  Measurement errors usually arise during the longitudinal data collection
process. Ignoring the effects of measurement errors will lead to invalid
estimates. The Lifestyle Education for Activity and Nutrition (LEAN) study was
designed to assess the effectiveness of intervention for enhancing weight loss
over nine months. The covariates systolic blood pressure (SBP) and diastolic
blood pressure (DBP) were measured at baseline, month 4, and month 9. At each
assessment time, there were two replicate measurements for SBP and DBP. The
replicate measurement errors of SBP follow different distributions, as does
DBP. To account for the distributional difference of replicate measurement
errors, a new method for analyzing longitudinal data with replicate covariate
measurement errors is developed based on the empirical likelihood method. The
asymptotic properties of the proposed estimator are established under some
regularity conditions. The confidence region for the parameters of interest can
be constructed based on the chi-squared approximation without estimating the
covariance matrix. Additionally, the proposed empirical likelihood estimator is
asymptotically more efficient than the estimator of Lin et al. (2018).
Extensive simulations demonstrate that the proposed method can eliminate the
effects of measurement errors in the covariate and has a high estimation
efficiency. The proposed method indicates the significant effect of the
intervention on BMI in the LEAN study.
