Cross-validation (Stone, 1974) can be used to access the appropriate number of factors to fit.

The data are split into groups. One group of observations is ommitted and the PLS model is fitted for the remaining data.

Predictions are made for the ommitted data and the sums of squares of predicted minus observed is calculated :

The procedure is repeated until each observation has been deleted once.

The total sums of squares of predicted minus observed is used as a measure of the predictive usefulness of the factor.