Comparison of Standardized and Adjusted Working Residuals for Gamma-Pareto Regression and Gamma-Pareto Ridge Regression Models

Saleem, Nasir; Akbar, Atif; Ullah, Muhammad Aman

doi:10.22034/jirss.2026.2083523.1177

Comparison of Standardized and Adjusted Working Residuals for Gamma-Pareto Regression and Gamma-Pareto Ridge Regression Models

Articles in Press

Document Type : Original Article

Authors

Nasir Saleem

Atif Akbar

Muhammad Aman Ullah

Department of Statistics, Bahauddin Zakariya University (BZU), Multan, Pakistan,60800

10.22034/jirss.2026.2083523.1177

Abstract

Influential observations can substantially affect the estimation, interpretation, and predictive performance of Gamma-Pareto regression models, particularly when multicollinearity is present. This study investigates the detection of influential observations in the Gamma-Pareto regression model and its ridge-based counterpart, the Gamma-Pareto ridge regression model. Several established diagnostic measures, including the Covariance Ratio, Welch Distance, and Hadi’s Measure, together with their ridge-regression counterparts, are considered for assessing the influence of individual observations. To enhance the reliability of influence diagnostics in the presence of dispersion-related effects, we used an extended Hadi’s Measure for the Gamma-Pareto ridge regression model based on standardized and adjusted working residuals. The diagnostic measures are evaluated through comprehensive analyses of both real and simulated datasets under varying levels of dispersion. The results demonstrate that the proposed Hadi’s Measure in Ridge provides a more effective and stable mechanism for identifying influential observations than the conventional diagnostics, with different dispersion settings. These findings highlight the usefulness of incorporating standardized and adjusted working residuals into influence diagnostics and provide a practical framework for detecting influential observations in Gamma-Pareto ridge regression model.

Keywords

Diagnostic Measures

G-PRM

G-PRRM

Influential Observations

Multicollinearity

Working Residuals

Subjects

Regression Models

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