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

Abstract

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.