Determining the number of components in PLS regression on incomplete data set.

Partial least squares regression - or PLS regression - is a multivariate method in which the model parameters are estimated using either the SIMPLS or NIPALS algorithm. PLS regression has been extensively used in applied research because of its effectiveness in analyzing relationships between an outcome and one or several components. Note that the NIPALS algorithm can provide estimates parameters on incomplete data. The selection of the number of components used to build a representative model in PLS regression is a central issue. However, how to deal with missing data when using PLS regression remains a matter of debate. Several approaches have been proposed in the literature, including the Q2 criterion, and the AIC and BIC criteria. Here we study the behavior of the NIPALS algorithm when used to fit a PLS regression for various proportions of missing data and different types of missingness. We compare criteria to select the number of components for a PLS regression on incomplete data set and on imputed data set using three imputation methods: multiple imputation by chained equations, k-nearest neighbour imputation, and singular value decomposition imputation. We tested various criteria with different proportions of missing data (ranging from 5% to 50%) under different missingness assumptions. Q2-leave-one-out component selection methods gave more reliable results than AIC and BIC-based ones.