Underlying Model
The general underlying model of multivariate PLS is
where is an matrix of predictors, is an matrix of responses; and are matrices that are, respectively, projections of X (the X score, component or factor matrix) and projections of Y (the Y scores); and are, respectively, and orthogonal loading matrices; and matrices and are the error terms, assumed to be i.i.d. normal. The decompositions of X and Y are made so as to maximise the covariance of T and U.
Read more about this topic: Partial Least Squares Regression
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