A class of beta regression models with multiplicative log-normal measurement errors

In this article, we propose a beta regression model with multiplicative log-normal measurement errors. Three estimation methods are presented, namely, naive, calibration regression, and pseudo likelihood. The nuisance parameters are estimated from a system of estimation equations using replicated data and these estimates are used to propose a pseudo likelihood function. A simulation study was performed to assess some properties of the proposed methods. Results from an example with a real dataset, including diagnostic tools, are also reported.