Diagnostic power of some graphical methods in geometric regression model addressing cervical cancer data

Zawar Hussain; Atif Akbar; Mohammed M. A. Almazah; A. Y. Al-Rezami; Fuad S. Al-Duais; Zawar Hussain; Atif Akbar; Mohammed M. A. Almazah; A. Y. Al-Rezami; Fuad S. Al-Duais

doi:10.3934/math.2024198

AIMS Mathematics

2024, Volume 9, Issue 2: 4057-4075. doi: 10.3934/math.2024198

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Research article Special Issues

Diagnostic power of some graphical methods in geometric regression model addressing cervical cancer data

1.
Govt Millat Graduate College Multan, Pakistan, 60800
2.
Department of Statistics, Bahauddin Zakariya University, Multan, Pakistan, 60800
3.
Department of Mathematics, College of Sciences and Arts (Muhyil), King Khalid University, Muhyil, 61421, Saudi Arabia
4.
Mathematics Department, College of Humanities and Science, Prince Sattam Bin Abdulaziz University, Al-Kharj, 16278, Saudi Arabia

Received: 15 August 2023 Revised: 25 December 2023 Accepted: 08 January 2024 Published: 12 January 2024
MSC : 00A71

In the framework of generalized linear models (GLM), this paper explores the design and applicability of partial residual (PRES), augmented partial residual (APRES), and conditional expectation and residuals (CERES) plots for visualizing an outlier's diagnostics as a function of selected variables. Here, a geometric regression as a GLM is thoroughly described. Additionally, plots for PRES, APRES, and CERES have been built. Due to how the response variable and the associated link function interact with various covariates, the effectiveness of these plots for creating an appealing visual impression may vary. On the cervical cancer data, specific methodologies are used to identify trends for effective modelling. When compared to other approaches, the power of the tests for various plots demonstrates that PRES, CERES (L) and CERES (K) have the greatest endurance for the outlier's diagnostics. On the basis of the power of residual plots, the use is recommended for outlier diagnostics in presence of conventional tests.
- visual impression,
- geometric regression,
- diagnostics,
- predictors transformations,
- cervical cancer
Citation: Zawar Hussain, Atif Akbar, Mohammed M. A. Almazah, A. Y. Al-Rezami, Fuad S. Al-Duais. Diagnostic power of some graphical methods in geometric regression model addressing cervical cancer data[J]. AIMS Mathematics, 2024, 9(2): 4057-4075. doi: 10.3934/math.2024198

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Abstract

In the framework of generalized linear models (GLM), this paper explores the design and applicability of partial residual (PRES), augmented partial residual (APRES), and conditional expectation and residuals (CERES) plots for visualizing an outlier's diagnostics as a function of selected variables. Here, a geometric regression as a GLM is thoroughly described. Additionally, plots for PRES, APRES, and CERES have been built. Due to how the response variable and the associated link function interact with various covariates, the effectiveness of these plots for creating an appealing visual impression may vary. On the cervical cancer data, specific methodologies are used to identify trends for effective modelling. When compared to other approaches, the power of the tests for various plots demonstrates that PRES, CERES (L) and CERES (K) have the greatest endurance for the outlier's diagnostics. On the basis of the power of residual plots, the use is recommended for outlier diagnostics in presence of conventional tests.

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