Modelling Count Data; A Generalized Linear Model Framework

Count Data Models allow for regression-type analyses when the dependent variable of interest is a numerical count. They can be used to estimate the effect of a policy intervention either on the average rate or on the probability of no event, a single event, or multiple events. The mostly used distribution for modeling count data is the Poisson distribution (Horim and Levy; 1981) which assume equidispersion (Variance is equal to the mean). Since observed count data often exhibit over or under dispersion, the Poisson model becomes less ideal for modeling. To deal with a wide range of dispersion levels, Negative Binomial Regression, Generalized Poisson Regression, Poisson Regression, and lately Conway-Maxwell-Poisson (COM-Poisson) Regression can be used as alternative regression models. We compared the Generalized Poisson regression to all other regression models and also stated their advantages and usefulness. Data were analyzed using these four methods, the results from the four methods are compared using the Akaike Information Criterion (AIC) and Bayesian Information Criterion with the Generalized Poisson Regression having the smallest AIC and BIC values. The Generalized Poisson Regression Model was considered a better model when analyzing road traffic crashes for the data set considered.