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By Spencer Bennett, David Bowers

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In other words, variables pertaining to the father are more closely related to each other than they are to those relating to the son, and vice versa. Moreover, the two factors are correlated to some extent, showing that some underlying variable (second-order factor) determines both father's and son's status. The nature of this influence is such that when the father's status is high, the son's also tends to be high. We can see that this is the case by referring back to Fig. 2. The dotted axes A and B pass through the centroids of the two clusters we have isolated.

In our example, this is found to happen after seven iterations have been carried out. 14 gives the final set of factor loadings and communalities. 77 0. 71 0. 63 0. 67 0. 15(a), (b) and (c) respectively. 15(c)) of the original principal component analysis. It can be seen that the principal factor analysis has accounted for the original correlations between the five variables much more satisfactorily than the principal component analysis, and also more parsimoniously, since only two factors are required rather than three components.

Another method, described in Comrey [1973], and known as the 'minimum residual method', utilises only off-diagonal entries in the correlation matrix so that no communality estimates are required. In addition, it is not necessary to estimate the number of factors to be extracted. As with the preceding methods, communality estimates emerge as a by-product of the analysis. This method is similar to the principal components and principal factor methods except that the entries in the principal diagonal differ: for principal components, the entries are unity; for principal factors they are communality estimates; and for minimum residuals, they are zeros.

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