Heirarchical Multivariate Modeling?
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