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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 maximum-likelihood, unweighted least-squares, 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).

  • 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. 279-301) New York: Praeger.
  • Spearman, C. (1904) General intelligence objectively determined and measured. American Journal of Psychology 15, 201-293.

Richard C. Bell

Establ. 2003
Last update: 15 February 2004