IDEAS home Printed from https://ideas.repec.org/a/wly/jjmath/v2025y2025i1n3440237.html

Influence Diagnostics in Gamma‐Pareto Regression Model With Cook’s Distance for Standardized and Adjusted Pearson, Deviance, and Likelihood Residuals: Simulation and Application

Author

Listed:
  • Nasir Saleem
  • Atif Akbar
  • Ateeq Ur Rehman Irshad
  • Burhanettin Ozdemir
  • Javaria Ahmad khan

Abstract

Influential analysis is the main diagnostic process to obtain reliable regression results. Same is true for the generalized linear model (GLM). The present article empirically compares the performance of different residuals of the gamma‐Pareto regression model (G‐PRM) to detect the influential points. The G‐PRM residuals are further divided into two categories, that is, standardized and adjusted residuals. Cook’s distance has been computed for both of the stated residuals, and then comparison of these residuals for the detection of influential points has been carried out with the help of simulation and a real dataset. The simulation results show that G‐PRM standardized and adjusted likelihood residuals perform better than standardized and adjusted forms of Pearson and deviance residuals for different values of dispersion parameters and different sample sizes, using Cook’s distance to detect influential points. But standardized likelihood residuals are noted better than adjusted likelihood residuals.

Suggested Citation

  • Nasir Saleem & Atif Akbar & Ateeq Ur Rehman Irshad & Burhanettin Ozdemir & Javaria Ahmad khan, 2025. "Influence Diagnostics in Gamma‐Pareto Regression Model With Cook’s Distance for Standardized and Adjusted Pearson, Deviance, and Likelihood Residuals: Simulation and Application," Journal of Mathematics, John Wiley & Sons, vol. 2025(1).
    • Handle: RePEc:wly:jjmath:v:2025:y:2025:i:1:n:3440237
    DOI: 10.1155/jom/3440237
    as

    Download full text from publisher

    File URL: https://doi.org/10.1155/jom/3440237
    Download Restriction: no
    File URL: https://libkey.io/10.1155/jom/3440237?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. A. Fielding, 1990. "Sensitivity Analysis in Linear Regression," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 153(1), pages 104-104, January.
    2. Hong‐Tu Zhu & Sik‐Yum Lee, 2001. "Local influence for incomplete data models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(1), pages 111-126.
    3. D. A. Williams, 1987. "Generalized Linear Model Diagnostics Using the Deviance and Single Case Deletions," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 36(2), pages 181-191, June.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Alejandra Tapia & Victor Leiva & Maria del Pilar Diaz & Viviana Giampaoli, 2019. "Influence diagnostics in mixed effects logistic regression models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(3), pages 920-942, September.
    2. Russo, Cibele M. & Paula, Gilberto A. & Aoki, Reiko, 2009. "Influence diagnostics in nonlinear mixed-effects elliptical models," Computational Statistics & Data Analysis, Elsevier, vol. 53(12), pages 4143-4156, October.
    3. Preisser, John S. & Garcia, Daniel I., 2005. "Alternative computational formulae for generalized linear model diagnostics: identifying influential observations with SAS software," Computational Statistics & Data Analysis, Elsevier, vol. 48(4), pages 755-764, April.
    4. M. Revan Özkale & Stanley Lemeshow & Rodney Sturdivant, 2018. "Logistic regression diagnostics in ridge regression," Computational Statistics, Springer, vol. 33(2), pages 563-593, June.
    5. Xiaowen Dai & Libin Jin & Maozai Tian & Lei Shi, 2019. "Bayesian Local Influence for Spatial Autoregressive Models with Heteroscedasticity," Statistical Papers, Springer, vol. 60(5), pages 1423-1446, October.
    6. Xiaowen Dai & Libin Jin & Lei Shi & Cuiping Yang & Shuangzhe Liu, 2016. "Local influence analysis in general spatial models," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 100(3), pages 313-331, July.
    7. R.A.B. Assumpção & M.A. Uribe-Opazo & M. Galea, 2014. "Analysis of local influence in geostatistics using Student's t -distribution," Journal of Applied Statistics, Taylor & Francis Journals, vol. 41(11), pages 2323-2341, November.
    8. Lee, Sik-Yum & Lu, Bin & Song, Xin-Yuan, 2006. "Assessing local influence for nonlinear structural equation models with ignorable missing data," Computational Statistics & Data Analysis, Elsevier, vol. 50(5), pages 1356-1377, March.
    9. Fernanda De Bastiani & Audrey Mariz de Aquino Cysneiros & Miguel Uribe-Opazo & Manuel Galea, 2015. "Influence diagnostics in elliptical spatial linear models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 24(2), pages 322-340, June.
    10. Manuel Galea & Alonso Molina & Isabelle S. Beaudry, 2025. "Diagnostic for Volatility and Local Influence Analysis for the Vasicek Model," JRFM, MDPI, vol. 18(2), pages 1-20, January.
    11. Lucia Santana & Filidor Vilca & V�ctor Leiva, 2011. "Influence analysis in skew-Birnbaum--Saunders regression models and applications," Journal of Applied Statistics, Taylor & Francis Journals, vol. 38(8), pages 1633-1649, July.
    12. Christian Caamaño‐Carrillo & Germán Ibacache‐Pulgar & Bladimir Morales, 2025. "A Partially Varying‐Coefficient Model With Skew‐T Random Errors for Environmental Data Modeling," Environmetrics, John Wiley & Sons, Ltd., vol. 36(6), September.
    13. Matos, Larissa A. & Bandyopadhyay, Dipankar & Castro, Luis M. & Lachos, Victor H., 2015. "Influence assessment in censored mixed-effects models using the multivariate Student’s-t distribution," Journal of Multivariate Analysis, Elsevier, vol. 141(C), pages 104-117.
    14. Clécio da Silva Ferreira & Gilberto A. Paula & Gustavo C. Lana, 2022. "Estimation and diagnostic for partially linear models with first-order autoregressive skew-normal errors," Computational Statistics, Springer, vol. 37(1), pages 445-468, March.
    15. Shi, Lei & Lu, Jun & Zhao, Jianhua & Chen, Gemai, 2016. "Case deletion diagnostics for GMM estimation," Computational Statistics & Data Analysis, Elsevier, vol. 95(C), pages 176-191.
    16. Jun Lu & Wen Gan & Lei Shi, 2022. "Local influence analysis for GMM estimation," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 106(1), pages 1-23, March.
    17. Camila Zeller & Victor Lachos & Filidor Labra, 2014. "Influence diagnostics for Grubbs’s model with asymmetric heavy-tailed distributions," Statistical Papers, Springer, vol. 55(3), pages 671-690, August.
    18. Ming Ouyang & Xinyuan Song, 2020. "Bayesian Local Influence of Generalized Failure Time Models with Latent Variables and Multivariate Censored Data," Journal of Classification, Springer;The Classification Society, vol. 37(2), pages 298-316, July.
    19. Camila Zeller & Rignaldo Carvalho & Victor Lachos, 2012. "On diagnostics in multivariate measurement error models under asymmetric heavy-tailed distributions," Statistical Papers, Springer, vol. 53(3), pages 665-683, August.
    20. Stefanie Gerold & Johannes Buhl & Sonja M. Geiger, 2024. "How to Enhance Time Wealth? Insights from Changes in Time Use and Working Conditions During the COVID-19 Lockdown in Germany," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 171(1), pages 349-371, January.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:wly:jjmath:v:2025:y:2025:i:1:n:3440237. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Wiley Content Delivery (email available below). General contact details of provider: https://onlinelibrary.wiley.com/journal/1469 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.