Analysis of unbalanced mixed model data: A case study comparison of ANOVA versus REML/GLS

Major transition has occurred in recent years in statistical methods for analysis of linear mixed model data from analysis of variance (ANOVA) to likelihood-based methods. Prior to the early 1990s, most applications used some version of analysis of variance because computer software was either not available or not easy to use for likelihood-based methods. ANOVA is based on ordinary least squares computations, with adoptions for mixed models. Computer programs for such methodology were plagued with technical problems of estimability, weighting, and handling missing data. Likelihood-based methods mainly use a combination of residual maximum likelihood (REML) estimation of covariance parameters and generalized least squares (GLS) estimation of mean parameters. Software for REML/GLS methods became readily available early in the 1990s, but the methodology still is not universally embraced. Although many of the computational inadequacies have been overcome, conceptual problems remain. Also, technical problems with REML/GLS have emerged, such as the need for adjustments for effects due to estimating covariance parameters. This article attempts to identify the major problems with ANOVA, describe the problems which remain with REML/GLS, and discuss new problems with REML/GLS.