Prediction error in partial least squares regression: a critique on the deviation used in The Unscrambler

Partial least squares (PLS) regression is commonly used for multivariate calibration of instruments. Because of the need to know the quality of the prediction in a specific unknown sample and the lack of theory, an ‘empirically found formula’ to express the uncertainty is utilized in The Unscrambler II software, the de-facto standard in computer software for PLS. In this critique the formula is examined theoretically and by simulation. It is concluded that this formula underestimates the root mean squared error of prediction in most practical applications of PLS. A change of the formula is planned in the next version of The Unscrambler. In the mean time users of The Unscrambler ver 5.5 or lower should multiply the reported deviation by a factor of at least 2(1 − (A+1)n), to get a reasonable estimate of the prediction error.