I have a 3x2x2 between subjects design. Participants are randomly assigned to 1 level of each of 3 factors (instruction, purpose, text). The main outcome variable is whether they answer a question correctly. This is assessed at both pre and post. I'm interested in testing whether any of the IVs predict endorsement of the correct answer at posttest, accounting for their response (correct/incorrect) at pretest. I also have a binary covariate (male/female).
IV1 (between subjects): during-reading instructions (3 levels: summarize, highlight, or reread)
IV2 (between subjects): reading purpose (2 levels: write an essay or take a test)
IV3 (between subjects): text (2 levels: easy text or difficult text)
DV (repeated measure): selection of correct response to a question with two options (correct/incorrect)
Will a multilevel mixed-effects logistic regression with three variables as fixed effects factors [3 (instruction) X 2 (purpose) X 2 (text)] and correct response as the within-subjects repeated measure work to answer this question? Would I use xtmelogit in a similar way to analysis of students nested within classrooms (just here it's pre/post response nested wtihin participant)?

Alternatively, I wondered whether there was another way to test if any of the IVs predict change in category membership (from incorrect -> correct would be of most interest).

Thank you in advance.