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.