Developing a Liu‐type estimator in beta regression model

Abstract

The beta regression model is a commonly used when the response variable has the form of fractions or percentages. The maximum likelihood (ML) estimator is used to estimate the regression coefficients of this model. However, it is known that multicollinearity problem affects badly the variance of ML estimator. Therefore, this paper introduces the Liu‐type estimator for the beta regression model to handle the multicollinearity problem. The performance of the proposed (Liu‐type) estimator is compared to the ML estimator and other biased (ridge and Liu) estimators depending on the mean squared error (MSE) criterion by conducting a simulation study and through an empirical application. The results indicated that the proposed estimator outperformed the ML, ridge, and Liu estimators.

A New Two-Parameter Estimator for Beta Regression Model: Method, Simulation, and Application

“…First, to check whether there is a multicollinearity problem or not, the correlation matrix and condition number (CN) are used. Based on the correlation matrix among the six explanatory variables that are presented, displayed by Algamal and Abonazel [19]. It is obviously seen that there are correlations >0.82 between x 1 and x 6 , x 1 and x 4 , x 2 and x 4 , and x 4 and x 6 .…”

“…For the LTBR estimator, we can use the optimal d parameter of the LTBR estimator that was proposed by Algamal and Abonazel [19]:…”

“…The response variable y i is generated as y i ∼ Beta(µ i , φ), with φ ∈ {0.5,1,1.5} and [19,26,[39][40][41].…”

“…We apply the proposed estimator to the football Spanish La Liga, season 2016-2017 [19]. The data contain 20 teams.…”

“…Furthermore, Liu [13] proved the supremacy of the Liu-type estimator over the ridge and Liu estimators. Details about Liu-type estimator, properties, and applications in regression models are shown in References Liu [14], Özkale and Kaciranlar [15], Li and Yang [16], Kurnaz and Akay [17], Sahriman and Koerniawan [18], and Algamal and Abonazel [19]. As a good alternative for the Liu-type estimator, Özkale and Kaciranlar [15] proposed the twoparameter estimator, and they proved that the two-parameter estimator utilizes the power of both the ridge estimator and the Liu estimator.…”