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

TL;DR

This paper introduces two-state Markov switching negative binomial models to analyze vehicle accident frequencies, demonstrating improved fit and revealing safety correlations with weather conditions on Indiana highways.

Contribution

The paper develops and applies a novel Markov switching negative binomial model for accident frequency analysis, incorporating unobserved safety states and Bayesian estimation methods.

Findings

More frequent state is safer and linked to better weather.

Less frequent state is less safe and associated with adverse weather.

Model outperforms standard negative binomial models in fit.

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.