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Latent class analysis of factors that influence weekday and weekend single-vehicle crash severities
Accident Analysis and Prevention 113 (2018) 187–192
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Accident Analysis and Prevention journal homepage: www.elsevier.com/locate/aap
Latent class analysis of factors that influence weekday and weekend singlevehicle crash severities
T
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Emmanuel Kofi Adanua, , Alexander Hainenb, Steven Jonesb a b
Alabama Transportation Institute, The University of Alabama Tuscaloosa, AL, United States Department of Civil, Construction and Environmental Engineering, The University of Alabama Tuscaloosa, AL, United States
A R T I C L E I N F O
A B S T R A C T
Keywords: Single-vehicle crash Weekend crash Weekday crash Latent class logit Crash-severity
This paper investigates factors that influence the severity of single-vehicle crashes that happen on weekdays and weekends. Crash data from 2012 to 2016 for the State of Alabama was used for this study. Latent class logit models were developed as alternative to the frequently used random parameters models to account for unobserved heterogeneity across crash-severity observations. Exploration of the data revealed that a high proportion of severe injury injury crashes happened on weekends. The study examined whether single-vehicle crash contributing factors differ between weekdays and weekends. The model estimation results indicate a significant association of severe injury crashes to risk factors such as driver unemployment, driving with invalid license, no seatbelt use, fatigue, driving under influence, old age, and driving on county roads for both weekdays and weekends. Research findings show a strong link between human factors and the occurrence of severe injury single-vehicle crashes, as it has been observed that many of the factors associated with severe-injury outcome are driver behavior related. To illustrate the significance of the findings of this study, a third model using the combined data was developed to explore the merit of using sub-populations of the data for improved and detailed segmentation of the crash-severity factors. It has also been shown that generally, the factors that influence single-vehicle crash injury outcomes were not very different between weekdays and weekends. The findings of this study show the importance of investigating sub-populations of data to reveal complex relationships that should be understood as a necessary step in targeted countermeasure application.
1. Introduction Single-vehicle crashes present an interesting area of research because of the predominant role of the driver involved. These manner of crashes occur either on the roadway or off the roadway. A high proportion of single-vehicle crashes comprise run-off-road and fixed-object collisions. In the United States, statistics show that more than half of annual fatal crashes involve single vehicles with some 70% of those being run-off-road crashes (Liu and Subramanian, 2006; IIHS, 2018; NHTSA, 2017). Understanding the contributing factors and circumstances under which single-vehicle crashes occur is important for countermeasure implementation. Many researches have previously been conducted to explore singlevehicle crash characteristics. Some of the common factors that have been identified as contributing circumstances to single-vehicle crashes include excessive speed, driver fatigue, driving under the influence of alcohol or other drugs (DUI), or the effect of these and other geometric, weather, site characteristics, and vehicle factors. Studies have also investigated how these factors influence the occurrence and severity of ⁎
single-vehicle crashes. For instance, Chen and Chen (2011) have found that, in adverse driving conditions such as bad weather and/or complex terrain, there is a high chance of trucks getting into single-vehicle crashes. Xie et al. (2012) studied driver injury severity in rural singlevehicle crashes using a latent class logit, where they found that fatal single-vehicle crashes occurred more often on rural roads. Also, Shaheed and Gkritza (2014) used latent class analysis to analyze singlevehicle motorcycle crash severities in Iowa. Their study revealed a significant relationship between the severity of injury outcomes and factors such as speeding, riding on rural roads, riding without a helmet, and impaired riding (riders under the influence of drug, alcohol or medication. Jung et al. (2010) investigated the effect of rainfall on single-vehicle crashes in Wisconsin. Their study used a backward sequential logistic regression model to predict crash severities and they observed that rainfall intensity, wind, speed, roadway terrain, and seatbelt use had significant effects on crash outcome. Multinomial logit was used by Shankar and Mannering (1996) to explore the factors that influenced single-vehicle motorcycle crash severities in Washington State. They found driver age, helmet use, pavement condition, speed,
Corresponding author. E-mail addresses: [email protected] (E.K. Adanu), [email protected] (A. Hainen), [email protected] (S. Jones).
https://doi.org/10.1016/j.aap.2018.01.035 Received 29 September 2017; Received in revised form 25 January 2018; Accepted 25 January 2018 0001-4575/ © 2018 Elsevier Ltd. All rights reserved.
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model was also developed for the study period to compare with results obtained for the sub-populations (i.e. weekday crashes and weekend crashes) and also to show the importance of analyzing segments of the data to gain in-depth insight into the factors that affect crash-severity.
drunk driving, and driver inattention to have varying effects on the severity of crashes. Maistros et al. (2014) used mixed logit models to compare contributing factors between alcohol-related single-vehicle motorcycle and car crashes in Ohio where they developed mixed logit models for motorcycles and passenger cars to quantify the effects of roadway geometry, speeds, and safety equipment usage on riders and drivers exposure to severe injuries. Wu et al. (2014) studied driver injury severity of single- and multi-vehicle crashes on rural two-lane highways in New Mexico using mixed logit, where they investigated similarities and differences in factors responsible for single-vehicle crashes and multi-vehicle crashes. They observed that the probability of having severe outcomes was higher when vans are involved, and when drivers wrongfully overtake in single-vehicle crashes. Morgan and Mannering (2011) assessed the effects that age and gender have on crash severities by considering single-vehicle crashes that occurred on dry, wet, and snow/ice-covered roadway surfaces in Indiana. Lee and Li (2014) used heteroscedastic ordered logit modeling techniques to analyze injury severity of drivers involved in single-vehicle and twovehicle collisions on provincial highways in Ontario, Canada, for the period from 2004 to 2008. They found increased drivers’ injury severity for single-vehicle collisions that happened on curved segments of the roads, collisions that involved female drivers and also among young drivers below the age of 30 years. On the other hand, they found decreased injury severity for crashes that occurred on roads with large number of lanes and crashes involving vehicles equipped with advanced safety features. Islam et al (2014) undertook a comprehensive study to identify factors associated with single- and multi-vehicle large truck at-fault crashes on rural and urban roads in Alabama. This study found increased injury severity for truck crashes related to driver fatigue in rural locations. Also, it was observed that crashes involving single-vehicle trucks that occurred between midnight and 7:00 A.M. at rural locations were more likely to result in major injuries. Crashes involving single-vehicle trucks that occurred at curved sections of urban locations were found to significantly result in either major injury or possible/no injury. Dabbour (2017) used logistic regression to investigate the temporal stability of risk factors affecting severity single-vehicle