[R-sig-ME] Heirarchical Multivariate Modeling?

[Ken Beath]

On 19/09/2008, at 8:41 AM, Adam D. I. Kramer wrote:

> 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.

It is possible to create multilevel versions of multivariate methods,  
maybe not PCA, but for factor analysis, yes. The sem package could  
probably be coerced into fitting them for linear models, otherwise the  
commercial programs Latent Gold and MPlus are the only solutions. The  
Mplus site has lots of modelling info.

Ken