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

Year 2023, Volume: 5 Issue: 2, 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

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