collision severities that occurred in North Carolina from 2007 to 2013. It was found in this study that severe injuries were consistently associated with undivided and rural roads, dark and unlit roadway conditions, male drivers, and crashes involving DUI. Older vehicles and light-duty trucks were also found to be associated with severe injuries. Also, Behnood and Mannering (2015) used mixed logit modeling to explore the temporal stability of the factors affecting driver injury-severities of singlevehicle in Chicago, Illinois. It was found that improvements in vehicle safety features and drivers’ response to those improvements contributed to the instability of crash contributing factors over the study period (2004 to 2012). Similarly, Xiong et al. (2014) observed instability in the factors affecting the severity of single-vehicle collisions in Indiana from 1995 to 1999. They attributed the temporal instability to ongoing changes in average annual daily traffic, international roughness index, and rut depth. Travel activities and driver behaviors are known to vary with time (time of day, day of the week, holidays, etc.) (e.g. Behnood and Mannering, 2016; Pahukula et al., 2015). Evidence suggests that risky driving behaviors (and related crashes) may be more prevalent during weekend periods (defined as 6 P.M. Friday to 5:59 A.M. Monday) than during regular weekdays (NHTSA, 2015). This necessitates an in-depth analysis of the risk factors associated with crash occurrence and severities of outcomes between weekdays and weekends to know who, where, and when these crashes occurred as these can dictate how countermeasures may be effectively implemented. This study therefore investigates the contributing factors that influence crash-severities between weekdays and weekends for single-vehicle crashes in the State of Alabama. The study uses latent class logit modeling techniques to develop separate models for weekday and weekend crashes. An overall
2. Methodology Accounting for unobserved heterogeneity across injury-severity observations is an important concern in traffic safety research. Ignoring the effect of unobserved variables in injury-severity studies can lead to biased estimates and incorrect inferences if the right methods are not used (Shaheed and Gkritza, 2014; Mannering et al., 2016). Discretechoice models, ordered (probit and logit models) and unordered models (such as the multinomial logit model), have particularly been used extensively to analyze crash injury severity due to the classification of the severities into discrete outcomes (see Savolainen et al., 2011 and Mannering and Bhat, 2014 for injury-severity methodology reviews). However, many of the discrete ordered and unordered models are unable to account for unobserved heterogeneity across injury-severity observations (see Savolainen et al., 2011). Random parameters (mixed logit) models (Milton et al., 2008; Morgan and Mannering, 2011; Anastasopoulos and Mannering, 2011; Kim et al., 2013) and latent class (finite mixture) models (Yasmin et al., 2014; Shaheed and Gkritza, 2014), or latent class with random parameters within each class, (Bujosa et al., 2010; Xiong and Mannering, 2013; Greene and Hensher, 2013) have the ability to capture unobserved heterogeneity by allowing parameters to differ across observations (Morgan and Mannering, 2011; Behnood and Mannering, 2015; Mannering et al., 2016). While random parameters technique uses continuous mixing distributions to capture heterogeneity, it requires the analyst to specify the functional form of the mixing distribution (for example, normal, log-normal, uniform, triangular, etc.). On the other hand, the latent class approach identifies unobserved classes without distributional assumptions. In effect, latent class model replaces the continuous distribution assumption of random parameter model with a discrete distribution in which unobserved heterogeneity is captured by membership of distinct classes (Greene and Hensher, 2003; Mannering and Bhat, 2014). Though it has been shown that random parameter models with heterogeneity in means and random parameter models with heterogeneity in means and variances perform better than conventional random parameters models (e.g. Greene et al., 2006; Venkataraman et al., 2014; Kim et al., 2013; Seraneeprakarn et al., 2017; Behnood and Mannering, 2017), the use of latent class analysis for sub-population models can help identify further distinctions of classes within the sub-populations that may not be known or explicitly defined (e.g. Xie et al., 2012; Eluru et al., 2012; Xiong and Mannering, 2013; Cerwick et al., 2014), instead of estimating separate models for pre-determined sub-populations (e.g. Islam and Mannering, 2006; Morgan and Mannering, 2011). Latent class logit model offers an alternative perspective to the conventional random parameters logit model in terms of accommodating heterogeneity (Greene and Hensher, 2003; Behnood et al., 2014; Mannering et al., 2016). In this paper, to model crash-injury severity, three discrete severity levels are considered: severe injury (fatal or incapacitating); minor injury (non-incapacitating or possible injury); and no injury (property damage only). Latent class logit model allows the crash severity to have C different classes so that each of the classes will have their own parameters with the probability given by (Behnood et al., 2014):
Pn (c ) =
exp (α c Zn ) ∑∀ C exp (α c Zn )
(1)
where Zn represents a vector that shows the probabilities of c for crash n , C is the possible classes c,and α c represents the estimable parameters (class specific parameters). The unconditional probability 188
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Table 1 Summary statistics of variables included in the latent class logit models.
Variables Dependent Severe injury Minor injury No injury Explanatory Invalid license Unemployed No seatbelt Fatigued DUI County road Senior Distracted Speed Female Runoff Close to home Young Over correction Dark Interstate Swerve Vehicle defect *
Description
Weekday (61.82%) Mean (Std. Dev)
Weekend (38.18%) Mean (Std. Dev)
Crash severity: fatal or incapacitating injury Crash severity: non incapacitating or possible injury Crash severity: property damage only
0.11 (0.31) 0.22 (0.42) 0.67 (0.47)
0.12 (0.33) 0.23 (0.42) 0.65 (0.48)
License status of causal driver: Invalid license (1 = Yes, 0 = No) Driver employment status: Unemployed (1 = Yes, 0 = No) Seatbelt use: No seatbelt (1 = Yes, 0 = No) Driver condition at time of crash: Fatigued (1 = Yes, 0 = No) Primary contributing factor: DUI (1 = Yes, 0 = No) Functional class of road: County road (1 = Yes, 0 = No) Driver age: more than 60 (1 = Yes, 0 = No) Primary contributing factor: Distracted driving (1 = Yes, 0 = No) Primary contributing factor: Speed (1 = Yes, 0 = No) Driver gender: Female (1 = Yes, 0 = No) Primary contributing factor: Runoff road (1 = Yes, 0 = No) Driver residence from crash location: Less than 25mi (1 = Yes, 0 = No) Driver age: less than 24 (1 = Yes, 0 = No) Primary contributing factor: Over correction (1 = Yes, 0 = No) Lighting condition at time of crash: Dark/Unlit (1 = Yes, 0 = No) Functional class of road: Interstate (1 = Yes, 0 = No) Primary contributing factor: Swerve to avoid collision (1 = Yes, 0 = No) Primary contributing factor: Vehicle defect (1 = Yes, 0 = No)
0.11 0.24 0.08 0.06 0.07 0.34 0.11 0.12 0.19 0.40 0.10 0.76 0.25 0.03 0.25 0.15 0.15 0.01
0.14 0.25 0.11 0.07 0.14 0.35 0.08 0.13 0.18 0.36 0.09 0.75 0.32 0.03 0.40 0.16 0.14 0.01
(0.31) (0.43) (0.28) (0.23) (0.26) (0.47) (0.32) (0.32) (0.39) (0.49) (0.29) (0.43) (0.43) (0.18) (0.43) (0.36) (0.35) (0.09)
(0.34) (0.43) (0.31) (0.25) (0.35) (0.48) (0.27) (0.33) (0.38) (0.48) (0.28) (0.44) (0.47) (0.16) (0.49) (0.37) (0.35) (0.09)
Total number of fatal single-vehicle crashes between 2012–2016 obtained from the CARE system was 1919 (899 occurred on weekends and 1020 occurred on weekdays).
alternative i (i ≠ q ) on the probability Pnq for crash n to result in outcome q . The final marginal effect of an explanatory variable is the sum of the marginal effects for each class weighted by their posterior latent class probabilities (Greene, 2007; Xie et al., 2012).
