Abuses of Factor Scores

A variant of the method of principal components which is due to Hotelling (1933), is currently perhaps the most popular choice for analyzing a group of variables into factors. The practitioner often refers to components analysis as analysis with l's in the diagonal. Kaiser's suggestion (1960; 1964) to retain only the same number of factors as there are latent roots greater than one of the matrix, R, of intercorrelations among the variables has gained wide acceptance. In a large percentage of analyses performed today called analysis, Kaiser's rule for selecting the number of factors to retain after the resolution of R into principal components is used, then these are rotated orthogonally by means of Kaiser's varimax procedure (Kaiser, 1958). Not all factor analysis experts would agree that the truth is thus revealed, but few of them object to this procedure on the grounds that it lacks good psychometric and statistical justification. However, the techniques often used by researchers to calculate as the final step in the analysis have the blessings of no factor analysis specialists. Many researchers operate under the misapprehension that following a components-type factor analysis scores on a factor are obtained by weighting scores on variables by the loadings of the variables on the rotated factor, or that scores on a factor are obtained by summing the scores on the variables which have high (in absolute value) loadings on the factor. As an illustration of these two procedures, suppose that four variables have the following loadings on a varimax rotated factor: