Measurement error usually occurs in practice whenever we can not exactly observe the variables in a model. It has been long recognized that measurement error will bias the estimates if we do not correct it. Thus, it is significant for us to take into account measurement error in our analysis in order to obtain valuable results. The Bayesian method is one of approaches for correcting measurement error in covariates
in both linear models and linear mixed effects models. Bayesian approach became feasible and straightforward for many problems due to the availability of modern computers and computational tools such as the Markov chain Monte Carlo (MCMC) methods and WinBUGS. In this paper, the first goal is to assess the effects of measurement error on naive analysis which ignore it in both linear models and linear mixed effects models. Then we focus on correcting measurement error through utilizing regression calibration methods and Bayesian methods, and comparing their performance in different situations. Estimating the regression coefficients using regression calibration methods and Bayesian methods in a linear mixed effects model with measurement error in time-varying covariates is mainly considered. We illustrate with real data analysis investigating the relationship between true dietary intake of beta-carotene and serum beta-carotene, and analyze the estimation results of naive methods, regression calibration methods and Bayesian methods.