that a crash will result in severity i is given by:
Pn (i) =
∑∀ C Pn (c )* Pn (i/c )
(2)
where Pn (i/ c ) is the probability of crash n to result in crash severity level i in class c . Based on the two equations above, the latent class logit model for class c will be:
Pn (i/ c ) =
3. Data description
exp (βic Xin ) ∑∀ I exp (βic Xin )
The study was based on 2012–2016 single-vehicle crash data for the State of Alabama, obtained from the Critical Analysis Reporting Environment (CARE) system developed by the University of Alabama Center for Advanced Public Safety. Observations with missing values were omitted from the dataset, resulting in a total of 129,967 observations. To investigate whether there are differences in crash-severity contributing factors, the data was grouped between weekdays and weekends. The distribution of crashes by severity outcome reveals that nearly 35% of the single-vehicle crashes during the study period resulted in an injury outcome. Though 38.18% of single-vehicle crashes occurred during weekends they contributed to about 47% of the fatal crashes (and 41% of severe injury crashes). This highlights the importance of identifying the factors that are associated with each severity outcome between weekdays and weekends and subsequently proposing countermeasures to improve safety. Altogether, more than 40 variables were considered in the latent class logit analysis, it was observed that some of the predictor variables were correlated. For instance, it was observed that DUI as driver condition at the time of the crash correlated strongly with DUI as primary contributing factor. Relationships between such variables and the response variables were also investigated. Such highly correlated variables were not, however, included in the final models in order to avoid multicollinearity. Table 1 shows the summary statistics of the variables that were found to be significant in the latent class logit models. It has been observed that the proportion of single-vehicle crashes involved drivers without valid driver’s licenses is slightly more on weekends (14% to 11% on weekdays). No seatbelt use was reported in 8% of weekday crashes and 11% of weekend crashes. One interesting finding was that crashes involving DUI comprised 7% of weekday crashes and 14% of weekend crashes. Also, drivers aged 60years and above were involved in 11% of crashes on weekdays and 8% of weekend crashes, while young drivers (aged less than 24years) were involved in 25% of
(3)
where I represents the possible number of injury severity levels and βic is a class-specific parameter vector that takes a finite set of values. The latent class logit model can be estimated with maximum likelihood procedures (Greene and Hensher, 2003). The latent class method however does not account for the variable randomness within a class since it assumes homogeneous characteristics of the within-class observations (Mannering and Bhat, 2014). Greene and Hensher (2013) and Bujosa et al. (2010) present the random parameter latent class model as an extension of the latent class logit model to capture interactions with observed contextual effects within the latent classes. This study attempted to use this method to model the crash data. However, no random variables were found within the homogeneous classes and there was no significant improvement in model fit statistics. Marginal effects are commonly computed from the partial derivative for each observation, to investigate the effect of individual parameters on the crash-severity outcome probabilities. Marginal effect in a latent class logit model is computed for each class as the difference in the estimated probabilities with the indicator changing from zero to one, while keeping all the other variables at their means. Greene (2007) has shown that the direct and cross-marginal effects can be computed respectively as follows:
∂Pni = βik Pni (1−Pni ) ∂x nik ∂Pnq ∂x nik
= −βik Pni Pnq
(4)
(5)
The direct marginal effect indicates the effect of a unit change in x nik on the probability, Pni, for crash n to result in severity i . The crossmarginal effect shows the impact of a unit change in variable k of 189
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Table 2 presents the detailed model estimation results for weekday and weekend single-vehicle crashes. To ascertain the merit of identifying latent classes within pre-defined sub-populations of the data, model results of the combined dataset are also been presented. Two distinct segments (classes) with homogeneous attributes were found significant for weekdays, weekends, and the combined data (in all cases, estimation results with more than two latent classes did not statistically improve the models in terms of data fit). The latent class probabilities for the weekday crash model were 0.69 (latent class 1) and 0.31 (latent class 2). The weekend model had latent class probabilities of 0.72 (latent class 1) and 0.28 (latent class 2). The combined dataset had latent classes with probabilities of 0.55 (latent class 1) and 0.45 (latent class 2). The class specific probabilities are a set of fixed constants (see Eq. (1)), as examining segmentation on the basis of crashspecific characteristics did not result in a superior model fit. A total of 18 variables were used and found to be statistically significant, at a 0.05 significance level. The same variables were used to develop all the models so as to examine their how they vary between weekdays and weekends. The model fit statistics are also shown in Table 2. Variables (and constant terms) that were not found to be statistically significant at a 0.05 significance level were not shown in Table 2. An interesting observation from the model estimation results is that without segmenting the data into weekdays and weekends, the latent class model for the combined crashes does not show seatbelt use and driver age (less than 24 years) to significantly influence the severity of the crashes. Similarly, the combined data shows over correction indicator to be significant contributor in minor injury crashes for latent class 2 but this variable did not show statistical significance in neither weekday nor weekend models. The latent class models reveal that the factors that influence severe crash outcome are consistent between weekdays and weekends for the classes with the higher proportions (i.e. latent class 1) in both cases. Crashes that occurred on county roads were generally more likely to be
weekday crashes and 32% of weekend crashes. Crashes that occurred on dark and unlit roadways make up 25% of weekday crashes and 40% of weekend crashes. 4. Estimation results Likelihood ratio test (Washington et al., 2011) was performed to determine whether separate models by time of the week was justified. The test statistic is given by: K
⎤ ⎡ X 2 = −2 ⎢LL (βT )− ∑ LL (βk ) ⎥, k=1 ⎦ ⎣
(6)
where LL (βT ) is the log-likelihood at convergence of the model estimated with all the data, LL (βk ) is the log-likelihood at convergence of the model using subset k data (weekday and weekend) and K is the total number of data subsets used. The X 2 statistic is chi-squared distributed with degrees of freedom equal to the sum of the number of estimated parameters in all subset models minus the number of estimated parameters in the full-sample model. The resulting X 2 statistic indicates whether or not the model for the subset data is significantly different than the model for the full-sample data. Log-likelihood test was further performed to determine whether or not the subset models have parameters that are statistically different. The test statistic used is given by:
X 2 = −2[LL (βT )−LL (βk )],
(7)
where LL (βT ) is the log-likelihood at convergence of the model estimated with all the data (weekday and weekend), LL (βk ) is the loglikelihood at convergence of the model using subset k data (weekday or weekend). Based on the likelihood ratio tests performed and study objectives, it was determined that two separate severity models (for weekdays and weekends) should be developed. Table 2 Latent class logit models estimation results. Weekday Variable
Defined for Severe injury Constant Invalid license Unemployed No seatbelt Fatigued DUI County road Senior
Weekend
Combined
Latent Class 1
Latent Class 2
Latent Class 1
Latent Class 2
Latent Class 1
Latent Class 2
Parameter
t-Statistic
Parameter
Parameter
t-Statistic
Parameter
t-Statistic
Parameter
Parameter
t-Statistic
−1.15
−13.35
−0.52
−4.50
0.37 0.37 2.40 0.66 0.24 0.23 0.43
8.97 11.61 46.09 12.14 4.59 5.98 9.30
0.17 0.37 3.04 1.05 0.16 0.17 0.57
2.41 5.87 24.46 10.34 2.08 2.79 5.32
0.83
7.67
−0.55
−2.53
0.35 0.32 0.27 0.45 0.23
10.32 10.04 12.10 8.02 7.36
0.63
9.04
0.96 0.60 0.26 −0.11
21.14 22.75 7.97 −3.23
0.45
55.18
Defined for Minor injury Distracted Speed Female Runoff Close to home Young Over correction Defined for No injury Constant Dark Interstate 0.31 Swerve 0.35 Vehicle defect 0.57 Latent Class Probability 0.69 Number of observations 80342 LL at convergence −64377.12 Restricted LL −88263.61 McFadden Pseudo R-sq 0.27
1.48 0.63 0.34 1.74 0.49 0.29
7.08 6.91 3.00 64.72
t-Statistic
6.71 6.65 5.33 5.43 8.06 4.16
−0.20 0.51 0.46 −0.29
−2.01 8.31 6.87 −4.05
0.31
28.41
0.21
1.96
−0.48
−3.61
−0.13
−2.20
0.74
5.95
0.72 49625 −40953.87 −54518.63 0.25
103.45
190
0.41
0.86 −0.70 0.17 −0.81 0.21 0.62
−2.55 1.13 1.84 −0.91 0.95 0.28
5.76
t-Statistic
0.67 0.84
12.96 14.33
1.12 0.36 0.32 0.47
14.92 5.52 9.03 7.64
5.15 −6.59 2.59 −6.09 2.88 7.30
−9.23 7.07 8.38 −2.84 2.13 40.46
−0.22 0.29 0.18 0.68 0.55 129967 −106474.71 −142782.24 0.25
−6.19 7.56 4.62 3.72 67.99
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weekdays. The results indicate that single-vehicle crashes that occurred on county roads had 16.08% and 14.97% higher likelihood to result in severe injury on weekdays and weekends respectively. The outcome of crashes involving old drivers were generally more likely to be severe injury for both weekdays and weekends. The outcome of crashes involving distracted driving were more likely to either be severe or lead to some form of injury for both weekdays and weekends. Speeding was the primary contributing factor in about 19% and 18% of weekday and weekend crashes, respectively. Interestingly, speed-related crashes that occurred on weekdays were more likely to result in minor injuries in 31% of the crashes. This finding appears to contradict findings of other research studies that found speeding to be a major contributing factor for severe injury crashes (e.g. Shankar and Mannering, 1996; Savolainen and Mannering, 2007). However, it should be noted that speeding as a crash contributing factor can result in any injury severity (ranging from no injury to fatal injury). The model estimation results have shown that speed-related crashes were less likely to result in minor injury in only 28% of the weekend crashes. This means crashes that were due to speeding in 72% of weekend crashes resulted in either severe injuries or no injury. Another interesting finding from this study is that, crashes involving young drivers had higher probability to result in severe or minor injury outcomes when those crashes occurred on weekends, whereas crashes involving young drivers were more likely to be minor and not severe injury on weekdays. Run-off-road collisions, crashes that occurred within 25 miles of the driver’s residence, and crashes in which overcorrection was suspected had higher likelihood to result in minor injury outcome. Crashes that occurred on dark or unlit roadways had 0.96% higher probability of not resulting in any form of injury during weekdays. However, weekend crashes that happened on dark or unlit roadways had 3.12% higher likely to be severe. Finally, crashes that occurred on interstates, or involved swerving to avoid collision, and crashes that resulted from vehicle defects were more likely to lead to no injuries.
