Factor Analysis
 Hierarchical Factor Analysis
Oblique
Factors. Some authors (e.g., Cattell & Khanna; Harman,
1976; Jennrich & Sampson, 1966; Clarkson & Jennrich, 1988) have
discussed in some detail the concept of oblique
(nonorthogonal) factors in order to achieve more interpretable
simple structure (refer to the Introductory
Overview). Specifically, computer (algorithmic) strategies
have been developed to rotate factors so as to best represent "clusters"
of variables, without the constraint of orthogonality of factors. However,
the oblique factors produced by such rotations are often not easily interpreted.
For example, suppose we analyzed the responses to a questionnaire asking
about people's satisfaction with various aspects of their lives. Let us
assume that the questionnaire contains 3 items designed to measure satisfaction
with one's work, 3 items designed to measure satisfaction with one's home
life, and 4 items designed to measure overall (miscellaneous) satisfaction.
Let us also assume that people's responses to those last 4 items are affected
about equally by their satisfaction at home (Factor
1) and at work (Factor 2).
In this case, an oblique rotation will likely produce two correlated factors
with lessthanobvious meaning, that is, with generally many crossloadings.
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 are computed, and
that correlation matrix of oblique factors is further factoranalyzed
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:
There is a general (secondary)
satisfaction factor that likely affects all types of satisfaction measured
by the 10 items;
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 examples of such hierarchical analyses in great
detail and how meaningful and interpretable secondary factors can be derived.