Abstract
It is first demonstrated that Aitken's selection formulas are equivalent to a linear transformation in the factor space. On this basis the Thomson-Ledermann theorem concerning the invariance of the number of common factors under selection, and a theorem concerning the invariance of factor loadings under selection are derived. A mathematical proof of the results of Thurstone, which are concerned with the invariance of simple structure under selection, is given. The paper provides a conclusive answer to the question, considered by Thurstone and Thomson, whether a multivariate selection is always reducible to successive univariate selections.
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References
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Ahmavaara, Y. The mathematical theory of factorial invariance under selection. Psychometrika 19, 27–38 (1954). https://doi.org/10.1007/BF02288991
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DOI: https://doi.org/10.1007/BF02288991