Power Testing of Graphical Methods for Identification of Outliers in Poisson Regression Model

Abstract This paper investigates the structure and utility of partial residual (PRES), augmented partial residual (APRES), and conditional expectation and residuals (CERES) plots for visualising influence diagnostics as a function of chosen predictors in the context of generalised linear models (GLMs). Here, predictor transformation is used to analyse Poisson regression as GLM, and PRES, APRES, and CERES plots are created. Due to the behaviour of the response variable and the linked link function with various variables, these plots' effectiveness in creating a strong visual impression may vary. In comparison to other approaches, PRES, CERES (L), and CERES (K) exhibit the highest power for influence diagnostics, according to the power of the tests for various plots.