Poisson, poisson-gamma and zero-inflated regression models of motor vehicle crashes: balancing statistical fit and theory

Lord, Dominique, Washington, Simon P. and Ivan, John N. (2005) Poisson, poisson-gamma and zero-inflated regression models of motor vehicle crashes: balancing statistical fit and theory. Accident Analysis and Prevention, 37 1: 35-46. doi:10.1016/j.aap.2004.02.004

Author Lord, Dominique
Washington, Simon P.
Ivan, John N.
Title Poisson, poisson-gamma and zero-inflated regression models of motor vehicle crashes: balancing statistical fit and theory
Journal name Accident Analysis and Prevention   Check publisher's open access policy
ISSN 0001-4575
Publication date 2005-01-01
Year available 2004
Sub-type Article (original research)
DOI 10.1016/j.aap.2004.02.004
Open Access Status Not yet assessed
Volume 37
Issue 1
Start page 35
End page 46
Total pages 12
Place of publication Oxford, United Kingdom
Publisher Elsevier
Language eng
Abstract There has been considerable research conducted over the last 20 years focused on predicting motor vehicle crashes on transportation facilities. The range of statistical models commonly applied includes binomial, Poisson, Poisson-gamma (or negative binomial), zero-inflated Poisson and negative binomial models (ZIP and ZINB), and multinomial probability models. Given the range of possible modeling approaches and the host of assumptions with each modeling approach, making an intelligent choice for modeling motor vehicle crash data is difficult. There is little discussion in the literature comparing different statistical modeling approaches, identifying which statistical models are most appropriate for modeling crash data, and providing a strong justification from basic crash principles. In the recent literature, it has been suggested that the motor vehicle crash process can successfully be modeled by assuming a dual-state data-generating process, which implies that entities (e.g., intersections, road segments, pedestrian crossings, etc.) exist in one of two states—perfectly safe and unsafe. As a result, the ZIP and ZINB are two models that have been applied to account for the preponderance of “excess” zeros frequently observed in crash count data. The objective of this study is to provide defensible guidance on how to appropriate model crash data. We first examine the motor vehicle crash process using theoretical principles and a basic understanding of the crash process. It is shown that the fundamental crash process follows a Bernoulli trial with unequal probability of independent events, also known as Poisson trials. We examine the evolution of statistical models as they apply to the motor vehicle crash process, and indicate how well they statistically approximate the crash process. We also present the theory behind dual-state process count models, and note why they have become popular for modeling crash data. A simulation experiment is then conducted to demonstrate how crash data give rise to “excess” zeros frequently observed in crash data. It is shown that the Poisson and other mixed probabilistic structures are approximations assumed for modeling the motor vehicle crash process. Furthermore, it is demonstrated that under certain (fairly common) circumstances excess zeros are observed—and that these circumstances arise from low exposure and/or inappropriate selection of time/space scales and not an underlying dual state process. In conclusion, carefully selecting the time/space scales for analysis, including an improved set of explanatory variables and/or unobserved heterogeneity effects in count regression models, or applying small-area statistical methods (observations with low exposure) represent the most defensible modeling approaches for datasets with a preponderance of zeros.
Keyword Bernoulli trials
Negative binomial distribution
Poisson distribution
Safety performance functions
Small area analysis
Zero-inflated models
Q-Index Code C1
Q-Index Status Provisional Code
Institutional Status UQ

Document type: Journal Article
Sub-type: Article (original research)
Collection: School of Civil Engineering Publications
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Citation counts: TR Web of Science Citation Count  Cited 286 times in Thomson Reuters Web of Science Article | Citations
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