeways.

However, in most of the previous crash severity analyses [vi,7,8], researchers collected weather information from historical crash reports, where constabulary officers recorded the weather information based on their subjective judgements at crash scenes or even their memories when they were back at their offices [8]. The vague information on weather condition conditions may lead to a biased estimation of their furnishings on crash severity. A better alternative is collecting existent-time data on conditions atmospheric condition from proximate weather ascertainment stations where precise information on wind speed, air temperature, precipitation, visibility, and humidity is unremarkably measured continuously by specific sensors and recorded at small intervals (e.g., 2 or 15 min) [9,10]. Incorporating them into crash severity models is expected to uncover a more explicit relationship between crash severity and weather conditions, as well equally the attributes related to drivers, vehicles, roadways, emergency medical service (EMS), and crash configuration.

A number of previous studies accept examined the impacts of real-time weather conditions on crash injury severity [8,9,eleven]. However, these studies are specific to certain crash types. Specifically, Jung, Qin, and Noyce [eleven] used sequential logistic models to appraise the effects of wind speed, temperature, rainfall intensity, and h2o pic depth on the injury severity of single-vehicle and multi-vehicle crashes respectively in rainy weather. They found that current of air speed has significant effects on the severity of both single-vehicle and multi-vehicle crashes and rainfall intensity has a significant effect on single-vehicle crashes merely. Naik et al. [nine] investigated the relationship between the injury severity of single-vehicle truck crashes and real-time atmospheric condition weather condition using mixed ordered and unordered logit regressions. The results showed that more severe injuries in single-vehicle truck crashes are associated with higher wind speed and air temperature, heavier precipitation, and lower humidity. Recently, Zhai et al. [8] developed a mixed logit model to analyze the impacts of weather conditions on pedestrian crash severity and found that higher air temperature and presence of rainfall were linked to a higher level of pedestrian injuries.

To the best of our cognition, there is only one reported written report [12] that focused on the effects of real-fourth dimension weather weather condition on the injury severity of thruway crashes (regardless of crash types). The importance of explanatory variables was estimated using the random forest method and temperature was identified as the merely important weather factor. Nonetheless, in that location are several limitations of the enquiry with respect to generalization and methodology. First, only two injury levels (no-injury versus injury) were classified, which may outcome in inadequate use of crash severity information and cannot provide a thorough understanding of the effects of significant factors on the likelihood of sure specific injury levels (e.g., fatality). Second, the factors related to drivers, vehicles, EMS, and crash configuration were non considered in the analysis. Third, the employed support vector machine, and fixed and mixed logit models cannot account for the spatial correlation among adjacent crashes, the significance of which has been demonstrated in extensive previous studies on modeling crash frequency/rate [13,xiv,15,16,17] and severity [18,19,20,21]. Using a more rigorous modeling scheme for the analysis of crash severity in a more than comprehensive metric with more external factors controlled is benign to ameliorate the accuracy of the estimated effects of existent-time weather weather condition on the agin outcomes of freeway crashes.

Methodologically, the substantial progress in analytical methods over the years has enabled a more precise decision of the influence of risk factors on crash severity. A wide range of sophisticated methods have been developed by accommodating the fundamental characteristics of crash severity data, including ordered nature [22,23], underreporting [24], endogeneity [25], inside-crash correlation [26,27], spatial and temporal correlation [19,20,28,29], unobserved heterogeneity [thirty,31], etc. Please refer to [32,33] for a comprehensive introduction and cess on the methodological alternatives. More recently, a Bayesian spatial generalized ordered logit model proposed by Zeng et al. [6] is one of the state-of-the-fine art methods for modeling crash severity. The model is able to account for the ordered nature and spatial correlation simultaneously. The thresholds are allowed to vary with the observed explanatory variables, which tin remove the restrictions imposed past the fixed thresholds in standard ordered response models [34]. Moreover, the conditional autoregressive (CAR) priors incorporated can accommodate not simply the spatial correlation across crashes simply also the unobserved heterogeneity [19].

In the current research, the Bayesian spatial generalized ordered logit model was adult to investigate the impacts of existent-time weather condition conditions on expressway crash severity. A comprehensive crash dataset collected from Kaiyang Freeway in Guangdong Province, Prc in 2014 and 2015 was used for the empirical investigation, where crash severity is categorized by Chinese law administration co-ordinate to an integrative assessment of the adverse crash outcomes, i.east., the number of people injured at various degrees (eastward.g., slight and serious injury, and fatality) and the corporeality of property damage. To demonstrate the superiority of the proposed spatial model, it is compared with a generalized ordered logit model in terms of model fit and parameter estimates.

The residue of this paper is organized every bit follows: In Section 2, we introduce the collected freeway crash dataset for the analysis. In Section 3, we specify the formulations of the traditional and spatial generalized ordered logit models, the criteria for model fit comparison, and the calculation of the marginal effects of run a risk factors. Department iv presents the Bayesian estimation procedure of the models and analyzes the results of the model comparing and estimation. In Section 5, some remarkable conclusions are drawn and several directions for future research are provided.

