ABSTRACT
This chapter briefly covers why random effects models are useful, and the topic of linear mixed models for balanced data. A concrete example comes from animal breeding. Model checking proceeds by looking at residual plots, from the fits to both the original and the aggregated data, since, approximately, these should look like samples of i.i.d. normal random variables. From the experimental aims, it is clear that fixed machine effects and random worker effects are appropriate. The general theory for mixed models of balanced experimental data is primarily of theoretical interest, for understanding the results used in classical mixed model ANOVA tables, and for motivating the use of particular reference distributions when conducting hypothesis tests for mixed models. A more general approach to mixed models, will require use of general large sample results from the theory of maximum likelihood estimation.
