Citation

Ünlü HK, Young DS, Yiğiter A, Hilal Özcebe L. Journal of Applied Statistics 2022; 49(4): 1003-1017.

Copyright

(Copyright © 2022, Sheffield City Polytechnic)

DOI

10.1080/02664763.2020.1843610

PMID

35707813

PMCID

PMC9042158

Abstract

The analysis of traffic accident data is crucial to address numerous concerns, such as understanding contributing factors in an accident's chain-of-events, identifying hotspots, and informing policy decisions about road safety management. The majority of statistical models employed for analyzing traffic accident data are logically count regression models (commonly Poisson regression) since a count - like the number of accidents - is used as the response. However, features of the observed data frequently do not make the Poisson distribution a tenable assumption. For example, observed data rarely demonstrate an equal mean and variance and often times possess excess zeros. Sometimes, data may have heterogeneous structure consisting of a mixture of populations, rather than a single population. In such data analyses, mixtures-of-Poisson-regression models can be used. In this study, the number of injuries resulting from casualties of traffic accidents registered by the General Directorate of Security (Turkey, 2005-2014) are modeled using a novel mixture distribution with two components: a Poisson and zero-truncated-Poisson distribution. Such a model differs from existing mixture models in literature where the components are either all Poisson distributions or all zero-truncated Poisson distributions. The proposed model is compared with the Poisson regression model via simulation and in the analysis of the traffic data.

Language: en

Keywords

Count data; EM algorithm; finite mixture models; identifiability; zero-truncated Poisson