Measures of explained variation in gamma regression models

The common R-2 measure provides a useful means to quantify the degree to which variation in the dependent variable can be explained by the covariates in a linear regression model. Recently, there have been various attempts to apply the definition of the R-2 measure to generalized linear models. This paper studies two different R-2 measure definitions for the gamma regression model. These measures are related to deviance and sum-of-squares residuals. Depending on the sample size and the number of covariates fitted, so-called unadjusted R-2 measures may be substantially inflated, and the use of adjusted R-2 measures is then preferred. We study several known adjustments previously proposed for R-2 measures in regression models and illustrate the effect on the two unadjusted R-2 measures for the gamma regression model. Comparing the resulting measures with underlying population values, we find the best adjustment via simulation.