Markov switching models: An application to roadway safety

In this research, two-state Markov switching models are proposed to study accident frequencies and severities. These models assume that there are two unobserved states of roadway safety, and that roadway entities (e.g., roadway segments) can switch between these states over time. The states are distinct, in the sense that in the different states accident frequencies or severities are generated by separate processes (e.g., Poisson, negative binomial, multinomial logit). Bayesian inference methods and Markov Chain Monte Carlo (MCMC) simulations are used for estimation of Markov switching models. To demonstrate the applicability of the approach, we conduct the following three studies. In the first study, two-state Markov switching count data models are considered as an alternative to zero-inflated models, in order to account for preponderance of zeros typically observed in accident frequency data. In this study, one of the states of roadway safety is a zero-accident state, which is perfectly safe. The other state is an unsafe state, in which accident frequencies can be positive and are generated by a given counting process – a Poisson or a negative binomial. Two-state Markov switching Poisson model, two-state Markov switching negative binomial model, and standard zero-inflated models are estimated for annual accident frequencies on selected Indiana interstate highway segments over a five-year time period. An important advantage of Markov switching models over zero-inflated models is that the former allow a direct statistical estimation of what states specific roadway segments are in, while the later do not. In the second study, two-state Markov switching Poisson model and two-state Markov switching negative binomial model are estimated using weekly accident frequencies on selected Indiana interstate highway segments over a five-year time period. In this study, both states of roadway safety are unsafe. Thus, accident frequencies can be positive and are generated by either Poisson or negative binomial processes in both states. It is found that the more frequent state is safer and it is correlated with better weather conditions. The less frequent state is found to be less safe and to be correlated with adverse weather conditions. In the third study, two-state Markov switching multinomial logit models are estimated for severity outcomes of accidents occurring on Indiana roads over a four-year time period. It is again 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. One of the most important results found in each of the three studies, is that in each case the estimated Markov switching models are strongly favored by accident frequency and severity data and result in a superior statistical fit, as compared to the corresponding standard (single-state) models.