On estimation and influence measures for the Negative Binomial regression model based on Q-function

Abstract

In this paper the influence measures for the Negative Binomial regression model are presented. Based on the conditional expectation of the complete-data log-likelihood function we derive some influence measures, such as case deletion (global influence) and local influence analysis. For the implementation of the influence measures we present explicit expressions and discuss an appropriate perturbation scheme. To illustrate the results, simulations and real data applications are presented. Results show that both global and local influence methods are effective in detecting possible observations that influence the parameter estimation, or at least in focusing researchers attention on those observations.