Count data analysis using poisson regression and handling of overdispersion

Abstract

Count data is very common in various fields such as in biomedical science, public health and marketing. Poisson regression is widely used to analyze count data. It is also appropriate for analyzing rate data. Poisson regression is a part of class of models in generalized linear models (GLM). It uses natural log as the link function and models the expected value of response variable. The natural log in the model ensures that the predicted values of response variable will never be negative. The response variable in Poisson regression is assumed to follow Poisson distribution. One requirement of the Poisson distribution is that the mean equals the variance. In real-life application, however, count data often exhibits overdispersion. Overdipersion occurs when the variance is significantly larger than the mean. When this happens, the data is said to be overdispersed. Overdispersion can cause underestimation of standard errors which consequently leads to wrong inference. Besides that, test of significance result may also be overstated. Overdispersion can be handled by using quasi-likelihood method as well as negative binomial regression. The simulation study has been done to see the performance of Poisson regression and negative binomial regression in analyzing data that has no overdispersion as well as data that has overdispersion. The results show that Poisson regression is most appropriate for data that has no overdispersion while negative binomial regression is most appropriate for data that has overdispersion.