Principal component analysis of event-related potentials: simulation studies demonstrate misallocation of variance across components.

Abstract

Simulated event-related potential (ERP) components were used to investigate the ability of principal component analysis (PCA), Varimax rotation and univariate analysis of variance (ANOVA) to reconstruct component wave shapes, to allocate variance correctly across components, and to identify the correct locus of simulated experimental treatments. The simulated ERPs consisted of 800 randomly weighted combinations of three 64-point components, corresponding to a 2 X 2 X 10 repeated-measures design with 20 subjects. Covariance PCAs, Varimax rotations and univariate ANOVAs were performed on each of 400 such simulations, 100 with no effect of any experimental treatment and 100 each with main effects on each of the 3 components. Eight hundred additional simulations were performed to investigate the effects of systematic variations in the size of the experimental treatments and the number of subjects per experiment. The wave shapes of the simulated components were reconstructed reasonably well, although not completely, by the rotated principal component (PC) loadings. However, comparison of rotated PC scores with the random weights used to generate the simulated ERPs indicated that PCA incorrectly allocated variance across overlapping components, producing dramatic increases in type I error (the largest in excess of 80%) for ANOVAs on one component when the true treatment effect was on another. Although these results should not be overgeneralized, they clearly demonstrate that the PCA-Varimax-ANOVA strategy can incorrectly distribute variance across components, resulting in serious misinterpretation of treatment effects. Additional simulation studies are needed to determine the generality of the variance misallocation problem; pending the outcome of such studies, results obtained with the PCA-Varimax-ANOVA strategy should be interpreted cautiously.