Performance of A New Bias Corrected Estimator in Beta Regression Model: A Monte Carlo Study

Year 2023, , 75 - 87, 31.12.2023

Yasin Asar

https://doi.org/10.47112/neufmbd.2023.11

Abstract

The primary approach for obtaining regression parameters in the beta regression model is the utilization of the maximum likelihood estimation technique. However, it is acknowledged that multicollinearity has a detrimental effect on the variance of the maximum likelihood estimator in the beta regression model, namely, the variance of the maximum likelihood estimator is inflated. To address this issue, a novel bias-adjusted estimator is introduced to tackle the problem of multicollinearity. The effectiveness of these new estimator is assessed through a numerical investigation using a Monte Carlo simulation experiment. The results indicate that the proposed estimators yield substantial improvements compared to other competing estimators in terms of both the mean squared error and squared bias values.

Keywords

Beta regression, Multicollinearity, Bias-adjeusted estimator, Maximum likelihood

Beta Regresyon Modelinde Yeni Bir Yanı Düzeltilmiş Tahmin Edicinin Performansı: Bir Monte Carlo Çalışması

Abstract

Beta regresyon modelinde regresyon parametrelerini elde etmek için birincil yaklaşım, maksimum olabilirlik tahmin tekniğinin kullanılmasıdır. Bununla birlikte, beta regresyon modelinde çoklu bağlantının maksimum olabilirlik tahmin edicisinin varyansı üzerinde negatif bir etkiye sahip olduğu, yani maksimum olabilirlik tahmin edicisinin varyansının şişirildiği kabul edilmektedir. Bu konuyu ele almak için, çoklu bağlantı sorununu çözmek için yeni bir yanı düzeltilmiş tahmin edici tanıtılmıştır. Bu yeni tahmin edicinin etkinliği, bir Monte Carlo simülasyon deneyi kullanılarak sayısal bir araştırma yoluyla değerlendirilmiştir. Sonuçlar, önerilen tahmin edicinin diğer rakip tahmin edicilere kıyasla hem hata kareler ortalaması hem de karesel yan değerleri bakımından önemli iyileştirmeler sağladığını göstermektedir.

Keywords

Beta regresyon, Çoklu bağlantı, Yanı düzeltilmiş tahmin edici, Maksimum olabilirlik

References

• S.L.P. Ferrari, F. Cribari-Neto, Beta regression for modelling rates and proportions, Journal of Applied Statistics. 31 (2004), 799-815. doi:10.1080/0266476042000214501.
• M. Qasim, K. Månsson, B.M. Golam Kibria, On some beta ridge regression estimators: method, simulation and application, Journal of Statistical Computation and Simulation. 91 (2021), 1699-1712. doi:10.1080/00949655.2020.1867549.
• A.E. Hoerl, R.W. Kennard, Ridge Regression: Biased Estimation for Nonorthogonal Problems, Technometrics. 12 (1970), 55-67. doi:10.1080/00401706.1970.10488634. E.O. Ogundimu, G.S. Collins, Predictive performance of penalized beta regression model for continuous bounded outcomes, Journal of Applied Statistics. 45 (2018), 1030-1040. doi:10.1080/02664763.2017.1339024.
• K. Liu, A new class of blased estimate in linear regression, Communications in Statistics - Theory and Methods. 22 (1993), 393-402. doi:10.1080/03610929308831027.
• P. Karlsson, K. Månsson, B.M.G. Kibria, A Liu estimator for the beta regression model and its application to chemical data, Journal of Chemometrics. 34 (2020), e3300. doi:10.1002/cem.3300.
• K. Liu, Using Liu-Type Estimator to Combat Collinearity, Communications in Statistics - Theory and Methods. 32 (2003), 1009-1020. doi:10.1081/STA-120019959.
• Z. Yahya Algamal, Abonazel, Developing a Liu-type estimator in beta regression model, Concurrency and Computation: Practice and Experience. 34 (2022), e6685. doi:10.1002/CPE.6685.
• R. Ospina, F. Cribari-Neto, K.L.P. Vasconcellos, Improved point and interval estimation for a beta regression model, Computational Statistics & Data Analysis. 51 (2006), 960-981. doi:10.1016/j.csda.2005.10.002.
• A.B. Simas, W. Barreto-Souza, A. V Rocha, Improved estimators for a general class of beta regression models, Computational Statistics and Data Analysis. 54 (2010), 348-366. doi:10.1016/j.csda.2009.08.017.
• [R. Ospina, S.L.P. Ferrari, On Bias Correction in a Class of Inflated Beta Regression Models, International Journal of Statistics and Probability. 1 (2012), p269. doi:10.5539/IJSP.V1N2P269.
• K. Kadiyala, A class of almost unbiased and efficient estimators of regression coefficients, Economics Letters. 16 (1984), 293-296. doi:10.1016/0165-1765(84)90178-2.
• K. Ohtani, On small sample properties of the almost unbiased generalized ridge estimator, Communications in Statistics - Theory and Methods. 15 (1986), 1571-1578. doi:10.1080/03610928608829203.
• Y. Asar, M. Korkmaz, Almost unbiased Liu-type estimators in gamma regression model, Journal of Computational and Applied Mathematics. 403 (2022), 113819. doi:10.1016/J.CAM.2021.113819.
• M. Amin, M. Qasim, A. Yasin, M. Amanullah, Almost unbiased ridge estimator in the gamma regression model, Communications in Statistics - Simulation and Computation. 51 (2022), 3830-3850. doi:10.1080/03610918.2020.1722837.
• M. Qasim, K. Månsson, M. Amin, B.M. Golam Kibria, P. Sjölander, Biased adjusted Poisson ridge estimators-method and application, Iran. J. Sci. Technol. Trans. A Sci. 44 (2020), 1775-1789. doi:10.1007/s40995-020-00974-5.
• M.I. Alheety, M. Qasim, K. Månsson, B.M.G. Kibria, Modified almost unbiased two-parameter estimator for the Poisson regression model with an application to accident data, SORT. 45 (2021), 121-142.
• A. Erkoç, E. Ertan, Z. Yahya Algamal, K. Ulaş Akay, The beta Liu-type estimator: simulation and application, Hacettepe Journal of Mathematics and Statistics. 52 (2023), 828-840. doi:10.15672/HUJMS.1145607.
• M.R. Abonazel, I.M. Taha, Beta ridge regression estimators: simulation and application, Communications in Statistics - Simulation and Computation. (2021), 1-13. doi:10.1080/03610918.2021.1960373.
• J. Xu, H. Yang, More on the Bias and Variance Comparisons of the Restricted Almost Unbiased Estimators, Communications in Statistics - Theory and Methods. 40 (2011), 4053-4064. doi:10.1080/03610926.2010.505693.
• M. Erişoğlu, N. Yaman, Ridge Tahminine Dayalı Kantil Regresyon Analizinde Yanlılık Parametresi Tahminlerinin Performanslarının Karşılaştırılması, Necmettin Erbakan University Journal of Science and Engineering. 1 (2019), 103-111.