Statistical variation in progressive scrambling

AbstractThe two methods most often used to evaluate the robustness and predictivity of partial least squares (PLS) models are cross-validation and response randomization. Both methods may be overly optimistic for data sets that contain redundant observations, however. The kinds of perturbation analysis widely used for evaluating model stability in the context of ordinary least squares regression are only applicable when the descriptors are independent of each other and errors are independent and normally distributed; neither assumption holds for QSAR in general and for PLS in particular. Progressive scrambling is a novel, non-parametric approach to perturbing models in the response space in a way that does not disturb the underlying covariance structure of the data. Here, we introduce adjustments for two of the characteristic values produced by a progressive scrambling analysis -- the deprecated predictivity ($Q_{\rm s}^{\ast^2}$) and standard error of prediction (SDEPs*) -- that correct for the effect of introduced perturbation. We also explore the statistical behavior of the adjusted values ($Q_{\rm 0}^{\ast^2}$ and SDEP0*) and the sensitivity to perturbation (dq2/dryy ′2). It is shown that the three statistics are all robust for stable PLS models, in terms of the stochastic component of their determination and of their variation due to sampling effects involved in training set selection.