Markov switching negative binomial models: An application to vehicle accident frequencies

Abstract

In this paper, two-state Markov switching models are proposed to study accident frequencies. These models assume that there are two unobserved states of roadway safety, and that roadway entities (roadway segments) can switch between these states over time. The states are distinct, in the sense that in the different states accident frequencies are generated by separate counting processes (by separate Poisson or negative binomial processes). To demonstrate the applicability of the approach presented herein, two-state Markov switching negative binomial models are estimated using five-year accident frequencies on Indiana interstate highway segments. 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) negative binomial model. 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.

Bias properties of Bayesian statistics in finite mixture of negative binomial regression models in crash data analysis

“…This approach provided useful information on features of the population. A similar approach by Malyshkina et al (2009) also demonstrated the usefulness of two-state Markov switching models in terms of goodness-of-fit and the capability of capturing unobserved heterogeneity. The finite mixture regression model rests on the assumption that there are a finite number of unobservable categories of observations and the heterogeneity arises from different values of regression coefficients caused by missing variables (Frühwirth-Schnatter, 2006).…”

The statistical analysis of crash-frequency data: A review and assessment of methodological alternatives

“…Recently, the problems associated with the long-term mean equal to zero have been discussed by other researchers (see, e.g., Malyshkina et al, 2009). As an alternative, have proposed a zero-sate Markov switching countdata model for circumventing the problem of having the long-term mean equal to zero.…”

Zero-state Markov switching count-data models: An empirical assessment

“…Two-state Markov switching count-data models of accident frequencies were first presented in Malyshkina et al (2009). Following that paper, we note that, although there are several major differences between Malyshkina et al (2009) and this study, many ideas and statistical estimation methods developed in Malyshkina et al (2009) apply in this study as well.…”