From dummy regression to prior probabilities in PLS‐DA

Different published versions of partial least squares discriminant analysis (PLS‐DA) are shown as special cases of an approach exploiting prior probabilities in the estimated between groups covariance matrix used for calculation of loading weights. With prior probabilities included in the calculation of both PLS components and canonical variates, a complete strategy for extracting appropriate decision spaces with multicollinear data is obtained. This idea easily extends to weighted linear dummy regression so that the corresponding fitted values also span the canonical space. Two different choices of prior probabilities are applied with a real dataset to illustrate the effect for the obtained decision spaces.