Influence diagnostics for the Poisson regression model using two-parameter estimator

Abstract

The identification of influential observations is an essential element in regression analysis as they posed a threat to the model building process. The existence of multicollinearity among the regressors complicates the presence of influential observations. Different influential diagnostics have been presented in literature so far using generalized linear models (GLM). In this paper, approximate deletion measures based on Sherman–Morrison Woodbury (SMW) theorem for the Poisson Two-Parameter regression model are proposed to detect influential observations in the presence of multicollinearity. Moreover, we conduct a Monte Carlo Simulation to evaluate the performance of the proposed measures. Finally, an example is presented to illustrate the proposed diagnostic measures.