Table 3 Estimated marginal effects of the variables included in the latent class logit model. Effects on probabilities of the severity outcomes (%) Weekday
Weekend
Variable
Serious Injury
Minor Injury
No Injury
Serious Injury
Minor Injury
No Injury
Invalid license Unemployed No seatbelt Fatigued DUI County road Senior Distracted Speed Female Runoff Close to home Young Over correction Dark Interstate Swerve Vehicle defect
2.42 5.76 8.82 2.55 0.87 16.08 9.55 2.27 −0.75 −1.26 −0.44 −2.76 −0.79 −0.37 −2.18 −3.49 −1.11 −0.24
−0.43 −0.88 −4.85 −0.47 −0.18 −1.96 −1.52 3.19 2.53 4.22 2.33 9.75 2.58 0.95 −2.11 −3.24 −1.15 −0.24
−0.49 −0.98 −5.43 −0.47 −0.19 −2.14 −1.52 −1.95 −0.79 −1.32 −0.97 −2.89 −0.83 −0.39 0.96 1.09 0.44 0.07
2.76 3.88 11.01 1.75 1.27 14.97 8.96 2.54 −0.81 −0.41 −0.48 −2.37 0.78 −0.26 3.12 −3.90 −1.16 −0.30
−0.54 −0.62 −6.09 0.26 0.27 −2.04 −1.38 2.39 2.53 1.38 1.34 8.10 2.51 0.68 −3.04 −3.61 −1.20 −0.29
−0.60 −0.69 −6.69 −0.28 −0.28 −2.20 −1.84 −1.59 −0.86 −0.42 −0.48 −2.49 −0.82 −0.27 1.57 1.31 0.50 0.08
severe when they happened on weekends, whereas there is no significant evidence that this is true for a third of the crashes that happened on weekdays. Similarly, crashes involving female drivers were more likely to result in minor injuries when they happened on weekends. Results also show that minor injury outcome was more likely for 31% of crashes involving female drivers that occurred on weekdays. Young drivers were more likely to be involved in crashes that resulted in minor injuries in only one of the classes of both weekday and weekend models. Crashes that happened on interstates were more likely to result in no injury on weekdays and also in latent class 2 of the weekend model. Crashes involving vehicle defects were more likely to result in no injury for latent class 1 of the weekday model and latent class 2 of the weekend model. Table 3 shows the marginal effects for the variables used in model building. The interpretation of the results would be based on the marginal effects as estimation results show evidence of heterogeneity between the two classes of the models (for instance, some of the parameters have the same sign across the two classes, opposite signs or the parameters are not significant in both classes). This means that the latent classes identified are not perfectly homogeneous.
6. Conclusions In this paper, latent class logit modeling was used to identify different factors that influence the severity of single-vehicle crash outcomes between weekdays and weekends. Latent class logit models were developed as alternative to the frequently used random parameters models to account for unobserved heterogeneity across crash-severity observations. Latent class models also have very significant advantages in interpretation over random parameter models. Single-vehicle crashes from 2012 to 2016 in Alabama were used in this study. Three crash injury outcomes were considered; severe injury (fatal and incapacitating crash injury), minor injury (non-incapacitating and possible crash injury), and no-injury crash outcomes as the third category. Two distinct subgroups each of crashes with homogeneous attributes were identified with specified probabilities, for both weekdays and weekends, and a total of 18 variables were found to be statistically significant, at a 0.05 significance level. The interpretation of the estimation results was based on marginal effects. The results indicate a significant association of severe injury crashes to risk factors such as driver unemployment, invalid drivers’ license, no seatbelt use, fatigue, DUI, old age, and driving on county roads for both weekdays and weekends. Female drivers have been shown to have higher likelihood to be involved in minor injury crashes. One interesting finding of this study is that speed-related crashes were less likely to result in severe injuries in some proportion of the data. This finding contradicts other research studies that found speeding to be a major contributing factor for severe injury crashes. However, this finding highlights the merit of using latent class analysis for crash severity studies. The study also revealed that DUI crashes were more likely to result in severe injuries on weekends than on weekdays, whereas crashes that occurred on county roads were more likely to be severe than crashes that happened on interstates. The findings of this study reveal a
5. Discussion The marginal effects results show that the probability of a severe injury outcome increased when the at-fault driver had no driver’s license regardless of the time of the week. This finding is consistent with past researches (e.g. Blows et al., 2005). Crashes involving unemployed drivers had 5.76% and 3.88% higher likelihood to be severe on weekdays and weekends respectively. While failure to use seatbelt may not lead to crash occurrence, it certainly affects the severity of the crash outcome (Abdel-Aty, 2003; Yau, 2004; Chen and Chen, 2011; Kim et al., 2013). The results from this study show that single-vehicle crashes in which the driver did not use seatbelt had 8.82% higher likelihood to result into severe injuries when those crashes occurred during weekdays. There was even a higher likelihood (11.01%) when those crashes happened on weekends. Fatigue-induced single-vehicle crashes were 2.55% more likely to lead to severe injuries when they occurred on weekdays compare to 1.75% for weekends. There was also 0.26% higher probability of fatigue crashes to result in minor injuries during weekends. Crashes involving DUI had 1.27% higher likelihood to result in severe injuries during weekends compared to 0.87% higher on 191
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strong link between human factors and the occurrence of severe injury single-vehicle crashes, as it can be observed that most of the factors associated with severe-injury outcome are driver behavior related. In view of the findings of this paper, it is recommended that law enforcement be intensified on county roads especially on weekends. Also, public education on seatbelt use has to be rigorous to alert the public about the dangers of not using them. The use of latent class analysis for crash studies can reveal how crash contributing factors and crash severities vary across sub-populations. This approach to crash-injury analysis can help decision-makers in the effective and efficient implementation of targeted countermeasures. To illustrate the significance of the findings of this study, the third model using the combined data was also developed to explore the merit of using sub-populations of data for improved and detailed classification of the crash-severity factors. The separate model estimation results have shown that generally, the factors that contribute to singlevehicle crash injury outcomes were not very different between weekdays and weekends. This finding is interesting, particularly because while a significantly high proportion of fatal (and to some extent incapacitating injury) crashes occurred on weekends, the contributing factors appeared to be similar to those that occurred on weekdays. This suggests that countermeasure strategies such as enforcement should be carried out with similar intensity throughout the week, or perhaps even more on weekends.
