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Maraun, Michael; Heene, Moritz (2016): A note on the implications of factorial invariance for common factor variable equivalence. In: Communications in Statistics-theory and Methods, Vol. 45, No. 14: pp. 4181-4193
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Abstract

There has come to exist within the psychometric literature a generalized belief to the effect that a determination of the level of factorial invariance that holds over a set of k populations j, j = 1..s, is central to ascertaining whether or not the common factor random variables j, j = 1..s, are equivalent. In the current manuscript, a technical examination of this belief is undertaken. The chief conclusion of the work is that, as long as technical, statistical senses of random variable equivalence are adhered to, the belief is unfounded.