2. Data Assembly

A comprehensive dataset from the Kaiyang Freeway in 2014 and 2015 was used in the current research. It was assembled with information from iii different resources on crash data, roadway inventory, and existent-time atmospheric condition weather condition, respectively.

2.1. Crash Data

We obtain the superhighway crash data from the Highway Maintenance and Administration Direction Arrangement, which is maintained by Guangdong Transportation Group (Guangzhou, Cathay). In the organisation, crash severity is classified into four ordered levels according to the criteria defined by the Ministry of Public Security in China. Specifically,

a "light crash" refers to ane resulting in a property damage value of no more than 1000 CNY, or no more than than two people slightly injured;
a "medium crash" refers to one resulting in a property damage value between 1000 and thirty,000 CNY, or more than two people slightly injured, or one or two people severely injured;
a "severe crash" refers to 1 resulting in a property damage value betwixt 30,000 and sixty,000 CNY, or 3 to x people severely injured, or one or two fatalities; and
a "very astringent crash" refers to one resulting in a property impairment value of over 60,000 CNY, or more than ten people severely injured, or more than eight people severely injured and one fatality, or more than five people severely injured and two fatalities, or no less than three fatalities.

Among all the 1424 thruway crashes reported in the two years, in that location were 756 light crashes (53.one%), 621 medium crashes (43.half-dozen%), 45 severe crashes (iii.two%), and merely two very severe crashes (0.1%). Due to the rareness of very severe crashes, they were combined with severe crashes, to plant the highest level (termed as "astringent crash" in the rest of the paper) of crash severity in the research.

Some important features of driver, vehicle, EMS, and crash configuration are also recorded in the system, including: whether the involved driver(south) were professional (i.e., those taking vehicle driving as their jobs) or non, the involved vehicles' types and license numbers, the Ems response time, and the crash type, time and location (recorded as kilometer markers on the freeway).

two.2. Roadway Inventory

We extracted more detailed roadway characteristics of crash locations from the state highway geometric profile provided by Guangdong Province Advice Planning and Blueprint Constitute Co., Ltd. (Guangzhou, Mainland china). These roadway characteristics include horizontal curvature, vertical class, and whether the crash location is on a bridge or about a ramp. To explore the spatial correlation in the crashes, Kaiyang Freeway was split into 154 segments according to the homogeneity in horizontal and vertical alignments, which is consequent to the freeway partition in our previous studies on freeway crash analysis [35,36].

2.iii. Real-Time Conditions Conditions

The conditions data from three county-level atmospheric condition stations along the state highway were fatigued from the Meteorological Data Management System (MIMS) maintained by the Guangdong Climate Center. In the MIMS, atmospheric condition indexes, which include current of air speed, air temperature, atmospheric precipitation, visibility, and humidity, are recorded hourly. The crashes are assigned to the nearest weather station in accordance with their crash locations [9,12]. For each crash, the weather indexes observed at the assigned weather station during the 60 minutes of the crash time were used to reveal the real-time weather conditions.

Table ane shows the definitions and descriptive statistics of the explanatory variables for the empirical analysis.

Table 1

Descriptive statistics of explanatory variables for analyzing throughway crash severity.

Covariates	Description	Mean	SD
Professional commuter	All drivers involved are non-professional = 0; otherwise = 1	0.039	0.193
Ems response time	Elapsing betwixt crash reporting and the arrival of EMS (min)	xix.4	16.6
Day of week	Crash occurred on a weekend = 1; otherwise = 0	0.345	0.476
VEHICLE Type
Passenger car *	All vehicles involved are rider cars = 1; otherwise = 0	0.579	0.494
Charabanc	At least ane coach was involved = i; otherwise = 0	0.064	0.245
Truck	At to the lowest degree one truck was involved = 1; otherwise = 0	0.313	0.464
Other vehicle	At to the lowest degree 1 other vehicle (e.yard., a vehicle with trailer) was involved = 1; otherwise = 0	0.099	0.299
Non-local vehicle	All vehicles involved were registered in Guangdong Province (local vehicles) = 0; otherwise (at least one non-local vehicle was involved) = 1	0.284	0.451
CRASH Type
Single-vehicle crash *	The crash involved only one vehicle = 1; otherwise = 0	0.454	0.498
Rear-end crash	The crash is a rear-end one = i; otherwise = 0	0.383	0.486
Angle crash	The crash is an bending one where the directions of involved vehicles are non parallel = 1; otherwise = 0	0.162	0.368
Time OF DAY
Before dawn *	Crash occurred during 12 a.1000. to vi a.chiliad. = 1; otherwise = 0	0.184	0.387
Morning	Crash occurred during 6 a.m. to 12 p.m. = 1; otherwise = 0	0.222	0.416
Afternoon	Crash occurred during 12 p.m. to half dozen p.thousand. = 1; otherwise = 0	0.372	0.483
Evening	Crash occurred during 6 p.grand. to 12 a.k. = i; otherwise = 0	0.222	0.416
ROADWAY GEOMETRY
Horizontal curvature	The horizontal curvature of the freeway segment where the crash occurred (0.ane km⁻¹)	one.84	1.23
Vertical grade	The grade of the freeway segment where the crash occurred (%)	0.710	0.592
Bridge	Crash occurred on a bridge = i; otherwise = 0	0.537	0.499
Ramp	Crash occurred in the proximity of a ramp = 1; otherwise = 0	0.244	0.430
Real-Time Weather condition Condition
Wind speed	Wind speed during the hr of crash time (m/due south)	3.83	2.06
Temperature	Air temperature during the hour of crash time (°C)	23.vii	6.08
Atmospheric precipitation	Precipitation during the 60 minutes of crash time (mm)	0.769	3.43
Visibility	Visibility during the hour of crash fourth dimension (km)	xviii.0	18.vii
Humidity	Humidity during the hour of crash time (%)	81.3	fifteen.five

