ABSTRACT

Linear regression is widely known as a useful tool for statistical analysis, but its role has been gradually replaced by LMM due to the flexibility of the latter as well as its ability to incorporate correlations in the observations. C. R. Henderson has been credited for the early developments of LMM, although the origination of the latter can be traced back to some time much earlier (e.g., [21], Chapter 2). Among many of Henderson’s contributions are analysis of variance (ANOVA) methods for mixed model analysis, known as Henderson’s methods I, II, and III [32]. The ANOVA methods are computationally simpler, compared to some of the methods used today. This fitted well with the earlier time, when computational resources and tools were Iimited. However, the ANOVA estimators are inefficient in that they may have large variation; they also suffer from possibilities of negative values for quantities that are supposed to be nonnegative, such as variances of the random effects. For such reasons, the ANOVA methods have given way to more sophisticated methods, such as ML and REML, once the latter became computationally feasible.