Adjustments for \(R^{2}\)-measures for Poisson regression models. (Q1583502)

In regression models not only the parameter estimates and significance of explanatory variables are of interest, but also the degree to which variation in the dependent variable can be explained by covariates. In recent publications, an \(R^{2}\)-measure based on deviance was recommended for Poisson regression models, one of the most frequently used modelling tools in epidemiological studies. However, when sample size is small relative to the number of covariates in the model, simple \(R^{2}\)-measures may be seriously inflated and may need to be adjusted according to the number of covariates in the model. Two new adjustments for the \(R^{2}\)-measure in Poisson regression models based on deviance residuals are presented and compared by simulation with population values. The proposed measures are also applied to real data sets.