3. Methodology

In this section, the structures of generalized ordered logit model and spatial generalized ordered logit model for analyzing crash severity are presented first (Section 3.i). We and then introduce two criteria for assessing the performance of the two models in the context of Bayesian inference (Section 3.2). Finally, the method for calculating the marginal effects of explanatory variables is described (Department 3.3).

3.1. Model Specification

3.1.1. Generalized Ordered Logit Model

Ordered nature is an important feature of crash-severity information [32,33]. The generalized ordered logit model can conform the feature appropriately, without suffering from inconsistent estimations caused by stock-still thresholds. Specifically, the severity level, $y_{i},$ of crash $i$ is formulated equally follows:

$y_{i} = {\begin{matrix} 1, & z_{i} \leq μ_{i, 1} \\ 2, & μ_{i, ane} < z_{i} \leq μ_{i, two} \\ 3, & z_{i} > μ_{i, two} \end{matrix},$

(1)

where $1, 2, 3$ denotes the crash severity levels categorized higher up, i.e., light crash, medium crash, and severe crash, respectively. $z_{i}$ is a latent variable indicating the latent severity propensity of crash $i$ and is assumed to be a linear function of the explanatory variables (including a constant element) ${Ten}_{i}$ :

where $β$ is a vector of estimable parameters respective to $X_{i}$ , and $ε_{i}$ is a residuum term which is assumed to follow a logistic distribution.

The thresholds $μ_{i, ane}$ and $μ_{i, 2}$ in Equation (1) represent the boundaries between the ordered severity levels for crash $i$ . To let flexibility in measuring the effects of explanatory variables, the relationship between the thresholds is defined as follows:

where $Z_{i}$ is a vector of explanatory variables (besides including a constant element) and $α$ is the corresponding parameter vector. For the uniqueness of identification, and without loss of generality, the threshold between light and medium crash levels, $μ_{i, 1}$ , is fixed to nix for all crashes.

Equally the residual term $ε_{i}$ is logistically distributed, the cumulative probability for crash $i$ to present a severity level upward to $j (= i, ii, iii)$ , $P_{i, j}$ , can be calculated as:

$P_{i, i} = \frac{\exp (μ_{i, one} - β X_{i})}{one + \exp (μ_{i, 1} - β X_{i})} = \frac{\exp (- β 10_{i})}{one + \exp (- β 10_{i})},$

(iv)

$P_{i, 2} = \frac{\exp (μ_{i, ii} - β X_{i})}{1 + \exp (μ_{i, 2} - β X_{i})} = \frac{\exp [\exp (α Z_{i}) - β X_{i}]}{1 + \exp [\exp (α Z_{i}) - β X_{i}]},$

(5)

Consequently, the probability for crash $i$ resulting in the $j$ th level of severity, $p_{i, j}$ , is calculated equally:

$p_{i, 1} = P_{i, 1} = \frac{\exp (- β {Ten}_{i})}{1 + \exp (- β {Ten}_{i})},$

(7)

$p_{i, 2} = P_{i, 2} - P_{i, 1} = \frac{\exp (- β X_{i}) [\exp (\exp (α Z_{i})) - one]}{[one + \exp (- β X_{i})] [1 + \exp (\exp (α Z_{i}) - β X_{i})]},$

(8)

$p_{i, iii} = 1 - P_{i, two} = \frac{1}{1 + \exp [\exp (α Z_{i}) - β X_{i}]} .$

(nine)

3.ane.2. Spatial Generalized Ordered Logit Model

Spatial correlation is also a fundamental feature of crash-severity data [32,33]. The spatial generalized ordered logit model is developed by accounting for the ordered nature and spatial correlation simultaneously [six]. Specifically, a residual term $φ_{yard}$ with Machine priors is added into the formulation of the latent severity propensity, that is,

