loadings = factoran (X, nfac) performs principal axis factoring to extract nfac factors from the $N\times \; P$ data matrix X, where rows correspond to observations and columns to variables. The output loadings is a $P\times$nfac matrix whose columns contain the loadings on each factor, in decreasing order of importance.

[loadings, specvar] = factoran (…) also returns a $P\times \; 1$ vector specvar containing the specific variances (unique variances) for each variable.

[loadings, specvar, fscores] = factoran (…) also returns the $N\times$nfac matrix fscores of estimated factor scores, computed using the regression method.

The analysis is performed on the correlation matrix of the standardized X. Initial communalities are set to 1. Iterations continue until the maximum change in communality is less than 1e-4 or 50 iterations are reached. The sign of each loading vector is chosen so that the element with largest absolute value is positive.

References

1. Harman, H. H., Modern Factor Analysis, 3rd Edition, University of Chicago Press, 1976.

See also: barttest, pca, pcacov, pcares

Source Code: factoran