Journal Article

Measurement exchangeability and normal one‐factor models

Henk Kelderman

in Biometrika

Published on behalf of Biometrika Trust

Volume 91, issue 3, pages 738-742
Published in print September 2004 | ISSN: 0006-3444
Published online September 2004 | e-ISSN: 1464-3510 | DOI: https://dx.doi.org/10.1093/biomet/91.3.738
Measurement exchangeability and normal one‐factor models

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The one‐factor model restricts the covariance structure of the observed variables on the basis of assumptions about their relationship with an unobserved variable. It is hard to justify these assumptions on substantive or empirical grounds. In this paper, alternative measurement models are proposed that are based on exchangeability of variables after admissible scale transformations. They provide an alternative interpretation of the model and do not involve unobserved variables. They also yield a new one‐factor model for sum scales.

Keywords: Difference scale; Exchangeability; Factor analysis; Factor indeterminancy; Interchangeability; Interval scale; Latent trait model; Measurement model; Permutation invariance; Symmetry model

Journal Article.  0 words. 

Subjects: Probability and Statistics

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