My question: how can I analyze the effects of multiple within-subjects factors when my design does NOT include the all combinations of their factor levels, as would be required by a standard factorial ANOVA?
Here's my design:
Each participant is trained to discriminate 2 categories in each of 2 domains. In one of the domains, they receive treatment A, and in the other, treatment B. Which treatment goes with which domain is selected randomly for each participant, as is which domain is shown first, so all 4 combinations of domain orders and treatment orders are possible and equally likely.
My DV is discrimination performance, which comes from a test administered right after treatment. There is one test for the first treatment / domain and another for the second.
There are actually 3 categories, rather than 2, in each domain, but a given participant only sees 2 of them. Which 2 they see is determined by another factor, called 'distance', taking levels 'near' and 'far'. If they are in the near condition, they get the 2 categories designated 'near' for both of the 2 domains, and likewise for far.
So, ignoring the random order of presentation of the 2 domains and the 2 treatments, I have 2 within-subject factors (domain, treatment) and 1 between-subject factor (distance). The problem is that I don't have the factorial combinations of the 2 within-subject factors: a given participant only sees 2 of the 4 possible combinations, e.g. domain 1 with treatment A and domain 2 with treatment B. So, if I plug the above factors into a standard ANOVA, it won't work because some combinations of the within-subjects factors don't appear.
Finally my question. What's the right model to analyze this data? Someone mentioned to me that this is a "nested design", but what I found on the net regarding this term didn't seem very relevant. Any help would be appreciated!