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Greetings,

I am exploring a problem in multivariate statistics where I will have  
a number of related response variables. For each response variable I  
would like to explore the extent to which a large number of potential  
predictor variables can "explain" the observed variation in the  
responses. I anticipate having up to k=200 predictors and several  
thousand observations (cases) to work with. I know that factor  
analysis and principal component analysis are two commonly used means  
of handling this problem. I was curious what other techniques might  
be used to statistically identify a subset of the potential predictors?

Thanks,

-Mark