The HPPLS Procedure

As discussed in the preceding sections, partial least squares depends on selecting factors of the predictors and of the responses that have maximum covariance, whereas principal components regression effectively ignores and selects to have maximum variance, subject to orthogonality constraints. In contrast, reduced rank regression selects to account for as much variation in the predicted responses as possible, effectively ignoring the predictors for the purposes of factor extraction. In reduced rank regression, the Y-weights are the eigenvectors of the covariance matrix of the responses that are predicted by ordinary least squares regression, and the X-scores are the projections of the Y-scores onto the X space.