The equivalence of partial least squares and principal component regression in the sufficient dimension reduction framework

• We establish the relationship between PCR and SDR.
• Based on the theory of SDR, we prove the equivalence of PCR and PLS.
• We define some indexes to evaluate the equivalence of PLS and PCR.

Partial least squares (PLS) and principal component regression (PCR) are two widely used techniques for dimension reduction in chemometrics. However, the relationship between PLS and PCR is not entirely understood. In this paper, we introduce the idea of sufficient dimension reduction (SDR) to chemometrics, and show that PLS and PCR are methods of SDR. Furthermore, this paper shows that these two methods are equivalent within the framework of SDR which means that there is no theoretical advantage of PLS over PCR in terms of prediction performance. The above conclusion is supported by the results of a simulated dataset and three real datasets.