Poisson, Poisson-gamma and zero-inflated regression models of motor vehicle crashes: balancing statistical fit and theory
Lord, Dominique, Washington, Simon, & Ivan, John (2005) Poisson, Poisson-gamma and zero-inflated regression models of motor vehicle crashes: balancing statistical fit and theory. Accident Analysis and Prevention, 37(1), pp. 35-46.
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
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|Item Type:||Journal Article|
|Keywords:||Zero-inflated models, Poisson distribution, Negative binomial distribution, Bernoulli trials, Safety performance functions, Small area analysis|
|Subjects:||Australian and New Zealand Standard Research Classification > MEDICAL AND HEALTH SCIENCES (110000) > PUBLIC HEALTH AND HEALTH SERVICES (111700)
Australian and New Zealand Standard Research Classification > COMMERCE MANAGEMENT TOURISM AND SERVICES (150000) > TRANSPORTATION AND FREIGHT SERVICES (150700)
Australian and New Zealand Standard Research Classification > PSYCHOLOGY AND COGNITIVE SCIENCES (170000) > PSYCHOLOGY (170100)
|Divisions:||Current > Research Centres > Centre for Accident Research & Road Safety - Qld (CARRS-Q)
Past > QUT Faculties & Divisions > Faculty of Built Environment and Engineering
Past > Schools > School of Urban Development
|Deposited On:||28 Oct 2010 03:51|
|Last Modified:||29 Feb 2012 14:18|
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