Can Generalized Poisson model replace any other count data models? An evaluation

Abstract

Background: Count data represents the number of occurrences of an event within a fixed period of time. In count data modelling, overdispersion is inevitable. Sometimes, this overdispersion may not be just due to the excess zeros but may be due to the presence of two or more mixtures. Hence the main objective is to examine for the presence of mixtures if any, with excess zeros and compare Generalized Poisson model, Mixture models with other count data models using real time and simulated data.

Methods: Three real time over-dispersed datasets were used for the comparison of the models. The real time data models were compared using information criteria like AIC and BIC and regression coefficients. Data was also simulated using mixture Poisson with excess zeros. The simulation was repeated for different sample sizes were used to identify the better model.

Results: Generalized Poisson showed consistently lower bias and MSE when compared to the other models for varying sample of sizes. AIC and BIC values were almost similar for Generalized Poisson, ZIP and Mixture Poisson model. Similar findings were also obtained from real time data.

Conclusion: Generalized Poisson models provides a better fit for overdispersed data due to excess zeros, consistently in real time and simulated with varying sample sizes. Negative Binomial models can be redistricted or reevaluated against Generalized Poisson model.