R2 measures for zero-inflated regression models for count data with excess zeros

Abstract

ABSTRACTGeneralized linear models are often used to analyse discrete data. There are many proposed measures for this class of models. For loglinear models for count data, Cameron and Windmeijer [An R-squared measure of goodness of fit for some common nonlinear regression models. J Econometrics. 1997;77:329–342] developed an -like measure based on a ratio of deviances. This quantity has since been adjusted to accommodate both overspecification and overdispersion. While these statistics are useful for Poisson and negative binomial regression models, count data often include many zeros, a phenomenon that is often handled via zero-inflated (ZI) regression models. Building on Cameron and Windmeijer's work, we propose statistics for the ZI Poisson and ZI negative binomial regression contexts. We also propose adjusted -like versions of these quantities to avoid inflation of these statistics due to the inclusion of irrelevant covariates in the model. The properties of the proposed measures of fit are examined via simulation, and their use is illustrated on two data sets involving counts with excess zeros.