Partial least squares analysis with cross-validation for the two-class problem: A Monte Carlo study

A method for statistical analysis of two independent samples with respect to difference in location is investigated. The method uses the partial least squares projections to latent structures (PLS) with cross-validation. The relation to classical methods is discussed and a Monte Carlo study is performed to describe how the distribution of the test-statistic employed depends on the number of objects, the number of variables, the percentage variance explained by the first PLS-component and the percentage missing values. Polynomial approximations for the dependency of the 50 per cent and the 5 per cent levels of the test-statistic on these factors are given. The polynomial for the 50 per cent level is complicated, involving several first-, second- and third-degree terms, whereas the polynomial for the 5 per cent level is dependent only on the number of objects and the size of the first component. A separate Monte Carlo experiment indicates that a moderate difference in sample size does not affect the distribution of the test-statistic. The multi-sample location problem is also studied and the effect of increasing the number of samples on the test-statistic is shown in simulations. Copyright © 1987 John Wiley & Sons Ltd.