The consequences of checking for zero-inflation and overdispersion in the analysis of count data

Abstract: Count data are ubiquitous in ecology and the Poisson generalized linear model (GLM) is commonly used to model the association between counts and explanatory variables of interest. When fitting this model to the data, one typically proceeds by first confirming that the data is not overdispersed and that there is no excess of zeros. If the data appear to be overdispersed or if there is any zero-inflation, key assumptions of the Poison GLM may be violated and researchers will then typically consider alternatives to the Poison GLM. An important question is whether the potential model selection bias introduced by this data-driven multi-stage procedure merits concern. In this paper, we conduct a large-scale simulation study to investigate the potential consequences of model selection bias that can arise in the simple scenario of analyzing a sample of potentially overdispersed, potentially zero-heavy, count data.