I have 3 trials each on 87 animals in each of 2 contexts (some missing data; no missing data = 64 animals). Within a context, I have many specific measures (time to enter, number of times returning to shelter, etc), so I want to develop 2 to 3 composite behavior scores that describe the behavior in that context (call them
C3). I want a
C1 that means the same thing over all 3 trials and 87 animals, so that I can do a regression to examine effect of age, sex, pedigree, and individual animal on the behavior. Then I want to examine how
C1 relates to the behavior scores in the other context, within the particular age. (At age 1, does activity in context 1 strongly predict activity in context 2?)
If this was not repeated measures, a PCA would work well – do a PCA on the multiple measures of a context, then use PC1, PC2, etc. to examine relationships (Spearman correlations) between PC1 in one context and PC1 (or 2 or 3) in the other context. The problem is the repeated measures, which falls into pseudoreplication. I've had a reviewer categorically say no-go, but I can't find any clear references as to whether this is problematic when doing data reduction.
My reasoning goes like this: repeated measures is not a problem, because what I am doing in the PCA is purely descriptive vis-à-vis the original measures. If I declared by fiat that I was using time to enter the arena as my "boldness" measure in context 1, I would have a context 1 boldness measure that was comparable across all individuals at all ages and no one would bat an eye. If I declare by fiat that I will use $0.5\cdot$ time-to-enter $+\ 0.5\cdot$ time-to-far-end, the same goes. So if I am using PCA purely for reductive purposes, why can't it be PC1 (that might be $0.28\cdot$ enter $+\ 0.63\cdot$ finish $+\ 0.02\cdot$ total time...), which is at least informed by my multiple measures instead of my guessing that time to enter is a generally informative and representative trait?
(Note I am not interested in the underlying structure of measures... my questions are on what we interpret the context-specific behaviors to be. "If I used context 1 and concluded that Harry is active compared to other animals, do I see Harry active in context 2? If he changes what we interpret as activity in context 1 as he gets older, does he also change his context 2 activity?)
I have looked at PARAFAC, and I have looked at SEM, and I am not convinced either of these approaches is better or more appropriate for my sample size. Can anybody weigh in? Thanks.