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

5 Scopus citations

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

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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