Principal component analysis of event‐related potentials: Misallocation of variance revisited

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Abstract
Misallocating variance, in event-related potential analysis, refers to attributing an experimental effect to components not actually affected. A vector interpretation of the relationship between mathematically derived and true underlying components shows that misallocation depends exclusively on incorrect identification of the affected component. Simulations, using seven imperfect rotations, confirmed all predictions from the vector interpretation concerning the presence, direction, and size of misallocated variance. Contrary to principal component analysis (PCA), Möucks's topographic component model (TCM) is not subject to rotation problems. These two methods were compared over 100 simulations in which the components had constant waveforms and topographies across participants. The group effect was always detected, but only PCA and not TCM showed significance on other components, except when their random weights happened to differ between groups.