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Accident Analysis and Prevention journal homepage: www.elsevier.com/locate/aap
Latent class analysis of factors that influence weekday and weekend singlevehicle crash severities
T
⁎
Emmanuel Kofi Adanua, , Alexander Hainenb, Steven Jonesb a b
Alabama Transportation Institute, The University of Alabama Tuscaloosa, AL, United States Department of Civil, Construction and Environmental Engineering, The University of Alabama Tuscaloosa, AL, United States
A R T I C L E I N F O
A B S T R A C T
Keywords: Single-vehicle crash Weekend crash Weekday crash Latent class logit Crash-severity
This paper investigates factors that influence the severity of single-vehicle crashes that happen on weekdays and weekends. Crash data from 2012 to 2016 for the State of Alabama was used for this study. Latent class logit models were developed as alternative to the frequently used random parameters models to account for unobserved heterogeneity across crash-severity observations. Exploration of the data revealed that a high proportion of severe injury injury crashes happened on weekends. The study examined whether single-vehicle crash contributing factors differ between weekdays and weekends. The model estimation results indicate a significant association of severe injury crashes to risk factors such as driver unemployment, driving with invalid license, no seatbelt use, fatigue, driving under influence, old age, and driving on county roads for both weekdays and weekends. Research findings show a strong link between human factors and the occurrence of severe injury single-vehicle crashes, as it has been observed that many of the factors associated with severe-injury outcome are driver behavior related. To illustrate the significance of the findings of this study, a third model using the combined data was developed to explore the merit of using sub-populations of the data for improved and detailed segmentation of the crash-severity factors. It has also been shown that generally, the factors that influence single-vehicle crash injury outcomes were not very different between weekdays and weekends. The findings of this study show the importance of investigating sub-populations of data to reveal complex relationships that should be understood as a necessary step in targeted countermeasure application.
1. Introduction Single-vehicle crashes present an interesting area of research because of the predominant role of the driver involved. These manner of crashes occur either on the roadway or off the roadway. A high proportion of single-vehicle crashes comprise run-off-road and fixed-object collisions. In the United States, statistics show that more than half of annual fatal crashes involve single vehicles with some 70% of those being run-off-road crashes (Liu and Subramanian, 2006; IIHS, 2018; NHTSA, 2017). Understanding the contributing factors and circumstances under which single-vehicle crashes occur is important for countermeasure implementation. Many researches have previously been conducted to explore singlevehicle crash characteristics. Some of the common factors that have been identified as contributing circumstances to single-vehicle crashes include excessive speed, driver fatigue, driving under the influence of alcohol or other drugs (DUI), or the effect of these and other geometric, weather, site characteristics, and vehicle factors. Studies have also investigated how these factors influence the occurrence and severity of ⁎
single-vehicle crashes. For instance, Chen and Chen (2011) have found that, in adverse driving conditions such as bad weather and/or complex terrain, there is a high chance of trucks getting into single-vehicle crashes. Xie et al. (2012) studied driver injury severity in rural singlevehicle crashes using a latent class logit, where they found that fatal single-vehicle crashes occurred more often on rural roads. Also, Shaheed and Gkritza (2014) used latent class analysis to analyze singlevehicle motorcycle crash severities in Iowa. Their study revealed a significant relationship between the severity of injury outcomes and factors such as speeding, riding on rural roads, riding without a helmet, and impaired riding (riders under the influence of drug, alcohol or medication. Jung et al. (2010) investigated the effect of rainfall on single-vehicle crashes in Wisconsin. Their study used a backward sequential logistic regression model to predict crash severities and they observed that rainfall intensity, wind, speed, roadway terrain, and seatbelt use had significant effects on crash outcome. Multinomial logit was used by Shankar and Mannering (1996) to explore the factors that influenced single-vehicle motorcycle crash severities in Washington State. They found driver age, helmet use, pavement condition, speed,
Corresponding author. E-mail addresses: [email protected] (E.K. Adanu), [email protected] (A. Hainen), [email protected] (S. Jones).
https://doi.org/10.1016/j.aap.2018.01.035 Received 29 September 2017; Received in revised form 25 January 2018; Accepted 25 January 2018 0001-4575/ © 2018 Elsevier Ltd. All rights reserved.
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model was also developed for the study period to compare with results obtained for the sub-populations (i.e. weekday crashes and weekend crashes) and also to show the importance of analyzing segments of the data to gain in-depth insight into the factors that affect crash-severity.
drunk driving, and driver inattention to have varying effects on the severity of crashes. Maistros et al. (2014) used mixed logit models to compare contributing factors between alcohol-related single-vehicle motorcycle and car crashes in Ohio where they developed mixed logit models for motorcycles and passenger cars to quantify the effects of roadway geometry, speeds, and safety equipment usage on riders and drivers exposure to severe injuries. Wu et al. (2014) studied driver injury severity of single- and multi-vehicle crashes on rural two-lane highways in New Mexico using mixed logit, where they investigated similarities and differences in factors responsible for single-vehicle crashes and multi-vehicle crashes. They observed that the probability of having severe outcomes was higher when vans are involved, and when drivers wrongfully overtake in single-vehicle crashes. Morgan and Mannering (2011) assessed the effects that age and gender have on crash severities by considering single-vehicle crashes that occurred on dry, wet, and snow/ice-covered roadway surfaces in Indiana. Lee and Li (2014) used heteroscedastic ordered logit modeling techniques to analyze injury severity of drivers involved in single-vehicle and twovehicle collisions on provincial highways in Ontario, Canada, for the period from 2004 to 2008. They found increased drivers’ injury severity for single-vehicle collisions that happened on curved segments of the roads, collisions that involved female drivers and also among young drivers below the age of 30 years. On the other hand, they found decreased injury severity for crashes that occurred on roads with large number of lanes and crashes involving vehicles equipped with advanced safety features. Islam et al (2014) undertook a comprehensive study to identify factors associated with single- and multi-vehicle large truck at-fault crashes on rural and urban roads in Alabama. This study found increased injury severity for truck crashes related to driver fatigue in rural locations. Also, it was observed that crashes involving single-vehicle trucks that occurred between midnight and 7:00 A.M. at rural locations were more likely to result in major injuries. Crashes involving single-vehicle trucks that occurred at curved sections of urban locations were found to significantly result in either major injury or possible/no injury. Dabbour (2017) used logistic regression to investigate the temporal stability of risk factors affecting severity single-vehicle collision severities that occurred in North Carolina from 2007 to 2013. It was found in this study that severe injuries were