Zero truncated Poisson model: an alternative approach for analyzing count data with excess zeros

Abstract

The inference procedure under generalized linear model breaks down when there exists too many zeros in count data that the parent distribution cannot accommodate. We argue that the process of separating ‘bad' zeros through so-called zero inflated count model will lead to a less optimal estimators of the regression parameters than that obtained by fitting zero truncated distribution after discarding ‘all’ zeros. In this paper extensive simulation studies have been carried out to compare performance of fitting zero-truncated Poisson (ZTP), Poisson hurdle (PH) and zero-inflated Poisson (ZIP) models when the data generating process is either ZIP or PH. This study reveals the fact that for analyzing Poisson count data subject to excess zeros, instead of fitting a zero-inflated model, the traditional ZTP would be the best choice. As an illustration, results have been compared by analyzing antenatal care seeking behavior data extracted from a demographic health survey of Bangladesh.