$φ_{grand} ~ Due north (\frac{\sum_{northward \neq m} ω_{m, n} φ_{n}}{\sum_{n \neq m} ω_{m, n}}, \frac{1}{τ_{φ} \sum_{north \neq grand} ω_{m, n}}),$

(11)

where the $φ_{m}$ captures the spatial effects of crashes (including crash $i$ ) occurring on roadway segment $m$ . The $ω_{one thousand, n}$ is the adjacency weight for roadway segments $m$ and $due north$ in the proximity matrix. The nearly extensively used structure [half-dozen,twenty,24], a binary first-order neighbour, was employed to define the proximity matrix in the current inquiry. Specifically, $ω_{g, northward} = 1$ , if segments $m$ and $n$ are connected; $ω_{thousand, n} = 0$ , otherwise. The $τ_{φ} (> 0)$ is the precision parameter of the spatial correlation term.

Thus, the probability for crash $i$ to exhibit the $j th$ severity level is formulated as:

$p_{i, 1} = \frac{\exp (- β X_{i} - φ_{m})}{1 + \exp (- β X_{i} - φ_{m})},$

(12)

$p_{i, ii} = \frac{\exp (- β X_{i} - φ_{chiliad}) [\exp (\exp (α Z_{i})) - 1]}{[1 + \exp (- β X_{i} - φ_{1000})] [one + \exp (\exp (α Z_{i}) - β X_{i} - φ_{grand})]},$

(xiii)

$p_{i, three} = \frac{1}{1 + \exp [\exp (α Z_{i}) - β X_{i} - φ_{grand}]} .$

(fourteen)

3.2. Assessment Criteria

The performances of the above models were compared via the deviance data criterion (DIC) and classification accuracy. As a Bayesian generalization of Akaike data criterion (AIC) and Bayes data benchmark (BIC), the DIC provides a combined measure of model fit and complication. Specifically, information technology is defined as [37]:

where $\bar{D}$ is the posterior mean deviance, which can be taken as a Bayesian measure of model fit, and $p_{D}$ is the effective number of model parameters that can be used to measure model complication. The lower the DIC value, the better the overall model functioning. Empirically, over 10 differences can dominion out the model with a higher DIC [38].

The nomenclature accuracy for the whole dataset is calculated as [6]:

$CA = \frac{\sum_{y_{i} = {\bar{y}}_{i}} y_{i} / y_{i}}{\sum_{i} y_{i} / y_{i}},$

(16)

where $\bar{y}$ is the predicted severity level of crash $i$ .

3.3. Marginal Effects

Agreement the impacts of explanatory variables within the framework of generalized ordered response modeling is not straightforward. The regression coefficients $β$ and $α$ in the proposed model practise non straight provide the magnitude of the effects of a sure explanatory variable on the likelihood of each severity level. For this purpose, the marginal effects of significant variables in the spatial model are calculated. Specifically, the marginal effect of a continuous variable $x$ on $p_{i, j}$ is computed by taking the first-club derivative with respect to $x$ [half dozen,39]:

$\frac{\partial p_{i, ane}}{\partial ten} = β^{x} p_{i, 1} (p_{i, 1} - i),$

(17)

$\frac{\partial p_{i, 2}}{\partial x} = α^{x} μ_{i} p_{i, iii} (1 - p_{i, 3}) + β^{x} p_{i, 2} (p_{i, 1} - p_{i, iii}),$

(18)

$\frac{\partial p_{i, 3}}{\partial x} = (β^{x} - α^{x} μ_{i}) p_{i, 3} (1 - p_{i, iii}),$

(19)

where $β^{x}$ and $α^{x}$ are the coefficient estimates associated with variable $10$ in the functions of latent propensity, $z_{i},$ and threshold, $μ_{i}$ , respectively.

For an indicator (binary) variable, $x$ , its marginal upshot on $p_{i, j}$ is calculated as the difference in the estimated probabilities with it varying from zero to one ( $Δ ten = 1$ ):

$\frac{Δ p_{i, ane}}{Δ x} = \frac{\exp (- \tilde{β} {\tilde{X}}_{i} - φ_{m}) [\exp (- β^{x}) - 1]}{[1 + \exp (- \tilde{β} {\tilde{X}}_{i} - φ_{chiliad})] [i + \exp (- \tilde{β} {\tilde{Ten}}_{i} - β^{x} - φ_{m})]},$

(20)

$\frac{Δ p_{i, ii}}{Δ x} = \frac{\exp (- \tilde{β} {\tilde{X}}_{i} - β^{ten} - φ_{m}) {\exp [\exp (\tilde{α} {\tilde{Z}}_{i} + α^{x})] - 1}}{{1 + \exp [\exp (\tilde{α} {\tilde{Z}}_{i} + α^{10}) - \tilde{β} {\tilde{X}}_{i} - β^{x} - φ_{m}]} {i + \exp [- \tilde{β} {\tilde{X}}_{i} - β^{10} - φ_{one thousand}]}} - \frac{\exp (- \tilde{β} {\tilde{X}}_{i} - φ_{thousand}) {\exp [\exp (\tilde{α} {\tilde{Z}}_{i})] - 1}}{{i + \exp [\exp (\tilde{α} {\tilde{Z}}_{i}) - \tilde{β} {\tilde{X}}_{i} - φ_{m}]} {1 + \exp [- \tilde{β} {\tilde{X}}_{i} - φ_{k}]}}$

