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Note for version 9 users: in version 9, use rotate. See [MV] factor postestimation for more details.

How can I obtain the correlation between the factors after an oblique rotation?

Title   Correlations between factors after oblique rotation
Authors Gene Fisher, Department of Sociology, University of Massachusetts
Kenneth Higbee, StataCorp
Date April 1999; minor revisions March 2001

After factor analysis (the factor command), you can obtain several matrices using the matrix get command (see [P] matrix get). These matrices include

        Ld    factor loadings
        Ev    eigenvalues
        Psi   uniqueness
        Co    correlation matrix
        SD    standard deviations
        Mean  means

In addition after rotation (the rotate command), you can obtain

        L     factor loadings after rotation

The correlation matrix of the rotated factors can be computed as

        Phi = T*T'

where

        T = inverse(L'*L) * L'*A

	L = the factor loadings matrix after rotation

        A = the factor loadings matrix before rotation

So to obtain the correlation matrix of the rotated factors you

 . factor ...
 . rotate ...

 . mat L = get(L)
 . mat T = syminv(L'*L)*L'*get(Ld)
 . mat Phi = T*T'
 . mat list Phi
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