A TEST OF SIGNIFICANCE FOR PARTIAL LEAST-SQUARES REGRESSION

Partial least squares (PLS) regression is a commonly used statistical technique for performing multivariate calibration, especially in situations where there are more variables than samples. Choosing the number of factors to include in a model is a decision that all users of PLS must make, but is complicated by the large number of empirical tests available. In most instances predictive ability is the most desired property of a PLS model and so interest has centred on making this choice based on an internal validation process. A popular approach is the calculation of a cross-validated r2 to gauge how much variance in the dependent variable can be explained from leave-one-out predictions. Using Monte Carlo simulations for different sizes of data set, the influence of chance effects on the cross-validation process is investigated. The results are presented as tables of critical values which are compared against the values of cross-validated r2 obtained from the user's own data set. This gives a formal test for predictive ability of a PLS model with a given number of dimensions.