Principal Themes Applied to Principal Components and Factor Analysis (PCA, FA) What Are PCA and FA and How Are They Similar to and

PCA and FA are exploratory multivariate methods that delineate the underlying dimensions in a large set of variables or individuals. Although we consider them multivariate methods, as they indeed handle multiple variables, both methods analyze only a single set of variables. Unlike the other methods discussed in this book, there is not the usual distinction between independent and dependent variables. Still, one of our central themes in multivariate methods is that of explaining the variance and covariance within and across sets of variables. To maintain this pervasive theme, we can consider the dimensions as a set of underlying independent variables (IVs) from which the actual measured (dependent) variables (DVs) emanate. We now elucidate how the 10 questions and themes relate to both PCA and FA.