(21)

$\frac{Δ p_{i, 3}}{Δ x} = \frac{\exp (- \tilde{β} {\tilde{X}}_{i} - φ_{k}) {\exp [\exp (\tilde{α} {\tilde{Z}}_{i})] - \exp [\exp (\tilde{α} {\tilde{Z}}_{i} + α^{x}) - β^{x}]}}{{i + \exp [\exp (\tilde{α} {\tilde{Z}}_{i}) - \tilde{β} {\tilde{X}}_{i} - φ_{m}]} {1 + \exp [\exp (\tilde{α} {\tilde{Z}}_{i} + α^{x}) - \tilde{β} {\tilde{X}}_{i} - β^{x} - φ_{k}]}},$

(22)

where ${\tilde{10}}_{i}$ and ${\tilde{Z}}_{i}$ are the vectors $X_{i}$ and $Z_{i}$ less element $x$ , respectively, and $\tilde{β}$ and $\tilde{α}$ are the corresponding parameter vectors (i.e., $β$ less $β^{x}$ and $α$ less $α^{x}$ , respectively).

The calculations of the marginal effects (no affair for continuous variables or indicator variables) are specific to a certain crash. To stand for the whole dataset, the average marginal furnishings for all observations are computed and reported.

4. Results and Word

4.1. Model Interpretation

Since the traditional maximum-likelihood method is not applicable to the models with CAR Gaussian priors [40], the parameters in the models were calibrated by Bayesian method which can be easily conducted via programming in WinBUGS [41]. To obtain the Bayesian estimates, specification of the prior distribution of each parameter in the models is required. In the absence of sufficient knowledge, noninformative (vague) prior distributions were used for the parameters. To be specific, a diffused normal distribution, $N o r yard a l (0, 10^{iv})$ , was used as the priors of the coefficients in $β$ and $α$ . A diffused gamma distribution, $chiliad a m m a (0.01, 0.01)$ , was used as the priors of the spatial precision parameter, $τ_{φ}$ . The CAR priors were specified by the function machine.normal in WinBUGS [40]. For each model, a chain of threescore,000 Markov chain Monte Carlo (MCMC) simulation iterations was run, with the first fifty,000 iterations acting as a burn down-in. The MCMC trace plots for the model parameters were inspected visually to ensure the simulations converge. In add-on, we monitored the ratios betwixt the Monte Carlo simulation errors and the corresponding estimates' standard deviations to ensure that they were less than 0.05 (a rule-of-thumb threshold). The estimation and assessment results for the traditional and spatial generalized ordered logit models are summarized in Tabular array 2 and Table 3, where only the factors that have statistically significant (at least at 90% credibility level) effects on the latent propensity or threshold are included.

Table 2

Estimation and assessment results for the generalized ordered logit model.

Variable	Latent Severity Propensity			Threshold betwixt Median and Severe Crash Levels
Variable	Mean	90% BCI ^a	95% BCI	Mean	90% BCI	95% BCI
Constant	0.64	(0.01, 1.29)	(−0.09, 1.39)	1.75	(i.32, 2.14)	(1.22, 2.21)
Precipitation	0.06	(0.02, 0.09)	(0.01, 0.10)	0.12	(0.02, 0.24)	(0.01, 0.26)
Rear-end crash	−ii.47	(−2.75, −ii.20)	(−2.81, −2.12)	−0.80	(−1.03, −0.55)	(−1.08, −0.50)
Angle crash	−2.10	(−2.42, −1.78)	(−2.49, −1.73)	−0.83	(−1.11, −0.56)	(−one.16, −0.51)
Professional driver	ii.11	(1.36, 2.97)	(1.2, 3.21)	0.32	(0.05, 0.60)	(0.001, 0.66)
Omnibus	0.59	(0.16, 1.01)	(0.06, 1.09)	—	—	—
Other vehicle	0.83	(0.44, ane.21)	(0.37, 1.29)	—	—	—
European monetary system response time	0.027	(0.019, 0.035)	(0.018, 0.036)	—	—	—
Wind speed	−0.07	(−0.13, −0.01)	(−0.14, 0.002)	—	—	—
Vertical form	—	—	—	−0.23	(−0.37, −0.11)	(−0.40, −0.08)
Afternoon	—	—	—	0.42	(0.xviii, 0.68)	(0.13, 0.73)
Evening	−0.45	(−0.79, −0.10)	(−0.85, −0.03)	—	—	—
$\bar{D}$	1720	—	—	—	—	—
$p_{D}$	41	—	—	—	—	—
DIC	1761	—	—	—	—	—
CA	75%	—	—	—	—	—

Table 3

Estimation and assessment results for the spatial generalized ordered logit model.

