The classic approach to mixed models involves fitting regular linear
models, but interpreting the “sums of squares” differently.
- Decompose sums of squares
- Decide which error terms to put in the denominator, which in the
numerator, how many degrees of freedom
- For simplest cases (e.g. one-way ANOVA), the answer is the same
either way
- Bestiary of experimental designs: nested, randomized block,
split-plot (Gotelli and Ellison, Quinn and Keough)
- Classic approaches will not work well if you have
- strongly unbalanced designs
- responses that you’d rather treat with a GLM(M) (e.g., binary
responses)
- For simple nested designs, you often can (and should) simplify your
model by simply aggregating at the bottom level (Murtaugh 2007)
- … doesn’t work for randomized block and other more complicated
designs
- works easily if perfectly balanced (equal samples per group); if
not, have to deal with weighting according to sample size
- works (although perhaps with very low power) for any sample
size
- sometimes gives negative variance estimates in complex situations
(e.g. population genetics)
