Application of the Hyper-Poisson Generalized Linear Model for Analyzing Motor Vehicle Crashes.
The hyper-Poisson distribution can handle both over- and underdispersion, and its generalized linear model formulation allows the dispersion of the distribution to be observation-specific and dependent on model covariates. This study's objective is to examine the potential applicability of a newly proposed generalized linear model framework for the hyper-Poisson distribution in analyzing motor vehicle crash count data. The hyper-Poisson generalized linear model was first fitted to intersection crash data from Toronto, characterized by overdispersion, and then to crash data from railway-highway crossings in Korea, characterized by underdispersion. The results of this study are promising. When fitted to the Toronto data set, the goodness-of-fit measures indicated that the hyper-Poisson model with a variable dispersion parameter provided a statistical fit as good as the traditional negative binomial model. The hyper-Poisson model was also successful in handling the underdispersed data from Korea; the model performed as well as the gamma probability model and the Conway-Maxwell-Poisson model previously developed for the same data set. The advantages of the hyper-Poisson model studied in this article are noteworthy. Unlike the negative binomial model, which has difficulties in handling underdispersed data, the hyper-Poisson model can handle both over- and underdispersed crash data. Although not a major issue for the Conway-Maxwell-Poisson model, the effect of each variable on the expected mean of crashes is easily interpretable in the case of this new model.
Zachry Department of Civil Engineering, Texas A&M University, College Station, TX, USA.
S Hadi
SH
Khazraee
Department of Statistics and Operations Research, University of Jáen, Spain.
Antonio Jose
AJ
Sáez-Castillo
Texas A&M Transportation Institute, Texas A&M University System, College Station, TX, USA.
Srinivas Reddy
SR
Geedipally
Zachry Department of Civil Engineering, Texas A&M University, College Station, TX, USA.
Dominique
D
Lord
D000063:Accidents, Traffic; D016014:Linear Models; D009864:Ontario; D016012:Poisson Distribution
Dispersion parameter; hyper-Poisson; underdispersion