The Invariance Problem in Factor Analysis

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Abstract
The aim was to determine how accurately the varimax and promax methods of rotation of axes would reproduce known factor matrices. Thirteen factor matrices were contrived, varying widely in percentage of univocal tests. It was found that only when all tests are univocal, or nearly so, could one be reasonably confident that an obtained factor matrix faithfully reproduces a contrived matrix. In some analyses, the pictures of factor structures were distorted and a few factors were entirely lost. Implications for empirical factor analyses are pointed out, with some suggested remedies.