A latent factor is a novel variate
constructed from the manifest variates (measured variables) included in
the factor analysis. In the principal component model each factor, referred
to as a component, is uniquely constructed and considered determinate in
nature. In most varieties of the common factor model, however, the factors
are not uniquely constructed and are hence indeterminate. The scores on
the common factors are equivalently indeterminate, meaning that an infinite
number of sets of factor scores can be computed for any given analysis
that satisfy the stipulations of the common factor model. For example,
consider a researcher who conducts an iterated principal axis factor analysis
on a particular data set. The researcher extracts two common factors from
the correlation matrix, computes the pattern coefficients and factor correlations,
and then labels the first factor as “agreeableness / disagreeableness”.
The indeterminate nature of the factor scores makes it possible to compute
an infinite number of sets of such scores that would all be consistent
with the pattern coefficients. Moreover, under certain conditions an individual
in the analysis with a high ranking on agreeableness according to one set
of factor scores could receive a low ranking on agreeableness according
to another set of factor scores and the researcher would have no way of
deciding which ranking is “true” based upon the obtained results. In other
words, there would be no way of telling whether the individual is “truly”
agreeable or disagreeable. This mathematical problem, referred to as *factor
indeterminacy* or *factor score indeterminacy*,
was discovered in the 1920s and has been a source of considerable controversy
ever since. Unfortunately, most psychologists appear to be unaware of the
indeterminacy problem and fail to realize the importance of examining the
degree of indeterminacy in any given common factor. They also appear to
be unaware of the importance of evaluating the properties of their estimated
factor scores; for instance, assessing the degree to which the estimated
factor scores correlate with their respective factors or with one another.