Influence Analysis in the Lognormal Regression Model with Fitted and Quantile Residuals - Muhammad Habib; Muhammad Amin; Sadiah M. A. Aljeddani (Axioms, 2025)
Influence analysis is a critical diagnostic tool in regression modeling to ensure reliable parameter estimates. This study evaluates the effectiveness of diagnostic methods for detecting influential observations in the lognormal regression model using fitted and quantile residuals. We assess Cook’s distance, modified Cook’s distance, covariance ratio, and the Hadi method through a Monte Carlo simulation with varying sample sizes, dispersion parameters, perturbation values, and numbers of explanatory variables, and a real-world application to an atmospheric environmental dataset. Simulation results demonstrate that Cook’s distance and the Hadi method achieve a good performance under all scenarios, with quantile residuals generally outperforming fitted residuals. The sensitivity analysis confirms their robustness, with minimal variation in detection rates. The covariance ratio performs well but shows slight variability in high-dispersion cases, while modified Cook’s distance consistently underperforms, particularly with quantile residuals. The real-world application confirms these findings, with Cook’s distance and the Hadi method effectively identifying influential points affecting ozone concentration estimates. These results highlight the superiority of Cook’s distance and the Hadi method for lognormal regression model diagnostics, with quantile residuals enhancing detection accuracy.