Nuisance sources of variance in principal components analysis of event-related potentials.

This paper describes a method of disentangling different sources of variance contributing to component extraction in Principal Components Analysis (PCA) of event-related potentials. Those sources not of interest for a given experiment may he easily discarded prior to component extraction. A real data example is presented for comparison of the different approaches, showing advantages for the new methods. They also exhibited more success in detecting experimental effects as shown in subsequent analysis of variance procedures on component scores. In the latter framework, various issues of validity of subsequent testing procedures for all principal component approaches are addressed theoretically as well as empirically hy a split-sample cross-validation study. It is claimed that data-adaptive computation of component scores does not constitute a crucial issue. Finally, a bootstrap simulation provides evidence that the methods proposed are superior to the usual PC.'V approach in capability and reliahility in the assessment of experimental effects. DESCRIPTORS: Event-related potentials. Principal Components Analysis, Sources of variance. Analysis of variance. Cross-validation. In Principal Components Analysis (PCA) of event-related potentials (ERPs), as proposed by Donchin and Heffley (1978), the variables are the time points of averaged ERPs, and observations consist of several potentials within each subject of a sample of subjects. Frequently observations within subjects refer to different electrode locations and to different experimental conditions. The goal of the analysis is usually to find components reflecting the experimentally induced variation. However, other sources of variance enter into the analysis in the same way and contribute to the components extracted. This was discussed, e.g., by Wastell (1981) who assumed that interindividual variance was a confounding source. The problem of different sources of variance led some authors to perform a separate PCA for each experimental condition This work has been performed as pari of the research program ofthe Sonderforschungsbereich 116 (project M2) at the University of Heidelberg and was made possible by financial suppon from the Deutsche Forschungsgemeinschaft. Note added in proof: We learned only recently that an approach quite similar to the methods given here was proposed in a different framework, by J. Fahrenberg and F. Foerster (1982): "Covariation and consistency of activation parameters," by J. Fahrenberg & F. Foerster, Biological Psychology, 15, 151-169. Address requests for reprints to: Joachim Mocks, Zentralinstitut fur Seelische Gesundheit, P.O.B. 5970, 6800 Mannheim 1, Federal Republic of Germany. 6 (Ruchkin, Munson, & Sutton, 1982), or several analyses with one 'grand' PCA using all of the data (Friedman, Vaughan, & Erlenmeyer-Kimling, 1981). The present paper describes a method which shows how different sources of variation may be separated from each other. Nuisance sources, understood as those not arising out of differences induced by experimental variation, may be discarded prior to component extraction. For illustration, we will give a real data application. Funher, we will address the problem of validity of ANOVA results performed with component scores by theoretical considerations and empirically by a splitsample cross-validation. The reliability of the assessment of experimental effects is funher investigated using a bootstrap simulation. As a by-product, the present approach allows funher insight into some methods which have been used to get rid ofthe interindividual variance, like standardizing amplitudes within subjects (Callaway, Halliday, & Herning, 1983) or using the averages across subjects as input (McCallum, Curry, Cooper, Pocock, & Papakostopoulos, 1983). Let us finally note that the present discussion is indifferent to the debate about the pros and cons of rotation (Rosier & Manzey, 1981; Wastell, 1981). Decomposition of Total Variance For the following we will use algebraic methods for the decomposition ofthe sum of squares, similar