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 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-squareds.