Principal component analysis
Andreas Pöge, Jost Reinecke
Abstract
Principal component analysis (PCA) belongs to a group of statistical procedures that are used to reduce the complexity of a given set of variables. For this purpose, PCA attempts to most adequately express a number of given variables by using a lower number of underlying dimensions (called components or factors). PCA shares this goal with factor analysis (FA), a related method, and is sometimes even subsumed under the topic of factor analysis. However, the two methods do differ in several respects, and some researchers adamantly differentiate between them. This chapter offers a brief overview of the basic concepts, history, and statistical fundamentals of the original PCA, as well as its estimation and evaluation, followed by an empirical example. In addition, we compare PCA and FA, after which we list some software programs and packages that offer PCA.