
Factor analysis


Factor analysis is a technique
which attempts to account for the covariation among observed variables
by positing the presence of latent or unobserved variables. The
technique was first promulgated by Spearman (1904) who used the concept
of ‘general intelligence’ to account for the covariation among
cognitive variables. It is akin to
the notion of partial correlation. Supposing we had two variables A and
B, which correlated 0.56; and each of them correlated with a third
variable
C, such that the correlation between A and C was 0.70 and that between
B
and C was 0.80. The partial correlation between A and B (taking
correlations
with C into account) would be 0.00. This was the gist of Spearman’s
argument,
C taking the role of general intelligence and A and B being the
performance on two cognitive tasks. Of course we don’t know the
correlation of any latent variable and factor analysis is a procedure
which attempts to estimate this. It is not a simple matter and involves
an iterative procedure which searches for values for common factor
loadings and unique variances which best match the data. There are
various criteria for judging the degree of match, such as
maximumlikelihood, unweighted leastsquares, and minres (minimum
residual). Some criteria (such as maximum likelihood) provide a
statistical test of
the fit of the factor model to the data. While the resultant matrix of
factor loadings provides a ‘best’ fit in some sense, it is not a unique
solution, and the factors are almost always rotated so that the
alignment of variables with factors enables the factors to be
interpreted in some substantive sense. Although factor analysis and principal components
often give similar results, an important practical distinction between
the
two lies in the fact that if the number of factors is changed, all the
loadings in a factor analysis will change while those from principal
components
do not. Factor analysis also has problems in estimation particularly
with
small samples and for this reason has rarely been used in the analysis
of repertory grid data (but see Pruzek (1988) for an exception). 

References


 Pruzek,
R. M. (1988) Latent variable methods for analyzing grid structures. In
J. C. Mancuso and M. L. G. Shaw (Eds.), Cognition and personal
structure: Computer access and analysis (pp. 279301) New York:
Praeger.
 Spearman,
C. (1904) General intelligence objectively determined and measured. American
Journal of Psychology 15, 201293.


Richard C. Bell


