Abstract
Procedures for oblique rotation of factors or principal components typically focus on rotating the pattern matrix such that it becomes optimally simple. An important oblique rotation method that does so is Harris and Kaiser's (1964) independent cluster (HKIC) rotation. In principal components analysis, a case can be made for interpreting the components on the basis of the component weights rather than on the basis of the pattern, so it seems desirable to rotate the components such that the weights rather than the pattern become optimally simple. In the present paper, it is shown that HKIC rotates the components such that both the pattern and the weights matrix become optimally simple. In addition, it is shown that the pattern resulting from HKIC rotation is columnwise proportional to the associated weights matrix, which implies that the interpretation of the components does not depend on whether it is based on the pattern or on the component weights matrix. It is also shown that the latter result only holds for HKIC rotation and slight modifications of it.
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This research has been made possible by a fellowship from the Royal Netherlands Academy of Arts and Sciences to the first author. The authors are obliged to an anonymous reviewer for the correction of some distrubing errors in the original manuscript.
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Kiers, H.A.L., Ten Berge, J.M.F. The Harris-Kaiser independent cluster rotation as a method for rotation to simple component weights. Psychometrika 59, 81–90 (1994). https://doi.org/10.1007/BF02294267
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DOI: https://doi.org/10.1007/BF02294267