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

Generalized linear models are often used to analyse discrete data. There are many proposed R2 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 R2-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 R2 statistics for the ZI Poisson and ZI negative binomial regression contexts. We also propose adjusted R2-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.