consistently associated with undivided and rural roads, dark and unlit roadway conditions, male drivers, and crashes involving DUI. Older vehicles and light-duty trucks were also found to be associated with severe injuries. Also, Behnood and Mannering (2015) used mixed logit modeling to explore the temporal stability of the factors affecting driver injury-severities of singlevehicle in Chicago, Illinois. It was found that improvements in vehicle safety features and drivers’ response to those improvements contributed to the instability of crash contributing factors over the study period (2004 to 2012). Similarly, Xiong et al. (2014) observed instability in the factors affecting the severity of single-vehicle collisions in Indiana from 1995 to 1999. They attributed the temporal instability to ongoing changes in average annual daily traffic, international roughness index, and rut depth. Travel activities and driver behaviors are known to vary with time (time of day, day of the week, holidays, etc.) (e.g. Behnood and Mannering, 2016; Pahukula et al., 2015). Evidence suggests that risky driving behaviors (and related crashes) may be more prevalent during weekend periods (defined as 6 P.M. Friday to 5:59 A.M. Monday) than during regular weekdays (NHTSA, 2015). This necessitates an in-depth analysis of the risk factors associated with crash occurrence and severities of outcomes between weekdays and weekends to know who, where, and when these crashes occurred as these can dictate how countermeasures may be effectively implemented. This study therefore investigates the contributing factors that influence crash-severities between weekdays and weekends for single-vehicle crashes in the State of Alabama. The study uses latent class logit modeling techniques to develop separate models for weekday and weekend crashes. An overall
2. Methodology Accounting for unobserved heterogeneity across injury-severity observations is an important concern in traffic safety research. Ignoring the effect of unobserved variables in injury-severity studies can lead to biased estimates and incorrect inferences if the right methods are not used (Shaheed and Gkritza, 2014; Mannering et al., 2016). Discretechoice models, ordered (probit and logit models) and unordered models (such as the multinomial logit model), have particularly been used extensively to analyze crash injury severity due to the classification of the severities into discrete outcomes (see Savolainen et al., 2011 and Mannering and Bhat, 2014 for injury-severity methodology reviews). However, many of the discrete ordered and unordered models are unable to account for unobserved heterogeneity across injury-severity observations (see Savolainen et al., 2011). Random parameters (mixed logit) models (Milton et al., 2008; Morgan and Mannering, 2011; Anastasopoulos and Mannering, 2011; Kim et al., 2013) and latent class (finite mixture) models (Yasmin et al., 2014; Shaheed and Gkritza, 2014), or latent class with random parameters within each class, (Bujosa et al., 2010; Xiong and Mannering, 2013; Greene and Hensher, 2013) have the ability to capture unobserved heterogeneity by allowing parameters to differ across observations (Morgan and Mannering, 2011; Behnood and Mannering, 2015; Mannering et al., 2016). While random parameters technique uses continuous mixing distributions to capture heterogeneity, it requires the analyst to specify the functional form of the mixing distribution (for example, normal, log-normal, uniform, triangular, etc.). On the other hand, the latent class approach identifies unobserved classes without distributional assumptions. In effect, latent class model replaces the continuous distribution assumption of random parameter model with a discrete distribution in which unobserved heterogeneity is captured by membership of distinct classes (Greene and Hensher, 2003; Mannering and Bhat, 2014). Though it has been shown that random parameter models with heterogeneity in means and random parameter models with heterogeneity in means and variances perform better than conventional random parameters models (e.g. Greene et al., 2006; Venkataraman et al., 2014; Kim et al., 2013; Seraneeprakarn et al., 2017; Behnood and Mannering, 2017), the use of latent class analysis for sub-population models can help identify further distinctions of classes within the sub-populations that may not be known or explicitly defined (e.g. Xie et al., 2012; Eluru et al., 2012; Xiong and Mannering, 2013; Cerwick et al., 2014), instead of estimating separate models for pre-determined sub-populations (e.g. Islam and Mannering, 2006; Morgan and Mannering, 2011). Latent class logit model offers an alternative perspective to the conventional random parameters logit model in terms of accommodating heterogeneity (Greene and Hensher, 2003; Behnood et al., 2014; Mannering et al., 2016). In this paper, to model crash-injury severity, three discrete severity levels are considered: severe injury (fatal or incapacitating); minor injury (non-incapacitating or possible injury); and no injury (property damage only). Latent class logit model allows the crash severity to have C different classes so that each of the classes will have their own parameters with the probability given by (Behnood et al., 2014):
Pn (c ) =
exp (α c Zn ) ∑∀ C exp (α c Zn )
(1)
where Zn represents a vector that shows the probabilities of c for crash n , C is the possible classes c,and α c represents the estimable parameters (class specific parameters). The unconditional probability 188
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Table 1 Summary statistics of variables included in the latent class logit models.
Variables Dependent Severe injury Minor injury No injury Explanatory Invalid license Unemployed No seatbelt Fatigued DUI County road Senior Distracted Speed Female Runoff Close to home Young Over correction Dark Interstate Swerve Vehicle defect *
Description
Weekday (61.82%) Mean (Std. Dev)
Weekend (38.18%) Mean (Std. Dev)
Crash severity: fatal or incapacitating injury Crash severity: non incapacitating or possible injury Crash severity: property damage only
0.11 (0.31) 0.22 (0.42) 0.67 (0.47)
0.12 (0.33) 0.23 (0.42) 0.65 (0.48)
License status of causal driver: Invalid license (1 = Yes, 0 = No) Driver employment status: Unemployed (1 = Yes, 0 = No) Seatbelt use: No seatbelt (1 = Yes, 0 = No) Driver condition at time of crash: Fatigued (1 = Yes, 0 = No) Primary contributing factor: DUI (1 = Yes, 0 = No) Functional class of road: County road (1 = Yes, 0 = No) Driver age: more than 60 (1 = Yes, 0 = No) Primary contributing factor: Distracted driving (1 = Yes, 0 = No) Primary contributing factor: Speed (1 = Yes, 0 = No) Driver gender: Female (1 = Yes, 0 = No) Primary contributing factor: Runoff road (1 = Yes, 0 = No) Driver residence from crash location: Less than 25mi (1 = Yes, 0 = No) Driver age: less than 24 (1 = Yes, 0 = No) Primary contributing factor: Over correction (1 = Yes, 0 = No) Lighting condition at time of crash: Dark/Unlit (1 = Yes, 0 = No) Functional class of road: Interstate (1 = Yes, 0 = No) Primary contributing factor: Swerve to avoid collision (1 = Yes, 0 = No) Primary contributing factor: Vehicle defect (1 = Yes, 0 = No)
0.11 0.24 0.08 0.06 0.07 0.34 0.11 0.12 0.19 0.40 0.10 0.76 0.25 0.03 0.25 0.15 0.15 0.01
0.14 0.25 0.11 0.07 0.14 0.35 0.08 0.13 0.18 0.36 0.09 0.75 0.32 0.03 0.40 0.16 0.14 0.01
(0.31) (0.43) (0.28) (0.23) (0.26) (0.47) (0.32) (0.32) (0.39) (0.49) (0.29) (0.43) (0.43) (0.18) (0.43) (0.36) (0.35) (0.09)
(0.34) (0.43) (0.31) (0.25) (0.35) (0.48) (0.27) (0.33) (0.38) (0.48) (0.28) (0.44) (0.47) (0.16) (0.49) (0.37) (0.35) (0.09)
Total number of fatal single-vehicle crashes between 2012–2016 obtained from the CARE system was 1919 (899 occurred on weekends and 1020 occurred on weekdays).
alternative i (i ≠ q ) on the probability Pnq for crash n to result in outcome q . The final marginal effect of an explanatory variable is the sum of the marginal effects for each class weighted by their posterior latent class probabilities (Greene, 2007; Xie et al., 2012).
