Influence diagnostics for the Gamma-Pareto regression: a DFFITS-based comparison of residuals

Document Type : Original Article

Authors
Nasir Saleem 1
Atif Akbar 2
Asad Abbas 3
1 Department of Statistics, Bahauddin Zakariya university, Multan Pakistan.
2 Department of Statistics, Bahauddin Zakariya University (BZU), Multan, Pakistan,60800
3 Department of Statistics Bahauddin Zakariya University (BZU), Multan, Pakistan,60800
10.22034/jirss.2026.2076260.1154
Abstract
The generalized linear models (GLMs) use Gamma-Pareto regression Model (G-PRM) to address the sensitivity of influential observations. Difference of Fits (DFFITS) is a popular technique for identifying influential observations. We apply DFFITS to the G-PRM with various residuals. We present illustrative real and simulated data. One class of adjusted Pearson residuals is more effective in detecting influential observations, considering small or large dispersion parameters. We calculate detection percentages to evaluate the proposed procedure's performance, replicating the process 10,000 times.

The generalized linear models (GLMs) use Gamma-Pareto regression Model (G-PRM) to address the sensitivity of influential observations. Difference of Fits (DFFITS) is a popular technique for identifying influential observations. We apply DFFITS to the G-PRM with various residuals. We present illustrative real and simulated data. One class of adjusted Pearson residuals is more effective in detecting influential observations, considering small or large dispersion parameters. We calculate detection percentages to evaluate the proposed procedure's performance, replicating the process 10,000 times.
Keywords
Difference of fits
Gamma-Pareto regression
Residuals
Inverse Link function
Influence diagnostics
Subjects
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Journal of the Iranian Statistical Society
Volume 24, Issue 2
December 2025
Pages 69-90

  • Receive Date 30 October 2025
  • Revise Date 05 January 2026
  • Accept Date 31 January 2026