I am rather new to both permutation tests and mixed effects models, so forgive me if this is a ridiculous question. I would like to run a permutation test for a model that has a random effect, although I am not interested in the random effect, just a fixed effect. I realize that for a standard permutation test one simply permutes the outcome. However, can one do this when there are random effects? Instinctively I would say yes, but my instincts often prove wrong! Thank you!
I assume that with a mixed effects model you refer to a design with both a within subject factor (repeated measures; fixed effect) and between subject factor (comparing separate groups; random effect). Such a model test each effect (fixed and random) separately as well as an interaction between those effects. to test the fixed effect you should permute the scores within each unit of measurement (e.g. subject), and for the random effect you should permute the labels of the grouping of subjects.
Example: You want to test the effect of 2 different food diets (fixed effect) on blood pressure in a group of patients and healthy controls (random effect). Using a permutation test, permute the labeling of the diet within each participant, and permute the group labeling of participants.