Comparison of Statistical Models in Modeling Over- Dispersed Count Data with Excess Zeros

Abstract

Generalised Linear Models such as Poisson and Negative Binomial models have been routinely used to model count data. But, these models assumptions are violated when the data exhibits over-dispersion and zero-inflation. Over-dispersion is as a result of excess zeros in the data. For modelling data with such characteristics several extensions of Negative Binomial and Poisson models have been proposed, such as zero-inflated and Hurdles models. Our study focus is on identifying the most statistically fit model(s) which can be adopted in presence of over-dispersion and excess zeros in the count data. We simulate data-sets at varying proportions of zeros and varying proportions of dispersion then fit the data to a Poisson, Negative Binomial, Zero-inflated Poisson, Zero-inflated Negative Binomial, Hurdles Poisson and Negative Binomial Hurdles. Model selection is based on AIC, log-likelihood, Vuong statistics and Box-plots. The results obtained, suggest that Negative Binomial Hurdles performed well in most scenarios compared to other models hence, the most statistically fit model for over- dispersed count data with excess zeros.