Variable	Latent Severity Propensity			Threshold between Median and Severe Crash Levels
Variable	Hateful	90% BCI ^a	95% BCI	Mean	90% BCI	95% BCI
Constant	2.seven	(i.35, 3.99)	(1.xx, 4.18)	1.73	(1.30, two.xiii)	(ane.23, 2.21)
Atmospheric precipitation	0.04	(0.004, 0.08)	(−0.01, 0.09)	0.xiii	(0.03, 0.25)	(0.02, 0.28)
Rear-end crash	−2.53	(−2.82, −2.24)	(−2.88, −2.19)	−0.eighty	(−ane.04, −0.57)	(−i.09, −0.53)
Angle crash	−1.84	(−2.19, −1.50)	(−2.27, −1.44)	−0.81	(−1.09, −0.55)	(−ane.15, −0.50)
Professional commuter	2.23	(ane.45, 3.11)	(1.33, 2.29)	0.33	(0.06, 0.60)	(0.004, 0.65)
Passenger vehicle	0.48	(0.23, 0.93)	(−0.05, 1.00)	—	—	—
Other vehicle	0.71	(0.30, i.eleven)	(0.23, 1.xviii)	—	—	—
Non-local vehicle	0.28	(0.01, 0.57)	(−0.06, 0.62)	—	—	—
EMS response fourth dimension	0.03	(0.025, 0.043)	(0.024, 0.045)	—	—	—
Horizontal curvature	0.13	(0.03, 0.23)	(0.01, 0.25)	—	—	—
Vertical grade	—	—	—	−0.24	(−0.38, −0.11)	(−0.41, −0.07)
Afternoon	—	—	—	0.42	(0.16, 0.68)	(0.11, 0.75)
Evening	−0.43	(−0.81, −0.02)	(−0.89, 0.05)	—	—	—
sd( $φ$ ) ^b	0.54	(0.36, 0.80)	(0.32, 0.84)	—	—	—
$\bar{D}$	1684	—	—	—	—	—
$p_{D}$	64	—	—	—	—	—
DIC	1748	—	—	—	—	—
CA	76%	—	—	—	—	—

four.2. Model Comparison

Comparing the results in Table 2 and Table 3, one can detect that the spatial generalized ordered logit model yields a lower $\bar{D}$ value, which indicates its amend plumbing equipment with the crash information. The outperformance of the spatial model in goodness-of-fit is further confirmed by its relatively higher nomenclature accuracy (76% for the spatial model versus 75% for the traditional model). The results are reasonable, because a number of previous studies [6,19,20] accept demonstrated that capturing spatial effects via CAR priors can significantly reduce model misspecification. While the generalized ordered logit model is more parsimonious (equally suggested by the lower $p_{D}$ value), the DIC value of the spatial model is 13 points lower than that of the traditional one, which implies the improve overall performance of the proposed spatial model.

In improver, the standard deviation of the spatial term, sd( $φ$ ), was estimated. Its posterior mean equals 0.56 and the 95% Bayesian credible interval is (0.32, 0.84), which manifest that there are significant spatial correlations amidst crashes occurring on adjacent motorway segments. The spatial correlations may be attributed to some omitted factors (e.thou., terrain feature and lighting condition) shared by next crashes.

Further comparison betwixt the 2 models shows that there are certain discrepancies in the identified significant factors of crash severity. For instance, horizontal curvature was found to be positively associated with the latent severity propensity only in the spatial model, while current of air speed was found to be negatively associated with the latent severity propensity only in the generalized ordered logit model. The results also imply that the spatial model is more than consistent with the findings in the literature than the traditional one. Note that many studies take reported that: (i) crashes occurring on segments with higher smaller horizontal curve radius tend to exist more than severe [7,42]; and (ii) stronger wind increases the likelihood of severe crashes [43].

4.3. Parameter and Marginal Effect Interpretation

The marginal furnishings of significant factors on the probability of each crash severity level were calculated for the spatial model via the method in Section 3.3. The results are shown in Table 4. This enquiry mainly aims to assess the impacts of existent-fourth dimension weather condition conditions on freeway crash severity. Therefore, we interpret the estimated regression coefficients and marginal furnishings of real-fourth dimension atmospheric condition index(es) first (Section iv.three.1) and so those of other meaning variables (Section 4.3.2).

Table four

Marginal furnishings of significant variables in the spatial generalized ordered logit model.

