Temporal stability of driver injury severities in animal-vehicle collisions: A random parameters with heterogeneity in means (and variances) approach

https://doi.org/10.1016/j.amar.2020.100120Get rights and content

Highlights

  • Affecting factors on the injury severity of animal vehicle collisions are investigated.

  • Mixed logit models with heterogeneity in means and variances are used.

  • Accounting for heterogeneity in means and variances improves overall model fit.

  • Explanatory variables show relatively similar marginal effects across different methodological approaches.

  • Explanatory variables show temporally unstable behavior across different time periods.

Abstract

This study investigates the determinants of driver injury severity in animal-vehicle collisions while systematically accounting for unobserved heterogeneity in the data by using three methodological approaches: mixed logit model, mixed logit model with heterogeneity in means, and mixed logit model with heterogeneity in means and variances. Using the data from Washington state from January 1, 2012 to December 31, 2016, a wide range of factors that could potentially affect the injury severity of drivers were examined. Moreover, the temporal stability and transferability of the models were investigated through a series of likelihood ratio tests. Marginal effects were also used to study the temporal stability of the explanatory variables. Model estimation results show that many parameters can potentially increase the likelihood of severe injuries in Animal-vehicle crashes including freeways/expressways, daylight crashes, early morning crashes, dry road surface and clear weather condition. Moreover, the model estimation results show that accounting for the heterogeneity in the means (and variances) of the random parameters can improve the overall fit of the model. Some variables showed relatively similar marginal effects among different methodological approaches while some others showed different marginal effects upon the application of different methods. With regard to temporal stability of explanatory variables, the findings of this study show how underestimating the temporal stability concept may lead to inaccurate and unreliable conclusions.

Introduction

The highway system plays an important role in everyday life as it allows for transportation of people and goods to every corner of the country. In the United States, public highways constitute more than four million miles, of which about 74% (2,939,042 miles) are rural highways (U.S. Department of Transportation/Federal Highway Administration, 2016). Such highways, especially rural roadways, cross through the habitat of many wildlife animals. Therefore, the probability of vehicles colliding with a wild animal such as deer and elk is quite high in such locations. Animal-vehicle collisions (Animal-vehicle crashes) are a major safety concern to travelers, highway administrators, and environmentalists. In the U.S., more than 270,000 animal-vehicle collisions reported annually leading to more than 13,000 human injuries and about 200 fatalities (NHTSA, 2015). In addition to human injuries and fatalities, the Animal-vehicle collisions cause more than one billion dollars in property damage in the U.S annually (Huijser et al., 2009). The National Insurance Crime Bureau (NICB) also provided statistics regarding the animal-vehicle collisions in the U.S. with a total of 1,740,425 insurance claims between 2014 and 2017 (NICB, 2018). The majority of these claims (i.e., 584,165) involved deer-related collisions. Statewide, more than 2500 Animal-vehicle collisions have been reported each year, with 167 human injuries and at least one human fatality by the Washington State Department of Transportation (WSDOT). Yet, these numbers are way below the actual Animal-vehicle collisions due to underreporting of such crashes.

Although there is an extensive body of knowledge on animal-vehicle collisions, a very limited understanding of the relationship between driver injury severity resulted from such collisions and how other factors, such as human-related, environmental conditions, roadway characteristics, crash characteristics, vehicle characteristics, and temporal characteristics can influence this relationship. A careful and thorough reviewing of the literature shows that injury severity sustained by drivers involved in the animal-vehicle collisions are highly overlooked because previous studies have mainly focused on crash frequency (Lao et al., 2011a, Lao et al., 2011b), temporal analysis (Hothorn et al., 2015), spatial analysis (Diaz-varela et al., 2011, Wilkins et al., 2019), countermeasures effectiveness (Hedlund et al., 2004, Knapp et al., 2003, Sullivan et al., 2004), predicting animal-vehicle collisions in urban areas (Found and Boyce, 2011), hotspot identification (Yang et al., 2019), driver behavior (Marcoux and Riley, 2010, Vanlaar et al., 2019).

