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AIMS Mathematics

2022, Volume 7, Issue 1: 1035-1057. doi: 10.3934/math.2022062
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Research article

A new modified ridge-type estimator for the beta regression model: simulation and application

  • 1.
    Department of Statistics, University of Sargodha, Sargodha, Pakistan
  • 2.
    Department of Mathematics, College of Science, University of Bisha, Bisha, Saudi Arabia
  • 3.
    Department of Mathematics, Damanhour University, Damanhour, Egypt
  • 4.
    Department of Statistics, Bahauddin Zakariya University, Multan, Pakistan
  • Received: 02 July 2021 Accepted: 13 October 2021 Published: 19 October 2021

  • MSC : 62F10, 62J07

  • The beta regression model has become a popular tool for assessing the relationships among chemical characteristics. In the BRM, when the explanatory variables are highly correlated, then the maximum likelihood estimator (MLE) does not provide reliable results. So, in this study, we propose a new modified beta ridge-type (MBRT) estimator for the BRM to reduce the effect of multicollinearity and improve the estimation. Initially, we show analytically that the new estimator outperforms the MLE as well as the other two well-known biased estimators i.e., beta ridge regression estimator (BRRE) and beta Liu estimator (BLE) using the matrix mean squared error (MMSE) and mean squared error (MSE) criteria. The performance of the MBRT estimator is assessed using a simulation study and an empirical application. Findings demonstrate that our proposed MBRT estimator outperforms the MLE, BRRE and BLE in fitting the BRM with correlated explanatory variables.

    Citation: Muhammad Nauman Akram, Muhammad Amin, Ahmed Elhassanein, Muhammad Aman Ullah. A new modified ridge-type estimator for the beta regression model: simulation and application[J]. AIMS Mathematics, 2022, 7(1): 1035-1057. doi: 10.3934/math.2022062

    Related Papers:

  • The beta regression model has become a popular tool for assessing the relationships among chemical characteristics. In the BRM, when the explanatory variables are highly correlated, then the maximum likelihood estimator (MLE) does not provide reliable results. So, in this study, we propose a new modified beta ridge-type (MBRT) estimator for the BRM to reduce the effect of multicollinearity and improve the estimation. Initially, we show analytically that the new estimator outperforms the MLE as well as the other two well-known biased estimators i.e., beta ridge regression estimator (BRRE) and beta Liu estimator (BLE) using the matrix mean squared error (MMSE) and mean squared error (MSE) criteria. The performance of the MBRT estimator is assessed using a simulation study and an empirical application. Findings demonstrate that our proposed MBRT estimator outperforms the MLE, BRRE and BLE in fitting the BRM with correlated explanatory variables.


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