Variable	Light Crashes (%)	Medium Crashes (%)	Severe Crashes (%)
Precipitation	−0.6	one.6	−ane.0
Rear-end crash	47.v	−47.3	−0.ii
Bending crash	36.i	−38.8	ii.7
Professional driver	−32.8	27.2	v.6
Jitney	−7.4	5.half dozen	ane.8
Other vehicle	−eleven.0	8.3	2.vii
Not-local vehicle	−4.3	3.4	0.9
European monetary system response time	−0.5	0.4	0.ane
Horizontal curvature	−1.9	ane.5	0.4
Vertical grade	0.0	−ii.two	2.2
Afternoon	0.0	3.3	−3.three
Evening	6.7	−5.four	−1.3

iv.three.i. Real-Time Atmospheric condition Conditions

According to the results in Table two and Table 3, precipitation has significantly positive furnishings on both the latent severity propensity and the threshold between medium and severe crashes. Specifically, a ane-millimeter increase in atmospheric precipitation during the hour of the crash time tends to effect in the likelihood of light and severe crashes decreasing past 0.6% and 1.0%, respectively, and the likelihood of medium crashes increasing by one.6%. The decreased likelihood of light crashes is predictable, considering precipitation makes the roadway surface wet or even slippery, thereby reducing skidding resistance [four,44]. The reduced skidding resistance increases the difficulties in manipulating vehicles, which could increment drivers' mental effort and thereby adversely influence driving behavior by occupying limited cerebral resources and interfering with information processing. Once an emergency occurs, drivers may need more time to perceive its existence and accept proper deportment to reduce the severity of an oncoming crash. Moreover, the reduced skidding resistance also increases stopping distance.

While it is somewhat counterintuitive, the decreased probability of severe crashes in heavy rain conforms to many existing findings of the effects of the wet route surface on crash severity [seven,45,46]. They argued that it could be illustrated by the risk compensation theory, which indicates that drivers tend to accommodate their driving beliefs (east.chiliad., driving more carefully and at a lower speed) in agin driving weather (e.g., heavy rain or wet route surface). In practice, some transportation engineering and direction strategies are implemented to enhance expressway safety. For example, the variable message signs (as shown in Effigy 1) deployed along the freeway would be activated to alert drivers to be cautious on rainy days. The transportation direction bureau unremarkably sets a more intensive police force patrol schedule in seasons with loftier precipitation.

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Furthermore, it is worth noting that precipitation impacts the likelihood of low-cal and severe crashes in the same direction, which cannot exist formulated in standard ordered response models. The fixed thresholds in standard ordered response models limit that the marginal effects of a certain factor on the probabilities of the lowest and highest severity levels always accept unlike signs [34]. The results justify the necessity of modeling crash severity under a generalized response framework.

4.3.2. Other Significant Variables

Regarding other significant variables, professional drivers were associated with a higher latent severity propensity and a higher threshold betwixt medium and severe crashes, which bespeak that the probability of lite crashes is expected to decrease past 32.8% and that the probabilities of medium and severe crashes are expected to increase by 27.2% and v.six%, respectively, when there are professional drivers involved in the crash. The result is generally consistent with the finding of our previous research [vi]. In the collected crash data, well-nigh professional drivers operated intercity buses. Considering of the long driving hours, they are more than likely to experience fatigue driving, which may increase the likelihood of astringent crashes [47].

The positive signs of the coefficients for coaches and other vehicles on the latent severity propensity imply that these 2 types of vehicles are more than likely to be involved in severe crashes. The estimated marginal furnishings showed that, when a coach is involved, the likelihood of a severe crash will increase by 1.viii%; while when another blazon of vehicle (eastward.thousand., a vehicle with trailer) is involved, the counterpart will increase by 2.7%. The results are reasonable, considering coaches and other types of vehicles possess stronger crash aggressivity, compared to automobiles [27]. The stronger crash aggressivity means that greater hazards would be imposed on the vehicle(south) colliding with them [48].

"Non-local vehicle" has a negative result on the latent severity propensity, which indicates that non-local vehicles are more likely to be involved in astringent crashes. Specifically, when at to the lowest degree one non-local vehicle is involved, the probabilities that the crash severity is medium and severe will increment by iii.iv% and 0.nine%, respectively. The consequence is generally consistent with engineering intuition: the drivers of not-local vehicles may be unfamiliar with the roadway and weather conditions. As a consequence, they may need more time to perceive and comprehend the driving environment. Thus, less time is left for them to slow downwardly or perform other actions that could alleviate the agin outcomes of an upcoming crash.

For the crash time of mean solar day, afternoon is linked to a higher threshold between medium and severe crashes, while evening is linked to a lower latent severity propensity. The results of marginal effects indicate that the probabilities of severe crashes in afternoon and evening decrease by 3.3% and 1.3%, respectively, compared to their counterparts earlier dawn (the reference category). Probably due to the light traffic, speeding is more likely to occur before dawn [26]. Moreover, human circadian rhythmicity may lead to more frequent fatigue/slumber-deprived driving during this flow [49]. Speeding and fatigue driving are major causes of severe crashes in China [six]. Moreover, drivers' vision is better in the afternoon than before dawn, which reserves more than time for drivers to recognize and respond to potential dangers [seven].

