STAT 425 Week 14 - Linear Models with Random Effects

Considers the extension of ANOVA models to include factors that are themselves random variables. This type of modeling is useful to account for batch correlations in the data, and is the appropriate analysis when the levels of a factor are meaningful only as representatives of a more general collection, as if sampled from a population, or representative of some hypothetical population. If the design is balanced, then the random effect analysis can be done with ANOVA calculations. In unbalanced cases maximum likelihood (ML) and restricted maximum likelihood (REML) are more commonly used. The latter methods also generalize to complex multilevel models. We also demonstrate likelihood based inferences, and Bootstrap tests and confidence intervals for the variance components.