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