Abstract
The allocation of a (treatment) condition-effect on the wrong principal component (misallocation of variance) in principal component analysis (PCA) has been addressed in research on event-related potentials of the electroencephalogram. However, the correct allocation of condition-effects on PCA components might be relevant in several domains of research. The present paper investigates whether different loading patterns at each condition-level are a basis for an optimal allocation of between-condition variance on principal components. It turns out that a similar loading shape at each condition-level is a necessary condition for an optimal allocation of between-condition variance, whereas a similar loading magnitude is not necessary.
Highlights
1.1 Condition Effects in Principal Component AnalysisPrincipal component analysis (PCA) has regularly been performed for the analysis of event-related potentials of the electroencephalogram (Dien, Khoe & Mangun, 2007; Dien, 2010; Kayser & Tenke, 2003, 2005)
According to Wood and McCarthy (1984) misallocation of variance occurs when a single between-condition effect that can in principle be allocated on a single principal component analysis (PCA) component is allocated on more than one component in a given PCA solution
The present study describes constraints that are to be imposed on the component loading matrices in order to avoid misallocation of variance
Summary
Principal component analysis (PCA) has regularly been performed for the analysis of event-related potentials of the electroencephalogram (Dien, Khoe & Mangun, 2007; Dien, 2010; Kayser & Tenke, 2003, 2005). In the context of event-related potentials, PCA is often performed for observed variables representing k levels of at least one (experimental) condition factor, so that the components represent a mixture of the between- and within-condition variance. (experimental) condition factors occur in several areas of research and PCA is performed in several areas of research and has been adapted to several different methodological contexts (Jolliffe & Cadima, 2016). It is interesting to know how experimental condition effects are optimally allocated on principal components
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