Chapter 4 - Restricted maximum likelihood and inference of random effects in linear mixed models

Abstract

Chapter 4 concerns the restricted maximum likelihood (REML) estimator and some other Bayes-type techniques applied in longitudinal data analysis. Therefore, Bayes’ theorem and Bayesian inference are reviewed first to familiarize the reader with the rationale of various Bayes-type models and methods included in the current and many of the succeeding chapters. Next, the general specifications and inference of the REML estimator are delineated. Two computational procedures are then displayed for the estimation of model parameters described in Chapter 3: the Newton–Raphson (NR) and the Expectation–Maximization (EM) algorithms. The best linear unbiased predictor (BLUP) is then presented, a popular method to approximate the subject-specific random effects in longitudinal data analysis. Corresponding to the specification of BLUP, statistical shrinkage is also introduced, which serves as a powerful statistical technique in linear predictions of longitudinal response outcomes. Lastly, an empirical illustration is provided, in which the analytic results from the ML and REML estimators are compared, and the longitudinal trajectory of the response variable is predicted.