Effect of Overdispersion and Sample Size on the Performance of Poisson Model and its Extensions in Frame of Generalized Linear Models (GLMs)

摘要

Mean equal variance assumption in Poisson model is constantly violated in real life count data leading to overdispersion. This study assessed empirically, the performance of Poisson Model and its extensions under varying overdispersion and sample size using R software. Increased values of overdispersion (K =2, 4, 8, 12, 20) have been introduced in count data following Poisson distribution with parameter μ_i ≈ 1 and various samples (n =25, 50, 100, 500, 1000) have been extracted. Poisson, quasi-Poisson, negative binomial and zero inflated Poisson models were fitted on the sampled data and the results were compared to the outcomes from linear regression after a log-transformation. The results showed that overdispersion and sample size impact the performance of the Poisson model and its extensions. Negative binomial model is better than the other models for all combinations of K with the large samples (n =500 and 1000). However, for small samples (n =25, 50), there was no model performing better in all combinations of n and K. The outputs also revealed that log-transformation of count data by using linear regression performs well only for some small samples.