Principal Component Analysis

A widely recognized fact about social, behavioral, and educational phenomena is that they are exceedingly complex. To understand them well, therefore, it is typically necessary to examine many of their aspects that are usually reflected in studied variables. For this reason, researchers commonly collect data from a large number of interrelated measures pertaining to a phenomenon under investigation. To comprehend this multitude of variables, it becomes desirable to reduce them to more fundamental measures with the property that each of them represents a subset of the initial interrelated variables. For example, an opinion questionnaire may contain numerous questions pertaining to several personality characteristics. Reducing these questions so as to be able to collectively summarize each of the characteristics would clearly help to more readily understand the latter. Principal component analysis (PCA) is a statistical technique that has

been specifically developed to address this data reduction goal. PCA not only allows such data reduction, but also accomplishes it in a manner that permits its results to be used in applications of other multivariate statistical methods (e.g., analysis of variance or regression analysis). In general terms, the major aim of PCA is to reduce the complexity of the interrelationships among a potentially large number of observed variables to a relatively small number of linear combinations of them, which are referred to as principal components. This goal typically overrides in empirical research its secondary aim, that is, interpretation of the principal components. To a large extent, the interpretation of principal components is generally guided by the degree to which each variable is associated with a particular component. Those variables that are found to be most closely related to a component in question are used as a guide for its interpretation. While interpretability of principal components is always desirable, a PCA is worthwhile undertaking even when they do not have a clear-cut substantive meaning.