The partial least squares (PLS) approach first constructs new explanatory variables, known as factors (or components), which are linear combinations of available predictor variables. A small subset of these factors is then chosen and retained for prediction.

Professors Prasad Naik and Chih-Ling Tsai study the performance of PLS in estimating single-index models, especially when the predictor variables exhibit high collinearity. The authors show that PLS estimates are consistent up to a constant of proportionality. They present three simulations studies that compare the performance of PLS in estimating single-index models with that of sliced inverse regression (SIR).