With respect to roadway characteristics, horizontal curvature has a positive effect on the latent severity propensity, which implies that the probabilities of medium and severe crashes will increase past 1.five% and 0.iv% respectively, for a 10⁻¹ km increase in horizontal curvature. A greater curvature (i.e., a smaller bend radius) makes for stronger centrifugal forces on vehicles negotiating the curve and brings about the harsher transition between tangent sections [50], which may lead to a reduction in vehicle control. Zegeer et al. [42] claimed that more caput-on crashes, stock-still object crashes, and rollover crashes tend to occur on horizontal curves. These crashes usually result in great casualties. "Vertical form" was found to exist negatively associated with the threshold between medium and astringent crashes. Specifically, a 1% increase in the vertical grade is expected to issue in a 2.2% increase in the probability of severe crashes. This finding may be attributed to a shorter sight distance rendered by a steeper class, which reduces the time available for drivers to react properly to potential hazards [7,46].

By providing first aid treatments and transportation to hospitals, EMS is a crucial post-crash countermeasure for mitigating the injuries sustained by the occupants involved in traffic crashes. It is predictable that the European monetary system response time has a positive impact on the latent severity propensity. Its estimated marginal furnishings reveal that an increase of 1 minute in EMS response time will increase the likelihood of medium and severe crashes by 0.4% and 0.1%, respectively, which is in line with the findings in many previous studies [vi,51,52].

With regard to crash type, the results in Table three betoken that both rear-end and angle crashes are linked to a reduction in the latent severity propensity and a reduction in the threshold between medium and severe crashes, as compared against single-vehicle crashes (the reference category). Specifically, the probability of light crashes increases by 47.5% and 36.1% for rear-cease and angle crashes, respectively. The probability of astringent crashes decreases past 0.2% for rear-cease crashes but increases past 2.7% for angle crashes. Similar findings can be found in [27,48], which ended that rear-end crashes are one of the to the lowest degree severe crash types.

5. Conclusions

This newspaper empirically investigated the impacts of real-fourth dimension weather atmospheric condition on thruway crash severity using a two-yr crash dataset nerveless from Kaiyang Pike in Mainland china, where the information on hourly wind speed, air temperature, atmospheric precipitation, visibility, and humidity were derived from three adjacent weather stations. A land-of-the-art method, the Bayesian spatial generalized ordered logit model, was used for the empirical analysis, to link the observed crash severity to real-time atmospheric condition conditions and factors related to drivers, vehicles, roadways, EMS, and crash configuration.

The results indicate that heavier precipitation during the hour of crash occurrence decreases the probabilities of light and severe crashes but increases the probability of medium crashes. The decreased probability of severe crashes may imply the effects of some implemented strategies for transportation safety management, including variable message signs and law patrol schedules. Even so, some other strategies may further improve freeway prophylactic operation on rainy days. For case, variable speed limits have the potential to reduce crash run a risk and severity in rainy weather, by continually regulating travel speed based on existent-fourth dimension traffic and weather atmospheric condition [53]. The advanced driver-help system and emerging connected and democratic vehicles constantly discover potential dangers and facilitate drivers to brand proper response decisions, which is specially helpful in inclement atmospheric condition.

The results also suggest that: (i) professional drivers, coaches, other vehicles (especially those with trailers), and non-local vehicles are more likely to exist involved in severe crashes; (ii) severe crashes tend to occur on freeway segments with pocket-size horizontal curve radius and high vertical gradient before dawn; (3) rapid response of Ems tin significantly decrease crash severity; (4) rear-end crashes usually issue in less severe outcomes than single-vehicle and angle crashes; (5) significant spatial correlation exists across the severities of adjacent crashes.

A limitation of the electric current research is that the weather information was recorded by hour. College-resolution weather data (e.g., at 1-, v-, or 10-min intervals) may provide a more precise assessment of their effects on crash severity. Methodology-wise, it is of interest to further business relationship for the heterogeneous furnishings of the observed factors in the proposed model by using methods such equally random-parameters [xxx], although it may significantly increase the complication of model structure and the fourth dimension-consumed in model estimation. In addition, more field data are required to demonstrate the random-parameters model.

Author Contributions

Conceptualization, Q.Z. and F.C.; methodology, Q.Z. and W.H.; validation, J.L.; formal analysis, Q.Z. and W.H.; writing—original draft preparation, Q.Z. and J.L.; writing—review and editing, F.C. All authors have read and agreed to the published version of the manuscript.

Funding

This inquiry was funded past (ane) the Natural Science Foundation of China nether grant no. 71801095; (2) the International Science & Engineering Cooperation Program of People's republic of china nether grant no. 2017YFE0134500; and (3) the Natural Science Foundation of Guangdong Province under grant no. 2017A030310161.

Conflicts of Interest

The authors declare no conflict of interest.

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