Article

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

School of Civil Engineering, 550 Stadium Mall Drive, Purdue University, West Lafayette, IN 47907, USA.
Accident; analysis and prevention (Impact Factor: 1.65). 01/2010; 42(1):122-30. DOI: 10.1016/j.aap.2009.07.012
Source: PubMed

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.

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Available from: Fred L. Mannering, Jul 25, 2014
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    • "Multivariate studies of the degree of severity of motor vehicle accident have used different modeling approaches. These include binary logit and binary probit models (Haleem and Abdel-Aty, 2010; Kononen et al., 2011; Moudon et al., 2011; Santolino et al., 2012), unordered response models including multinomial logit models and nested logit models (Schneider et al., 2009; Malyshkina and Mannering, 2010; Haleem and Abdel-Aty, 2010; Hu and Donnell, 2010; Wu et al.,2013; Rifaat et al., 2011; Ye and Lord, 2011; Schneider and Savolainen, 2011; Eluru, 2013; Yasmin and Eluru, 2013), and the ordered response models including ordered probit model and ordered logit model (Ferreira and Couto, 2012; Jiang et al., 2013 ; Eluru, 2013 ; Mergia et al., 2013; Yasmin and Eluru, 2013; Ye and Lord, 2014). We focus here on studies where the level of injury is a target variable. "
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    • "The latter one can be extended to many states and allows mixing with respect to both zeros and positives (Cameron and Trivedi, 1998). More recently, Malyshkina et al. (2010) developed the zero-state Markov switching negative binomial (MSNB) model to estimate five-year crash frequencies in Indiana. The MSNB model allows specific roadway segments to switch between the zero states and non-zero states over time. "
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    • "The latter one can be extended to many states and allows mixing with respect to both zeros and positives (Cameron and Trivedi, 1998). More recently, Malyshkina et al. (2010) developed the zero-state Markov switching negative binomial (MSNB) model to estimate five-year crash frequencies in Indiana. The MSNB model allows specific roadway segments to switch between the zero states and non-zero states over time. "
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