Markov switching multinomial logit model: an application to accident injury severities

arXiv:0811.3644v1 [stat.AP] 21 Nov 2008 Markov switching multinomial logit model: an application to accident injury severities Nataliya V. Malyshkina ∗, Fred L. Mannering School of Civil Engineering, 550 Stadium Mall Drive, Purdue University, West Lafayette, IN 47907, United States Abstract In this study, two-state Markov switching multinomial logit models are proposed for statistical modeling of accident injury severities. These models assume Markov switching in time between two unobserved states of roadway safety. The states are distinct, in the sense that in different states accident severity outcomes are generated by separate multinomial logit processes. To demonstrate the applicability of the approach presented herein, two-state Markov switching multinomial logit models are estimated for severity outcomes of accidents occurring on Indiana roads over a four-year time interval. Bayesian inference methods and Markov Chain Monte Carlo (MCMC) simulations are used for model estimation. The estimated Markov switching models result in a superior statistical fit relative to the standard (single- state) multinomial logit models. It is found that the more frequent state of roadway safety is correlated with better weather conditions. The less frequent state is found to be correlated with adverse weather conditions. Key words: Accident injury severity; multinomial logit; Markov switching; Bayesian; MCMC 1 Introduction Vehicle accidents result in property damage, injuries and loss of people lives. Thus, research efforts in predicting accident severity are clearly very impor- tant. In the past there has been a large number of studies that focused on mod- eling accident severity outcomes. Common modeling approaches of accident ∗Corresponding author. Email addresses: nmalyshk@purdue.edu (Nataliya V. Malyshkina), flm@ecn.purdue.edu (Fred L. Mannering). Preprint submitted to Accident Analysis and Prevention severity include multinomial logit models, nested logit models, mixed logit models and ordered probit models (O’Donnell and Connor, 1996; Shankar and Mannering, 1996; Shankar et al., 1996; Duncan et al., 1998; Chang and Mannering, 1999; Carson and Mannering, 2001; Khattak, 2001; Khattak et al., 2002; Kockelman and Kweon, 2002; Lee and Mannering, 2002; Abdel-Aty, 2003; Kweon and Kockelman, 2003; Ulfarsson and Mannering, 2004; Yamamoto and Shankar, 2004; Khorashadi et al., 2005; Eluru and Bhat, 2007; Savolainen and Mannering, 2007; Milton et al., 2008). All these models involve nonlinear regression of the observed accident injury severity outcomes on various accident characteristics and related factors (such as roadway and driver characteristics, environmental factors, etc). In our earlier paper, Malyshkina et al. (2008), which we will refer to as Pa- per I, we presented two-state Markov switching count data models of accident frequencies. In this study, which is a continuation of our work on Markov switching models, we present two-state Markov switching multinomial logit models for predicting accident severity outcomes. These models assume that there are two unobserved states of roadway safety, roadway entities (road- way segments) can switch between these states over time, and the switching process is Markovian. The two states intend to account for possible hetero- geneity effects in roadway safety, which may be caused by various unpre- dictable, unidentified, unobservable risk factors that influence roadway safety. Because the risk factors can interact and change, roadway entities can switch between the two states over time. Two-state Markov switching multinomial logit models assume separate multinomial logit processes for accident severity data generation in the two states and, therefore, allow a researcher to study the heterogeneity effects in roadway safety. 2 Model specification Markov switching models are parametric and can be fully specified by a like- lihood function f(Y|Θ, M), which is the conditional probability distribution of the vector of all observations Y, given the vector of all parameters Θ of model M. First, let us consider Y. Let Nt be the number of accidents ob- served during time period t, where t = 1, 2, . . . , T and T is the total number of time periods. Let there be I discrete outcomes observed for accident sever- ity (for example, I = 3 and these outcomes are fatality, injury and property damage only). Let us introduce accident severity outcome dummies δ(i) t,n that are equal to unity if the ith severity outcome is observed in the nth accident that occurs during time period t, and to zero otherwise. Here i = 1, 2, . . . , I, n = 1, 2, . . . , Nt and t = 1, 2, . . . , T. Then, our observations are the accident severity outcomes, and the vector of all observations Y = {δ(i) t,n} includes all outcomes observed in all accidents that occur during all time periods. Sec- ond, let us consider model specification variable M. It is M = {M, Xt,n} 2 and includes the model’s name M (for example, M = “multinomial

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