Comparing patterns of component loadings: Principal Component Analysis (PCA) versus Independent Component Analysis (ICA) in analyzing multivariate non-normal data

Principal component analysis identifies uncorrelated components from correlated variables, and a few of these uncorrelated components usually account for most of the information in the input variables. Researchers interpret each component as a separate entity representing a latent trait or profile in a population. However, the components are guaranteed to be independent and uncorrelated only when the multivariate normality of the variables is assumed. If the normality assumption does not hold, components are guaranteed to be uncorrelated, but not independent. If the independence assumption is violated, each component cannot be uniquely interpreted because of contamination by other components. Therefore, in the present study, we introduced independent component analysis, whose components are uncorrelated and independent even when the multivariate normality assumption is violated, and each component carries unique information.