It is shown that problems of rotational equivalence of restricted factor loading matrices in orthogonal factor analysis are equivalent to problems of identification in simultaneous equations systems with covariance restrictions. A necessary (under a regularity assumption) and sufficient condition for local uniqueness is given and a counterexample is provided to a theorem by J. Algina concerning necessary and sufficient conditions for global uniqueness.
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Paul A. Bekker (1986) studied this question.
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