Principal Components Analysis , Exploratory Factor Analysis , and Confirmatory Factor Analysis

Principal components analysis and factor analysis are common methods used to analyze groups of variables for the purpose of reducing them into subsets represented by latent constructs (Bartholomew, 1984; Grimm & Yarnold, 1995). Even though PCA shares some important characteristics with factor analytic methods such as exploratory factor analysis (EFA) and confirmatory factor analysis (CFA), the similarities between the two types of methods are superficial. The most important distinction to make is that PCA is a descriptive method, whereas EFA and CFA are modeling techniques (Unkel & Trendafilov, 2010). Together, PCA, EFA, and CFA are used to analyze multiple variables for the purposes of data reduction, scale construction and improvement, and evaluation of validity and psychometric utility describes the appropriate problems to which each might be correctly applied, and discusses the similarities and differences between these three methods. Principal components analysis (PCA; Goodall, 1954) is a method for explaining the maximum amount of variance among a set of items by creating linear functions of those items for the purpose of identifying the smallest number of linear functions necessary to explain the total variance observed for the item set in the correlation matrix (Grimm & Yarnold, 1995). Put another way, PCA identifies the smallest number of factors or components necessary to explain as much (or all) of the variance as possible. In this context, a factor or component is a set of variables that, when combined in a linear fashion, explains some portion of the observed variance (Mulaik, 1990). The foundational assumption of PCA is that the total variance of each