This post follows on from this one.
I am trying to analyse a dataset: $S$ subjects were tested for $A$ measures in $B\times C$ conditions. I have worked out that I can perform a repeated measures analysis by using a mixed-effects design where the subjects are random factors. Then I am left with a '3 way' $A\times B \times C$ ANOVA, which I perform with MATLAB's
Where I am stuck is: what model structure should I be using, and what do I report? Specifically, what, if not all, (random) interactions, i.e. $?\times S$, should I be including in the model?
(If I don't include all $?\times S$ interactions, MATLAB reverts to using the MSE of the error degrees of freedom as the denominator in the F-statistic calculations. I don't know whether that's good or bad.)
Nomenclature: Am I performing an $A \times B \times C$ repeated measures ANOVA, or an $S \times A \times B \times C$ mixed-effects ANOVA, or maybe an$A \times B \times C$ repeated-measures mixed effects ANOVA?
Should I be including all the $?\times S$ interaction terms in the analysis, or is this a choice-of-model question?
Should I report the effects of $S$ and/or the $?\times S$ interactions? Do I want some kind of $\eta^2$ effect measure to communicate how much variance is due the subjects?