ABSTRACT
The primary difference, conceptually, between exploratory factor analysis and principal components analysis is that in EFA, one postulates that there is a smaller set of unobserved (latent) variables or constructs that underlie the variables that actually were observed or measured; whereas, in PCA. one is simply trying to mathematically derive a relatively small number of variables to use to convey as much of the information in the observed/measured variables as possible. In other words, EFA is directed at understanding the relations among variables by understanding the constructs that underlie them, whereas PCA is simply directed toward enabling one to use fewer variables to provide the same information that one would obtain from a larger set of variables. There are actually a number of different ways of computing factors for factor analysis; in this chapter, we will only use one of these methods, principal axis factor analysis (PA), We selected this approach because it is highly similar mathematically to PCA. The primary difference, computationally, between PCA and PA is that in the former, the analysis typically is performed on an ordinary correlation matrix, complete with the correlations of each item or variable with itself, whereas in PA factor analysis, the correlation matrix is modified such that the correlations of each item with itself are replaced with a “communality”—a measure of that item’s relation to all other items (usually a squared multiple correlation). Thus, PCA is trying to reproduce all information (variance and covariance) associated with the set of variables, whereas PA factor analysis is directed at understanding only the covariation among variables.
