Estimation in linear mixed-effects model with errors in covariate

In this paper, we consider the estimation methods of parameters and the variance component in the linear mixed-effects model with measurement error. The likelihood-based methods are commonly used in random effects models, but it needs some assumption on the error distribution and the computation of likelihood-based methods is difficult. In this paper, two corrected methods based on least square are proposed to estimate regression parameters and variance components. The estimations are free from the distribution of the model error and random effect, which is different from likelihood-based methods. Simulation studies are carried out to compare the efficiency of the two methods, and the results suggest the proposed estimation is practicable for finite samples. From the simulation we can see, if the effects of measurement error to the estimation are ignored, then the estimators may be biased.