Influence diagnostic methods in the Poisson–Inverse Gaussian regression with diverse residuals

The Poisson-Inverse Gaussian (PIG) distribution is a useful substitute for modeling overdispersion and long-tailed count data. The Poisson-Inverse Gaussian regression model (PIGRM) assumes that the response variable follows the PIG distribution. Influential observations may be present in the PIGRM. The observation has a significant impact on the coefficient estimates of the regression model. In this study, we consider two diagnostic measures for the PIGRM to detect these observations with different residuals. For this purpose, a comparative analysis has been carried out between Cook’s distance and difference in fits (DFFITS) methods using three residuals i.e. Pearson residual, working residual and quantile residual. The Monte Carlo simulation study and two real-life examples are considered for evaluation purposes of the PIGRM’s influence diagnostics. The simulation results showed that Cook’s distance with quantile and working residuals performs well as compared to the DFFITS. Moreover, for applications, the DFFITS with working and quantile residuals are performed well. So, we conclude that Cook’s distance with quantile and working residuals performs better than the Cook’s distance with Pearson residuals and the DFFITS with all residuals for the detection of influential observations in PIGRM.