that a crash will result in severity i is given by:
Pn (i) =
∑∀ C Pn (c )* Pn (i/c )
(2)
where Pn (i/ c ) is the probability of crash n to result in crash severity level i in class c . Based on the two equations above, the latent class logit model for class c will be:
Pn (i/ c ) =
3. Data description
exp (βic Xin ) ∑∀ I exp (βic Xin )
The study was based on 2012–2016 single-vehicle crash data for the State of Alabama, obtained from the Critical Analysis Reporting Environment (CARE) system developed by the University of Alabama Center for Advanced Public Safety. Observations with missing values were omitted from the dataset, resulting in a total of 129,967 observations. To investigate whether there are differences in crash-severity contributing factors, the data was grouped between weekdays and weekends. The distribution of crashes by severity outcome reveals that nearly 35% of the single-vehicle crashes during the study period resulted in an injury outcome. Though 38.18% of single-vehicle crashes occurred during weekends they contributed to about 47% of the fatal crashes (and 41% of severe injury crashes). This highlights the importance of identifying the factors that are associated with each severity outcome between weekdays and weekends and subsequently proposing countermeasures to improve safety. Altogether, more than 40 variables were considered in the latent class logit analysis, it was observed that some of the predictor variables were correlated. For instance, it was observed that DUI as driver condition at the time of the crash correlated strongly with DUI as primary contributing factor. Relationships between such variables and the response variables were also investigated. Such highly correlated variables were not, however, included in the final models in order to avoid multicollinearity. Table 1 shows the summary statistics of the variables that were found to be significant in the latent class logit models. It has been observed that the proportion of single-vehicle crashes involved drivers without valid driver’s licenses is slightly more on weekends (14% to 11% on weekdays). No seatbelt use was reported in 8% of weekday crashes and 11% of weekend crashes. One interesting finding was that crashes involving DUI comprised 7% of weekday crashes and 14% of weekend crashes. Also, drivers aged 60years and above were involved in 11% of crashes on weekdays and 8% of weekend crashes, while young drivers (aged less than 24years) were involved in 25% of
(3)
where I represents the possible number of injury severity levels and βic is a class-specific parameter vector that takes a finite set of values. The latent class logit model can be estimated with maximum likelihood procedures (Greene and Hensher, 2003). The latent class method however does not account for the variable randomness within a class since it assumes homogeneous characteristics of the within-class observations (Mannering and Bhat, 2014). Greene and Hensher (2013) and Bujosa et al. (2010) present the random parameter latent class model as an extension of the latent class logit model to capture interactions with observed contextual effects within the latent classes. This study attempted to use this method to model the crash data. However, no random variables were found within the homogeneous classes and there was no significant improvement in model fit statistics. Marginal effects are commonly computed from the partial derivative for each observation, to investigate the effect of individual parameters on the crash-severity outcome probabilities. Marginal effect in a latent class logit model is computed for each class as the difference in the estimated probabilities with the indicator changing from zero to one, while keeping all the other variables at their means. Greene (2007) has shown that the direct and cross-marginal effects can be computed respectively as follows:
∂Pni = βik Pni (1−Pni ) ∂x nik ∂Pnq ∂x nik
= −βik Pni Pnq
(4)
(5)
The direct marginal effect indicates the effect of a unit change in x nik on the probability, Pni, for crash n to result in severity i . The crossmarginal effect shows the impact of a unit change in variable k of 189
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Table 2 presents the detailed model estimation results for weekday and weekend single-vehicle crashes. To ascertain the merit of identifying latent classes within pre-defined sub-populations of the data, model results of the combined dataset are also been presented. Two distinct segments (classes) with homogeneous attributes were found significant for weekdays, weekends, and the combined data (in all cases, estimation results with more than two latent classes did not statistically improve the models in terms of data fit). The latent class probabilities for the weekday crash model were 0.69 (latent class 1) and 0.31 (latent class 2). The weekend model had latent class probabilities of 0.72 (latent class 1) and 0.28 (latent class 2). The combined dataset had latent classes with probabilities of 0.55 (latent class 1) and 0.45 (latent class 2). The class specific probabilities are a set of fixed constants (see Eq. (1)), as examining segmentation on the basis of crashspecific characteristics did not result in a superior model fit. A total of 18 variables were used and found to be statistically significant, at a 0.05 significance level. The same variables were used to develop all the models so as to examine their how they vary between weekdays and weekends. The model fit statistics are also shown in Table 2. Variables (and constant terms) that were not found to be statistically significant at a 0.05 significance level were not shown in Table 2. An interesting observation from the model estimation results is that without segmenting the data into weekdays and weekends, the latent class model for the combined crashes does not show seatbelt use and driver age (less than 24 years) to significantly influence the severity of the crashes. Similarly, the combined data shows over correction indicator to be significant contributor in minor injury crashes for latent class 2 but this variable did not show statistical significance in neither weekday nor weekend models. The latent class models reveal that the factors that influence severe crash outcome are consistent between weekdays and weekends for the classes with the higher proportions (i.e. latent class 1) in both cases. Crashes that occurred on county roads were generally more likely to be
weekday crashes and 32% of weekend crashes. Crashes that occurred on dark and unlit roadways make up 25% of weekday crashes and 40% of weekend crashes. 4. Estimation results Likelihood ratio test (Washington et al., 2011) was performed to determine whether separate models by time of the week was justified. The test statistic is given by: K
⎤ ⎡ X 2 = −2 ⎢LL (βT )− ∑ LL (βk ) ⎥, k=1 ⎦ ⎣
(6)
where LL (βT ) is the log-likelihood at convergence of the model estimated with all the data, LL (βk ) is the log-likelihood at convergence of the model using subset k data (weekday and weekend) and K is the total number of data subsets used. The X 2 statistic is chi-squared distributed with degrees of freedom equal to the sum of the number of estimated parameters in all subset models minus the number of estimated parameters in the full-sample model. The resulting X 2 statistic indicates whether or not the model for the subset data is significantly different than the model for the full-sample data. Log-likelihood test was further performed to determine whether or not the subset models have parameters that are statistically different. The test statistic used is given by:
X 2 = −2[LL (βT )−LL (βk )],
(7)
where LL (βT ) is the log-likelihood at convergence of the model estimated with all the data (weekday and weekend), LL (βk ) is the loglikelihood at convergence of the model using subset k data (weekday or weekend). Based on the likelihood ratio tests performed and study objectives, it was determined that two separate severity models (for weekdays and weekends) should be developed. Table 2 Latent class logit models estimation results. Weekday Variable
Defined for Severe injury Constant Invalid license Unemployed No seatbelt Fatigued DUI County road Senior
Weekend
Combined
Latent Class 1
Latent Class 2
Latent Class 1
Latent Class 2
Latent Class 1
Latent Class 2
Parameter
t-Statistic
Parameter
Parameter
t-Statistic
Parameter
t-Statistic
Parameter
Parameter
t-Statistic
−1.15
−13.35
−0.52
−4.50
0.37 0.37 2.40 0.66 0.24 0.23 0.43
8.97 11.61 46.09 12.14 4.59 5.98 9.30
0.17 0.37 3.04 1.05 0.16 0.17 0.57
2.41 5.87 24.46 10.34 2.08 2.79 5.32
0.83
7.67
−0.55
−2.53
0.35 0.32 0.27 0.45 0.23
10.32 10.04 12.10 8.02 7.36
0.63
9.04
0.96 0.60 0.26 −0.11
21.14 22.75 7.97 −3.23
0.45
55.18
Defined for Minor injury Distracted Speed Female Runoff Close to home Young Over correction Defined for No injury Constant Dark Interstate 0.31 Swerve 0.35 Vehicle defect 0.57 Latent Class Probability 0.69 Number of observations 80342 LL at convergence −64377.12 Restricted LL −88263.61 McFadden Pseudo R-sq 0.27
1.48 0.63 0.34 1.74 0.49 0.29
7.08 6.91 3.00 64.72
t-Statistic
6.71 6.65 5.33 5.43 8.06 4.16
−0.20 0.51 0.46 −0.29
−2.01 8.31 6.87 −4.05
0.31
28.41
0.21
1.96
−0.48
−3.61
−0.13
−2.20
0.74
5.95
0.72 49625 −40953.87 −54518.63 0.25
103.45
190
0.41
0.86 −0.70 0.17 −0.81 0.21 0.62
−2.55 1.13 1.84 −0.91 0.95 0.28
5.76
t-Statistic
0.67 0.84
12.96 14.33
1.12 0.36 0.32 0.47
14.92 5.52 9.03 7.64
5.15 −6.59 2.59 −6.09 2.88 7.30
−9.23 7.07 8.38 −2.84 2.13 40.46
−0.22 0.29 0.18 0.68 0.55 129967 −106474.71 −142782.24 0.25
−6.19 7.56 4.62 3.72 67.99
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weekdays. The results indicate that single-vehicle crashes that occurred on county roads had 16.08% and 14.97% higher likelihood to result in severe injury on weekdays and weekends respectively. The outcome of crashes involving old drivers were generally more likely to be severe injury for both weekdays and weekends. The outcome of crashes involving distracted driving were more likely to either be severe or lead to some form of injury for both weekdays and weekends. Speeding was the primary contributing factor in about 19% and 18% of weekday and weekend crashes, respectively. Interestingly, speed-related crashes that occurred on weekdays were more likely to result in minor injuries in 31% of the crashes. This finding appears to contradict findings of other research studies that found speeding to be a major contributing factor for severe injury crashes (e.g. Shankar and Mannering, 1996; Savolainen and Mannering, 2007). However, it should be noted that speeding as a crash contributing factor can result in any injury severity (ranging from no injury to fatal injury). The model estimation results have shown that speed-related crashes were less likely to result in minor injury in only 28% of the weekend crashes. This means crashes that were due to speeding in 72% of weekend crashes resulted in either severe injuries or no injury. Another interesting finding from this study is that, crashes involving young drivers had higher probability to result in severe or minor injury outcomes when those crashes occurred on weekends, whereas crashes involving young drivers were more likely to be minor and not severe injury on weekdays. Run-off-road collisions, crashes that occurred within 25 miles of the driver’s residence, and crashes in which overcorrection was suspected had higher likelihood to result in minor injury outcome. Crashes that occurred on dark or unlit roadways had 0.96% higher probability of not resulting in any form of injury during weekdays. However, weekend crashes that happened on dark or unlit roadways had 3.12% higher likely to be severe. Finally, crashes that occurred on interstates, or involved swerving to avoid collision, and crashes that resulted from vehicle defects were more likely to lead to no injuries.
