A Comparison of Estimators in Mixed Models

Mixed models are frequently used in inference for the repeated measurement data of biological and biomedical studies. In this paper, we consider the efficiency of the estimated generalized least squares estimator for the linear mixed model. We find that it works well with respect to consistency and empirical efficiency and has similar precision with the generalized least squares estimator. For the nonlinear mixed model, we notice that the approximate extended least squares estimator based on linearization may have serious bias in mean parameter estimates, especially when the variability in random coefficients is large. On the other hand, the extended least squares estimator using Monte Carlo method produces estimates close to that of exact extended least squares estimator and both procedures yield good estimates and confidence intervals for the mean parameters.