Efficient variable screening for multivariate analysis

It is shown how known algorithms for the comparison of all variables subsets in regression analysis can be adapted to subset comparisons in multivariate analysis, according to any index based on Wilks, Lawley-Hotelling, or Bartllet-Pillai statistics and, in some special cases, according to any function of the sample squared canonical correlations. The issues regarding the choice of an appropriate comparison criterion are discussed. The computational effort of the proposed algorithms is studied, and it is argued that, for a moderate number of variables, they should be preferred to stepwise selection methods. A software implementation of the methods discussed is freely available and can be downloaded from the Internet.