[R-sig-ME] Heirarchical Multivariate Modeling?

[Adam D. I. Kramer]

Dear colleagues,

  	I have an interest in what I would call "heirarchical multivariate
modeling." In a sense, I'm interested in extending the mixed model procedure
to an "unpredicted" multivariate case, or an analysis which would be an
extension to princomp() or prcomp() just as lmer() is an extension to lm().

  	My actual interest is in 1. estimating an aggregate PCA based on the
factor structures that exist within many individuals, each of which is based
on a different number of observations among the same set of variables, and
2. testing whether factor structures differ across people (e.g., whether
prediction improves if I model a random effect for subject). This can be
thought of as adding and testing a random effect to a PCA, or something
similar.

  	My first intuition of how to go about this would be to use the glmer
procedure, and attempt to model the entire set of variables as being
predicted by a random "intercept" for each subject, but before I undertake
this analysis, I thought it might be wise to see if anyone on this list had
any suggestions of a better way to go about this in R (or suggestions that
the above way is inappropriate).

  	Also, if anybody could recommend an article or two on the topic (I
have not seen any), I would be quite interested.

Cordially,
Adam Kramer