Table 3 Estimated marginal effects of the variables included in the latent class logit model. Effects on probabilities of the severity outcomes (%) Weekday
Weekend
Variable
Serious Injury
Minor Injury
No Injury
Serious Injury
Minor Injury
No Injury
Invalid license Unemployed No seatbelt Fatigued DUI County road Senior Distracted Speed Female Runoff Close to home Young Over correction Dark Interstate Swerve Vehicle defect
2.42 5.76 8.82 2.55 0.87 16.08 9.55 2.27 −0.75 −1.26 −0.44 −2.76 −0.79 −0.37 −2.18 −3.49 −1.11 −0.24
−0.43 −0.88 −4.85 −0.47 −0.18 −1.96 −1.52 3.19 2.53 4.22 2.33 9.75 2.58 0.95 −2.11 −3.24 −1.15 −0.24
−0.49 −0.98 −5.43 −0.47 −0.19 −2.14 −1.52 −1.95 −0.79 −1.32 −0.97 −2.89 −0.83 −0.39 0.96 1.09 0.44 0.07
2.76 3.88 11.01 1.75 1.27 14.97 8.96 2.54 −0.81 −0.41 −0.48 −2.37 0.78 −0.26 3.12 −3.90 −1.16 −0.30
−0.54 −0.62 −6.09 0.26 0.27 −2.04 −1.38 2.39 2.53 1.38 1.34 8.10 2.51 0.68 −3.04 −3.61 −1.20 −0.29
−0.60 −0.69 −6.69 −0.28 −0.28 −2.20 −1.84 −1.59 −0.86 −0.42 −0.48 −2.49 −0.82 −0.27 1.57 1.31 0.50 0.08
severe when they happened on weekends, whereas there is no significant evidence that this is true for a third of the crashes that happened on weekdays. Similarly, crashes involving female drivers were more likely to result in minor injuries when they happened on weekends. Results also show that minor injury outcome was more likely for 31% of crashes involving female drivers that occurred on weekdays. Young drivers were more likely to be involved in crashes that resulted in minor injuries in only one of the classes of both weekday and weekend models. Crashes that happened on interstates were more likely to result in no injury on weekdays and also in latent class 2 of the weekend model. Crashes involving vehicle defects were more likely to result in no injury for latent class 1 of the weekday model and latent class 2 of the weekend model. Table 3 shows the marginal effects for the variables used in model building. The interpretation of the results would be based on the marginal effects as estimation results show evidence of heterogeneity between the two classes of the models (for instance, some of the parameters have the same sign across the two classes, opposite signs or the parameters are not significant in both classes). This means that the latent classes identified are not perfectly homogeneous.
6. Conclusions In this paper, latent class logit modeling was used to identify different factors that influence the severity of single-vehicle crash outcomes between weekdays and weekends. Latent class logit models were developed as alternative to the frequently used random parameters models to account for unobserved heterogeneity across crash-severity observations. Latent class models also have very significant advantages in interpretation over random parameter models. Single-vehicle crashes from 2012 to 2016 in Alabama were used in this study. Three crash injury outcomes were considered; severe injury (fatal and incapacitating crash injury), minor injury (non-incapacitating and possible crash injury), and no-injury crash outcomes as the third category. Two distinct subgroups each of crashes with homogeneous attributes were identified with specified probabilities, for both weekdays and weekends, and a total of 18 variables were found to be statistically significant, at a 0.05 significance level. The interpretation of the estimation results was based on marginal effects. The results indicate a significant association of severe injury crashes to risk factors such as driver unemployment, invalid drivers’ license, no seatbelt use, fatigue, DUI, old age, and driving on county roads for both weekdays and weekends. Female drivers have been shown to have higher likelihood to be involved in minor injury crashes. One interesting finding of this study is that speed-related crashes were less likely to result in severe injuries in some proportion of the data. This finding contradicts other research studies that found speeding to be a major contributing factor for severe injury crashes. However, this finding highlights the merit of using latent class analysis for crash severity studies. The study also revealed that DUI crashes were more likely to result in severe injuries on weekends than on weekdays, whereas crashes that occurred on county roads were more likely to be severe than crashes that happened on interstates. The findings of this study reveal a
5. Discussion The marginal effects results show that the probability of a severe injury outcome increased when the at-fault driver had no driver’s license regardless of the time of the week. This finding is consistent with past researches (e.g. Blows et al., 2005). Crashes involving unemployed drivers had 5.76% and 3.88% higher likelihood to be severe on weekdays and weekends respectively. While failure to use seatbelt may not lead to crash occurrence, it certainly affects the severity of the crash outcome (Abdel-Aty, 2003; Yau, 2004; Chen and Chen, 2011; Kim et al., 2013). The results from this study show that single-vehicle crashes in which the driver did not use seatbelt had 8.82% higher likelihood to result into severe injuries when those crashes occurred during weekdays. There was even a higher likelihood (11.01%) when those crashes happened on weekends. Fatigue-induced single-vehicle crashes were 2.55% more likely to lead to severe injuries when they occurred on weekdays compare to 1.75% for weekends. There was also 0.26% higher probability of fatigue crashes to result in minor injuries during weekends. Crashes involving DUI had 1.27% higher likelihood to result in severe injuries during weekends compared to 0.87% higher on 191
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strong link between human factors and the occurrence of severe injury single-vehicle crashes, as it can be observed that most of the factors associated with severe-injury outcome are driver behavior related. In view of the findings of this paper, it is recommended that law enforcement be intensified on county roads especially on weekends. Also, public education on seatbelt use has to be rigorous to alert the public about the dangers of not using them. The use of latent class analysis for crash studies can reveal how crash contributing factors and crash severities vary across sub-populations. This approach to crash-injury analysis can help decision-makers in the effective and efficient implementation of targeted countermeasures. To illustrate the significance of the findings of this study, the third model using the combined data was also developed to explore the merit of using sub-populations of data for improved and detailed classification of the crash-severity factors. The separate model estimation results have shown that generally, the factors that contribute to singlevehicle crash injury outcomes were not very different between weekdays and weekends. This finding is interesting, particularly because while a significantly high proportion of fatal (and to some extent incapacitating injury) crashes occurred on weekends, the contributing factors appeared to be similar to those that occurred on weekdays. This suggests that countermeasure strategies such as enforcement should be carried out with similar intensity throughout the week, or perhaps even more on weekends.
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