In a longitudinal study, two groups of subjects have been measured over a period of two years at 6 months intervals. During these measurements subjects have been assessed with a series of $k$ measures ($M_1$ to $M_k$).
From other sources we expect to see a difference between the groups and a decline in the performance of only one group. The question is: which of the $M_1$ to $M_k$ measures can pick up the decline of performance over the time.
If we had only one measure M, I suppose we could simply get an answer using:
fit.0 <- lme(M ~ Group * Time, random=~1|Subject)
Then we could simply check the significance of the interaction effect. However, I guess looking at $M_1$ to $M_k$ measures one by one might not be ideal. Although differences between the two groups are assumed to be real according other sources, still some form of multiple comparison might be going on.
Another way to look at the problem might be to try to address our research problem directly, i.e. trying something like this:
fit.1 <- lme(Group:Time ~ Group + Time + M0 + M1 + ... Mk, random~1|Subject)
This way, I could directly see which $M_1$ to $M_k$ terms is a significant predictor of the interaction term (or I could add the $M_1$ to $M_k$ terms one by one or use some other model selection method). However the main problem is that it does not work! It seems R does not like to have an interaction term as the dependent variable.
So here is what I want to know: is the basic idea behind the second approach sound? If yes, is there a way to make
Comment 1: The problem of finding the measures that can predict decline in longitudinal studies is not that rare, at least not in my corner of the world. For instance consider the case of neuro-degenrative diseases like Parkinson's or MS. From all kind of sources we know that these diseaes progress constantly and slowly. Thus it is interesting to find the measures that reflect the progress of the disease.