Dawoud–Kibria Estimator for Beta Regression Model: Simulation and Application

Abstract

The linear regression model becomes unsuitable when the response variable is expressed as percentages, proportions, and rates. The beta regression (BR) model is more appropriate for the variable of this form. The BR model uses the conventional maximum likelihood estimator (BML), and this estimator may not be efficient when the regressors are linearly dependent. The beta ridge estimator was suggested as an alternative to BML in the literature. In this study, we developed the Dawoud–Kibria estimator to handle multicollinearity in the BR model. The properties of the new estimator are derived. We compared the performance of the estimator with the existing estimators theoretically using the mean squared error criterion. A Monte Carlo simulation and a real-life application were carried out to show the benefits of the proposed estimator. The theoretical comparison, simulation, and real-life application results revealed the superiority of the proposed estimator.

Performance of the Ridge and Liu Estimators in the zero‐inflated Bell Regression Model

“…In this section, we generated explanatory variables that are collinear and a response variable y that follows a zeroinflated bell distribution. e explanatory variables are obtained in line with the following studies [42][43][44][45][46][47][48]:…”

A New Tobit Ridge-Type Estimator of the Censored Regression Model With Multicollinearity Problem

“…[14], Abonazel and Dawoud [27], Algamal and Abonazel [28], Abonazel et al [15], and Abonazel et al [29]. So, the dependent variable has been censored using Equation (2).…”

“…Recently, Kibria and Lukman [9] proposed a new ridge-type estimator (NRTE). The NRTE has been extended in different regression models in different studies, such as Lukman et al [10], Lukman et al [11], Akram et al [12], Dawoud and Abonazel [13], Awwad et al [14], and Abonazel et al [15]. The multicollinearity is known to be a terrible problem in the Tobit model like in the LRM.…”

The beta Liu-type estimator: simulation and application

“…, x ip ) ′ is the vector of p regressors and η i is the linear predictor. This link function is strictly monotonic and twice differentiable [1,2,5,8,13,25]. Different link functions may be used for fitting the BRM as logit, probit, log-log, complementary log-log, and Cauchy link functions.…”

“…To prevent the undesirable effects of multicollinearity, many researchers have chosen to generalize the biased estimators used for linear regression models to apply on BRMs. For more detailed information about these proposed biased estimators in GLMs and BRMs, the articles [1][2][3][4][6][7][8][9][10]12,17,18,20,21,26,27] can be reviewed.…”