I have a question about how to best analyze data from an experimental psychology study. Briefly, 250 participants were asked to assign four different pictures (Pictures A - D) to two different conditions (Conditions A - B). I would like to know whether Pictures A, B, and C were more likely to be assigned to Condition A relative to Picture D, after adjusting for relevant participant characteristics (e.g., demographic factors). The original plan was to fit a multilevel (random-intercepts) logistic model, in which participants were considered a random factor to account for the fact participants' picture assignments are likely correlated across the four pictures (i.e., within-subject picture assignment correlation). This is the general code I used in Stata (for the crude, unadjusted model).
xtmelogit condition_A pic_A pic_B pic_C || id:, variance OR
However, I have a few questions about the appropriateness of this method of analysis. First, by setting up the model in this way, does this essentially make the sample size within the level 2 groups four (i.e., the four pictures within each level 1, participant, group)? Also, I know that participant characteristics aren't really a random-sample of all possible characteristics, but they are characteristics of the level 2 groups, and thus I included these as level 2 covariates. Is this correct? Thank you so much!!