R-Squared measures for count data regression models with applications to health-care utilization

R-squared measures of goodness of fit for count data are rarely, if ever, reported in empirical studies or by statistical packages. We propose several R-squared measures based on various definitions of residuals for the basic Poisson regression model and for more general models such as negative binomial that accommodate overdispersed data The preferred R-squared measure is based on the deviance residual. An application to data on health-care-service utilization measured in counts illustrates the performance and usefulness of the various R-squared measures.