What is the maximal linear mixed effects model of a 2 x 2 within-subject and
within-item factorial design with multiple observations for each subject-item-factor level combination:
m1 (as I have seen quite often) but why not
m2 or even
m1: Y ~ 1 + A*B + (1 + A*B|subject) + (1 + A*B|item) m2: Y ~ 1 + A*B + (1 + A*B|subject) + (1 + A*B|item) + (1|subject:item) m3: Y ~ 1 + A*B + (1 + A*B|subject) + (1 + A*B|item) + (1 + A*B|subject:item)
I know that these models are often over-parameterized but if one wants to start with the maximal model and try to find an 'optimal' model via reduction, then it should be the correct maximal model in the first place.