Errors-in-variables beta regression models

TL;DR

This paper extends beta regression models to account for measurement errors in explanatory variables, proposing estimation methods and residual analysis, validated through simulations and real data application.

Contribution

It introduces three estimation methods for beta regression with measurement errors and develops residual analysis techniques, advancing modeling accuracy.

Findings

Proposed maximum likelihood, pseudo-likelihood, and calibration estimators perform well in simulations.

Residual analysis methods effectively diagnose measurement error impacts.

Application to real data demonstrates practical utility.

Abstract

Beta regression models provide an adequate approach for modeling continuous outcomes limited to the interval (0,1). This paper deals with an extension of beta regression models that allow for explanatory variables to be measured with error. The structural approach, in which the covariates measured with error are assumed to be random variables, is employed. Three estimation methods are presented, namely maximum likelihood, maximum pseudo-likelihood and regression calibration. Monte Carlo simulations are used to evaluate the performance of the proposed estimators and the na\"ive estimator. Also, a residual analysis for beta regression models with measurement errors is proposed. The results are illustrated in a real data set.