On the performance of link functions in the beta ridge regression model: Simulation and application

Abstract

AbstractThe beta regression model (BRM) is appropriate when the response variable is continuous and is in the form of ratios and proportions. For the estimation of the BRM, the maximum likelihood estimation (MLE) method is used with a specific link function. However, the MLE provides unstable results when the explanatory variables are correlated. In this study, we consider some ridge parameters for the beta ridge regression estimator (BRRE) under different link functions. However, mostly the researchers do not pay much attention to the suitable link function. So, we consider five link functions to see the performance of ridge parameters in the BRRE. For the performance assessment of ridge parameters and different link functions, a Monte Carlo simulation and a real application are considered, where mean squared error is used as the evaluation criterion. Both the simulation and example findings demonstrate that the BRRE with the log–log link function provides efficient results.