A mixture model with Poisson and zero-truncated Poisson components to analyze road traffic accidents in Turkey |
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Authors: | Hande Konuk Ünlü Derek S Young Ayten Yiiter L Hilal
zcebe |
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Institution: | aInstitute of Public Health, Hacettepe University, Ankara, Turkey;bDepartment of Statistics, University of Kentucky, Lexington, KY, USA;cDepartment of Statistics, Faculty of Science, Hacettepe University, Ankara, Turkey;dDepartment of Public Health, Faculty of Medicine, Hacettepe University, Ankara, Turkey |
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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. |
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Keywords: | Count data EM algorithm finite mixture models identifiability zero-truncated Poisson |
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