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

TL;DR

This paper introduces a two-state Markov switching count-data model as an effective alternative to zero-inflated models for transportation accident data, allowing dynamic state switching and direct state estimation, with superior fit demonstrated on highway data.

Contribution

The paper develops and empirically tests a Markov switching model for count data, providing a novel approach that improves fit and enables direct state estimation compared to traditional zero-inflated models.

Findings

Markov switching model outperforms zero-inflated models in fit.

Model allows direct estimation of roadway segment states.

Bayesian inference used for model estimation.

Abstract

In this study, a two-state Markov switching count-data model is proposed as an alternative to zero-inflated models to account for the preponderance of zeros sometimes observed in transportation count data, such as the number of accidents occurring on a roadway segment over some period of time. For this accident-frequency case, zero-inflated models assume the existence of two states: one of the states is a zero-accident count state, in which accident probabilities are so low that they cannot be statistically distinguished from zero, and the other state is a normal count state, in which counts can be non-negative integers that are generated by some counting process, for example, a Poisson or negative binomial. In contrast to zero-inflated models, Markov switching models allow specific roadway segments to switch between the two states over time. An important advantage of this Markov switching approach is that it allows for the direct statistical estimation of the specific roadway-segment state (i.e., zero or count state) whereas traditional zero-inflated models do not. To demonstrate the applicability of this approach, a two-state Markov switching negative binomial model (estimated with Bayesian inference) and standard zero-inflated negative binomial models are estimated using five-year accident frequencies on Indiana interstate highway segments. It is shown that the Markov switching model is a viable alternative and results in a superior statistical fit relative to the zero-inflated models.