Influence analysis for count data based on generalized Poisson regression models

This work develops influence diagnostics for generalized Poisson regression (GPR) models based on global and local influence analysis. The one-step approximations of the estimates in the case-deletion model are given and case-deletion measures and local influence measures are obtained. At the same time, it is shown that the case-deletion model is equivalent to the mean shift outlier model (MSOM) in GPR models and an outlier test is presented based on the MSOM. Furthermore, we discuss score tests for significance and homogeneity of the dispersion parameter in GPR models, respectively. Finally, two count data sets are given to illustrate our methodology and the properties of score test statistics are investigated through Monte Carlo simulations.