A mixture model with Poisson and zero-truncated Poisson components to analyze road traffic accidents in Turkey

Hande Konşuk Ünlü, Derek S. Young, Ayten Yiğiter, L. Hilal Özcebe

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish
Pages (from-to)1003-1017
Number of pages15
JournalJournal of Applied Statistics
Volume49
Issue number4
DOIs
StatePublished - 2022

Bibliographical note

Funding Information:
We would like to thank the Department of Traffic Education and Research of the General Directorate of Security in Turkey for their valuable contributions in providing the data for this research. We would also like to thank an associate editor and two anonymous reviewers for their comments to help improve the focus and presentation of this paper.

Publisher Copyright:
© 2020 Informa UK Limited, trading as Taylor & Francis Group.

Keywords

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

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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