A Comparison of Models for Count Data with an Application to Over-Dispersion Data

Abstract

Count models have been widely used in various fields, such as medicine, biology, and public health. The most frequently used count models are Poisson regression, negative binomial regression, and discrete Weibull regression models. The objective of this study was to compare the performance of Poisson, negative binomial, and discrete Weibull regression models using two different sets of data with over-dispersion. The AIC, BIC, and log-likelihood fit statistics were used as the criteria to compare the count models. The results revealed that the negative binomial and discrete Weibull regression were the best fit models as they produced the smallest AIC, BIC, and log-likelihood fit statistics.