A new almost unbiased estimator for beta regression model under multicollinearity

Randa Alharbi; Abdulaziz S. Alghamdi; Randa Alharbi; Abdulaziz S. Alghamdi

doi:10.3934/math.2026005

AIMS Mathematics

2026, Volume 11, Issue 1: 85-126. doi: 10.3934/math.2026005

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Research article

A new almost unbiased estimator for beta regression model under multicollinearity

Randa Alharbi ^{1
,},
Abdulaziz S. Alghamdi ^{2
,
,}

1.
Department of Statistics, Faculty of Science, University of Tabuk, Tabuk, Saudi Arabia; ralharbi@ut.edu.sa
2.
Department of Mathematics, College of Science & Arts, King Abdulaziz University, P. O. Box 344, Rabigh 21911, Saudi Arabia

Received: 26 October 2025 Revised: 24 November 2025 Accepted: 03 December 2025 Published: 04 January 2026
MSC : 62H12, 62J07, 62J10, 62J12, 62P10

The beta regression model (BRM) is designed to model continuous response variables constrained to the open interval (0, 1). It is particularly suitable for analyzing proportions, rates, and other fractional data. Maximum likelihood estimation (MLE) is the most common way to estimate parameters in the BRM. However, when multicollinearity is present, i.e., when explanatory variables exhibit high intercorrelation, the MLE may produce unstable and biased parameter estimates, inflated variance, and increased scalar mean squared error (MSE), ultimately undermining the model's statistical reliability. To address the effects of multicollinearity, some biased estimators have been proposed for the BRM. In this study, we introduce a new almost unbiased estimator for the BRM. A theoretical comparison of the proposed estimator with existing estimators is derived using the matrix mean squared error (MMSE) and MSE. The performance of the proposed estimator is subsequently assessed and contrasted with existing estimators via a comprehensive Monte Carlo simulation study and applied to two real-world datasets. The simulation and applications consistently show that the proposed estimator is better than other existing estimators, providing more accurate and stable parameter estimates for the BRM under multicollinearity.
- beta regression model,
- biased estimator,
- almost unbiased estimator,
- modified ridge-type estimator,
- multicollinearity
Citation: Randa Alharbi, Abdulaziz S. Alghamdi. A new almost unbiased estimator for beta regression model under multicollinearity[J]. AIMS Mathematics, 2026, 11(1): 85-126. doi: 10.3934/math.2026005

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Abstract

The beta regression model (BRM) is designed to model continuous response variables constrained to the open interval (0, 1). It is particularly suitable for analyzing proportions, rates, and other fractional data. Maximum likelihood estimation (MLE) is the most common way to estimate parameters in the BRM. However, when multicollinearity is present, i.e., when explanatory variables exhibit high intercorrelation, the MLE may produce unstable and biased parameter estimates, inflated variance, and increased scalar mean squared error (MSE), ultimately undermining the model's statistical reliability. To address the effects of multicollinearity, some biased estimators have been proposed for the BRM. In this study, we introduce a new almost unbiased estimator for the BRM. A theoretical comparison of the proposed estimator with existing estimators is derived using the matrix mean squared error (MMSE) and MSE. The performance of the proposed estimator is subsequently assessed and contrasted with existing estimators via a comprehensive Monte Carlo simulation study and applied to two real-world datasets. The simulation and applications consistently show that the proposed estimator is better than other existing estimators, providing more accurate and stable parameter estimates for the BRM under multicollinearity.

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