Influence Analysis in the Lognormal Regression Model with Fitted and Quantile Residuals
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...
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MDPI AG
2025-06-01
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| Online Access: | https://www.mdpi.com/2075-1680/14/6/464 |
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| author | Muhammad Habib Muhammad Amin Sadiah M. A. Aljeddani |
| author_facet | Muhammad Habib Muhammad Amin Sadiah M. A. Aljeddani |
| author_sort | Muhammad Habib |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-3d12f9c2c4dc49bfaea65fb0caca9339 |
| institution | Kabale University |
| issn | 2075-1680 |
| language | English |
| publishDate | 2025-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj-art-3d12f9c2c4dc49bfaea65fb0caca93392025-08-20T03:32:31ZengMDPI AGAxioms2075-16802025-06-0114646410.3390/axioms14060464Influence Analysis in the Lognormal Regression Model with Fitted and Quantile ResidualsMuhammad Habib0Muhammad Amin1Sadiah M. A. Aljeddani2Department of Statistics, University of Sargodha, Sargodha 40100, PakistanDepartment of Statistics, University of Sargodha, Sargodha 40100, PakistanMathematics Department, Al-Lith University College, Umm Al-Qura University, Al-Lith 21961, Saudi ArabiaInfluence 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.https://www.mdpi.com/2075-1680/14/6/464influential observationlognormal regression modelcook’s distancemodified Cook’s distancecovariance ratioHadi method |
| spellingShingle | Muhammad Habib Muhammad Amin Sadiah M. A. Aljeddani Influence Analysis in the Lognormal Regression Model with Fitted and Quantile Residuals Axioms influential observation lognormal regression model cook’s distance modified Cook’s distance covariance ratio Hadi method |
| title | Influence Analysis in the Lognormal Regression Model with Fitted and Quantile Residuals |
| title_full | Influence Analysis in the Lognormal Regression Model with Fitted and Quantile Residuals |
| title_fullStr | Influence Analysis in the Lognormal Regression Model with Fitted and Quantile Residuals |
| title_full_unstemmed | Influence Analysis in the Lognormal Regression Model with Fitted and Quantile Residuals |
| title_short | Influence Analysis in the Lognormal Regression Model with Fitted and Quantile Residuals |
| title_sort | influence analysis in the lognormal regression model with fitted and quantile residuals |
| topic | influential observation lognormal regression model cook’s distance modified Cook’s distance covariance ratio Hadi method |
| url | https://www.mdpi.com/2075-1680/14/6/464 |
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