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

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, which has accident probabilities that 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. While zero-inflated models have come under some criticism with regard to accident-frequency applications - one fact is undeniable - in many applications they provide a statistically superior fit to the data. The Markov switching approach we propose seeks to overcome some of the criticism associated with the zero-accident state of the zero-inflated model by allowing individual roadway segments to switch between zero and normal-count 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-accident or normal-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.

A latent variable representation of count data models to accommodate spatial and temporal dependence: Application to predicting crash frequency at intersections

“…The field has long matured in the area of univariate count models, with the approaches discussed above and their many variants (see, for example, Malyshkina and Mannering, 2010) already extensively used for univariate count data. However, this has not been the case for correlated count data, especially for the case of general dependency structures for more than two correlated counts.…”

Performance Assessment of Road Barriers in Indiana

“…Recent advancements in crash-frequency modeling include random parameter models (Anastasopoulos & Mannering, 2009;Mitra & Washington, 2012) and finite mixture/Markov switching frequency models (Malyshkina & Mannering, 2010;Park & Lord, 2009). The major difference between the two approaches is that the former assumes a continuous distribution (e.g., normal distribution) on the parameters for different observations while the latter uses a discrete distribution (e.g., distinct subgroups).…”

Predicting Work Zone Collision Probabilities via Clustering: Application in Optimal Deployment of Highway Response Teams

“…Another class of advanced statistical techniques includes random parameter [44][45][46][47], generalized additive [48,49], Markov switching [50][51][52], and hierarchical models [53,54]. We do not spend extensive time discussing these methods here, primarily because existing literature in this area focuses on nonwork zone crash frequency modeling applications, which is not the focus of this paper.…”