Component Analysis versus Common Factor Analysis: Some issues in Selecting an Appropriate Procedure

Abstract

Should one do a component analysis or a factor analysis? The choice is not obvious, because the two broad classes of procedures serve a similar purpose, and share many important mathematical characteristics. Despite many textbooks describing common factor analysis as the preferred procedure, principal component analysis has been the most widely applied. Here we summarize relevant information for the prospective factor/component analyst. First, we discuss the key algebraic similarities and differences. Next, we analyze a number of theoretical and practical issues. The more practical aspects include: the degree of numeric similarity between solutions from the two methods, some common rules for the number of factors to be retained, effects resulting from overextraction, problems with improper solutions, and comparisons in computational efficiency. Finally, we review some broader theoretical issues: the factor indeterminacy issue, the differences between exploratory and confirmatory procedures, and the issue of latent versus manifest variables.