Profile Factor Analysis and Variable Factor Analysis

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Abstract
Nunnally (1962) mentions three types of profile factor analyses: correlational, covariance, and raw score sums of crossproducts. When principal components factors are used, each of these profile analyses corresponds to a precisely equivalent factor analysis of variables. In particular, if variables have previously been standardized over Ss, factor analysis of raw sums of profile crossproducts yields exactly the same results as factor analysis of correlations among variables. An example is worked out in which it is shown that factor analysis of raw sums of profile crossproducts yields exactly the same factors as factor analysis of correlations between variables. It is concluded that, of the procedures considered, factor analysis of correlations between variables is generally the most useful, because findings are easiest to communicate, and because results can be used to estimate results of the other possible factor analyses.