The Probability of Chance Correlation Using Partial Least Squares (PLS)

Abstract The frequency of chance correlation using partial least squares (PLS) has been measured experimentally for variously dimensioned data, comprising either completely random numbers, random numbers containing a perfect correlation within, and CoMFA field descriptors. This frequency, much lower than that for stepwise multiple regression, is maximal for datasets in which the number of descriptors equals the number of compounds, and surprisingly decreases indefinitely as the number of descriptors becomes much greater than the number of compounds. However, perfect correlations involving descriptor subsets are not detected by PLS if the number of irrelevant descriptors is excessive. In CoMFA applications, the probability of chance correlation is usually negligible. For example with 21 compounds a crossvalidated r 2 value greater than 0.25 will occur by chance in less than 5% of trials.