Adjusted R2 measures for the inverse Gaussian regression model

The R-2 measure is a commonly used tool for assessing the predictive ability of a linear regression model. It quantifies the amount of variation in the outcome variable, which is explained by the covariates. Various attempts have been made to carry the R-2 definition to other types of regression models as well. Here, two different R-2 measure definitions for the Inverse Gaussian regression model will be studied. They are motivated by deviance and sums-of-squares residuals. Depending on sample size and number of covariates fitted, these R-2 measures may show substantially inflated values, and a proper bias-adjustment is necessary. Several possible adjusted R-2 measure definitions for the Inverse Gaussian regression model will be compared in a simulation study. The use of adjusted R-2 measures is recommended in general.