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Improved shrinkage estimators in the beta regression model with application in econometric and educational data

Author

Listed:
  • Reza Arabi Belaghi

    (Uppsala University
    University of Tabriz)

  • Yasin Asar

    (Necmettin Erbakan University)

  • Rolf Larsson

    (Uppsala University)

Abstract

Although beta regression is a very useful tool to model the continuous bounded outcome variable with some explanatory variables, however, in the presence of multicollinearity, the performance of the maximum likelihood estimates for the estimation of the parameters is poor. In this paper, we propose improved shrinkage estimators via Liu estimator to obtain more efficient estimates. Therefore, we defined linear shrinkage, pretest, shrinkage pretest, Stein and positive part Stein estimators to estimate of the parameters in the beta regression model, when some of them have not a significant effect to predict the outcome variable so that a sub-model may be sufficient. We derived the asymptotic distributional biases, variances, and then we conducted extensive Monte Carlo simulation study to obtain the performance of the proposed estimation strategy. Our results showed a great benefit of the new methodologies for practitioners specifically in the applied sciences. We concluded the paper with two real data analysis from economics and education.

Suggested Citation

  • Reza Arabi Belaghi & Yasin Asar & Rolf Larsson, 2023. "Improved shrinkage estimators in the beta regression model with application in econometric and educational data," Statistical Papers, Springer, vol. 64(6), pages 1891-1912, December.
    • Handle: RePEc:spr:stpapr:v:64:y:2023:i:6:d:10.1007_s00362-022-01355-3
    DOI: 10.1007/s00362-022-01355-3
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    References listed on IDEAS

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    1. Silvia Ferrari & Francisco Cribari-Neto, 2004. "Beta Regression for Modelling Rates and Proportions," Journal of Applied Statistics, Taylor & Francis Journals, vol. 31(7), pages 799-815.
    2. Shakhawat Hossain & Trevor Thomson & Ejaz Ahmed, 2018. "Shrinkage estimation in linear mixed models for longitudinal data," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 81(5), pages 569-586, July.
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