An Introduction to Factor Analysis

The factor loadings k are parameters to be estimated that tap how the unobserved factors account for the observed variables: the larger the values of k, the more a particular variable is said to ‘‘load’’ on the corresponding factor. Note that the factor loadings k vary across survey items, but not across individuals. Put differently, items vary in the way they are explained by the underlying factors, but the relationships between underlying factors and observed responses is constant across individuals (hence the absence of an i subscript indexing k). Note also that there are fewer underlying factors than there are variables (p < k), consistent with the notion that like any statistical procedure, factor analysis is a device for ‘‘data reduction’’, taking a possibly rich though unwieldy set of survey responses and summarizing them with a simpler underlying structure.