An Alternative Pearson Residual-Based Method for Outlier Detection in a Gamma Regression Model

Abstract

This study develops six novel outlier-detection methods for Gamma regression (TSPR, TJPR, TAPR, GASPR, GAJPR, and GAAPR) that combine Pearson residuals scaling with Tukey’s boxplot rules and grouped absolute residuals, where thresholds are adapted from the residual behavior within successive groups of observations. These methods address outlier detection when the response is nonnegative and right-skewed, a common situation in applied settings. We compare the new procedures to six existing methods (SPRs, JPRs, APRs, Z, Z*, and G) using three performance metrics: pout (probability of detecting all true outliers), pmask (probability of masking true outliers as inliers), and pswamp (probability of misclassifying inliers as outliers). Performance is evaluated via simulation (uncontaminated data and contamination at 5% and 10%) and on a real dataset. Results show that GAJPR and GAAPR achieve the best detection power in simulations, while GASPR and GAJPR perform best on the real data; overall, GAJPR is the most effective method. The grouped absolute residuals approach prioritizes sensitivity and reduces masking but tends to increase false positives, so we recommend grouped-absolute-residuals screening followed by casewise validation or conservative re-testing before excluding observations.