# Factor Analysis as a Classification Method - Hierarchical Factor Analysis

Instead of computing loadings for often difficult to interpret oblique factors, the Factor Analysis module in STATISTICA uses a strategy first proposed by Thompson (1951) and Schmid and Leiman (1957), which has been elaborated and popularized in the detailed discussions by Wherry (1959, 1975, 1984). In this strategy, STATISTICA first identifies clusters of items and rotates axes through those clusters; next the correlations between those (oblique) factors is computed, and that correlation matrix of oblique factors is further factor-analyzed to yield a set of orthogonal factors that divide the variability in the items into that due to shared or common variance (secondary factors), and unique variance due to the clusters of similar variables (items) in the analysis (primary factors). To return to the example above, such a hierarchical analysis might yield the following factor loadings:

 STATISTICA FACTOR ANALYSIS Secondary & Primary Factor Loadings Factor Second. 1 Primary 1 Primary 2 WORK_1 .483178 .649499 .187074 WORK_2 .570953 .687056 .140627 WORK_3 .565624 .656790 .115461 HOME_1 .535812 .117278 .630076 HOME_2 .615403 .079910 .668880 HOME_3 .586405 .065512 .626730 MISCEL_1 .780488 .466823 .280141 MISCEL_2 .734854 .464779 .238512 MISCEL_3 .776013 .439010 .303672 MISCEL_4 .714183 .455157 .228351

Careful examination of these loadings lead to the following conclusions:

1. There is a general (secondary) satisfaction factor that likely affects all types of satisfaction measured by the 10 items;

2. There appear to be two primary unique areas of satisfaction that can best be described as satisfaction with work and satisfaction with home life.

Wherry (1984) discusses in great detail examples of such hierarchical analyses, and how meaningful and interpretable secondary factors can be derived.

Confirmatory Factor Analysis. Over the past 15 years, so-called confirmatory methods have become increasingly popular (e.g., see Jöreskog and Sörbom, 1979). In general, one can specify a priori, a pattern of factor loadings for a particular number of orthogonal or oblique factors, and then test whether the observed correlation matrix can be reproduced given these specifications. Confirmatory factor analyses can be performed via STATISTICA's general Structural Equation Modeling (SEPATH) module. Note that the Examples section of SEPATH includes several examples of such analyses.