On Testing for Inflation of Zero Observations

The preponderance and heterogeneity of zero observations is observed in many count and ordinal datasets. Numerous studies make a distinction between the different types of zeros. So called zero-inflated models have been developed to address the sample differentiation. Many statistical software packages routinely offer a test for inflation of zero observations (for example, comparing the Poisson and zero-inflated Poisson models) using the Vuong test for non-nested models. This paper argues that the choice of the Vuong test is not valid in this context, simply because these models are actually nested. However, the classical LR test is not applicable either because the standard regularity conditions are violated, and its asymptotic null distribution has to be adjusted as suggested by Andrews (2001). The Monte Carlo simulations illustrate the issue.