Influence Diagnostics in Gamma‐Pareto Regression Model With Cook’s Distance for Standardized and Adjusted Pearson, Deviance, and Likelihood Residuals: Simulation and Application

Source abstract

Influential analysis is the main diagnostic process to obtain reliable regression results. Same is true for the generalized linear model (GLM). The present article empirically compares the performance of different residuals of the gamma‐Pareto regression model (G‐PRM) to detect the influential points. The G‐PRM residuals are further divided into two categories, that is, standardized and adjusted residuals. Cook’s distance has been computed for both of the stated residuals, and then comparison of these residuals for the detection of influential points has been carried out with the help of simulation and a real dataset. The simulation results show that G‐PRM standardized and adjusted likelihood residuals perform better than standardized and adjusted forms of Pearson and deviance residuals for different values of dispersion parameters and different sample sizes, using Cook’s distance to detect influential points. But standardized likelihood residuals are noted better than adjusted likelihood residuals.