In terms of injury severity analysis, Savolainen and Ghosh (2008) examined contributing factors to injury severity of drivers involved in deer-vehicle crashes occurred in Michigan state. However, their study did not account for unobserved heterogeneity in the crash data because they developed a multinomial logit model. Moreover, the previous studies assumed that the explanatory variables that impact injury severity are temporally stable (i.e., constant over time), which is not the case in the accident data analyses because the fundamental change of human behavior over time and the fact that a vehicle accident is a rare event. Above it all, the way that the crash data being aggregated over time (weeks, months or years) to obtain sufficient observations may arise concern with temporal instability in the crash data analyses (Mannering, 2018). Recently, several efforts have been made to remediate temporal instability in crash data analyses (Alnawmasi and Mannering, 2019, Behnood and Mannering, 2019, Behnood and Mannering, 2015, Behnood and Mannering, 2016, Mannering, 2018).

Given the sparse literature on injury severity of drivers involved in animal-vehicle collisions and the continuing rising of animal-vehicle crashes, there is a crucial need for decision makers and safety engineers to better understand the factors contributing to the animal-vehicle collisions and to identify the high-risk locations for mitigating the effects of these crashes through prioritizing appropriate countermeasures. Consequently, the current paper seeks to investigate injury severity sustained by drivers involved in animal-vehicle collisions in rural highways in Washington state. To do so, an appropriate analysis approach needs to be utilized to overcome the limitations in the crash data, namely the unobserved heterogeneity (Mannering et al., 2016) and temporal instability (Mannering, 2018). In the current paper, a mixed logit model was used to capture any heterogenous effect in the determinants of driver injury severities involved in animal-vehicle collisions while capturing the heterogeneity in the means and variances of the random parameters. As such, this research contributes to our understanding of the animal-vehicle collisions in two ways: empirically and methodologically. In terms of empirical contribution, an extensive list of contributing factors that impact injury severity incurred by drivers involved in animal-vehicle collisions was used. Methodologically, to the best of the authors’ knowledge, this is the first attempt to account for unobserved heterogeneity and temporal instability in crash data pertaining to animal-vehicle collisions as long as such collisions highly suffer from underreporting issues that if overlooked could lead to erroneous inferences. To achieve the overarching objective of this paper, five years of Washington state crash data of animal-vehicle collisions is used. This data includes Animal-vehicle collisions crashes involved deer and elk that occurred in rural highways in Washington state.

The rest of paper is organized as follows. Section 2 presents the methodological approach used in this study. Section 3 describes the data source and injury severity categorization. The temporal stability tests are presented in Section 4. The estimation results along with its interpretations are provided in Section 5. Finally, Section 6 concludes the paper and presents directions for future research.

Section snippets

Methodology

Police-reported crashes are the main sources of crash data in roadway safety studies. Such reports provide detailed information about the involved individuals, vehicles, roadways, and traffic and environmental factors. Still, these reports lack some determinants that could potentially affect the likelihood of a crash or its resulting injury severity. This could be attributed to the failure of police officers who collect the useful information about highway crashes at the crash scenes. In other

Empirical setting

In this study, five-year single-vehicle crash data drawn from the Washington State Department of Transportation (WSDOT) on animal-vehicle collisions was used. This data includes the animal-vehicle collisions that occurred in rural highways in Washington state from January 1, 2012 to December 31, 2016. To test for the temporal instability, the crash data was split into three time periods: 2012–2013, 2014, and 2015–2016.

Injury severity levels sustained by drivers in animal-vehicle collisions are

Temporal stability tests

A series of likelihood ratio tests were applied to statistically test if injury-severities in animal-vehicle collisions were significantly different across different time periods (2012–13, 2014, and 2015–16).1

Discussion of estimation results

As discussed in previous section, the results of the temporal stability tests indicated that the null hypothesis that different time periods produced equal parameters rejected with over 99% confidence level. The model estimation results based on 2012–2016 data, 2012–2013 data, 2014 data, and 2015–2016 data are provided in Table 4, Table 5, Table 6, Table 7, respectively. It can be seen that although some of the explanatory variables are repeated across different models, there are significant

Summary and conclusions

Animal-vehicle collisions are a major safety concern to roadway users, highway administrators, and environmentalists. Using the data on Animal-vehicle collisions in Washington state from January 1, 2012 to December 31, 2016, this paper applied three methods including a standard mixed logit model, a mixed logit model with heterogeneity in means, and a mixed logit model with heterogeneity in means and variances to explore the determinants of driver-injury severities in animal-vehicle collisions.

Acknowledgements

The authors would like to acknowledge and thank the Washington Department of Transportation for their time and effort regarding the crash data used for this study.

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