Shrinkage Estimators for Beta Regression Models

TL;DR

This paper introduces shrinkage estimators, specifically ridge and LASSO, for beta regression models to address collinearity issues, with evaluation through simulations and real data application.

Contribution

It develops and assesses ridge and LASSO estimators for beta regression models using a penalized likelihood approach with a logit link.

Findings

Shrinkage estimators improve parameter estimation in collinear beta regression models.

Simulation results demonstrate the effectiveness of the proposed estimators.

Application to real data shows practical utility of the methods.

Abstract

The beta regression model is a useful framework to model response variables that are rates or proportions, that is to say, response variables which are continuous and restricted to the interval (0,1). As with any other regression model, parameter estimates may be affected by collinearity or even perfect collinearity among the explanatory variables. To handle these situations shrinkage estimators are proposed. In particular we develop ridge regression and LASSO estimators from a penalized likelihood perspective with a logit link function. The properties of the resulting estimators are evaluated through a simulation study and a real data application