Breaking Our Silence on Factor Score Indeterminacy

Autor/in	Waller, Niels G.
Titel	Breaking Our Silence on Factor Score Indeterminacy
Quelle	In: Journal of Educational and Behavioral Statistics, 48 (2023) 2, S.244-261 (18 Seiten)Infoseite zur Zeitschrift PDF als Volltext Verfügbarkeit
Sprache	englisch
Dokumenttyp	gedruckt; online; Zeitschriftenaufsatz
ISSN	1076-9986
DOI	10.3102/10769986221128810
Schlagwörter	Statistics Education; Multivariate Analysis; Factor Analysis; Factor Structure; Scores; Equations (Mathematics); Computation; Algorithms + Suchen Sie Ihr Suchwort? Multivariate Analyse; Faktorenanalyse; Faktorenstruktur; Equations; Mathematics; Gleichungslehre; Algorithm; Algorithmus
Abstract	Although many textbooks on multivariate statistics discuss the common factor analysis model, few of these books mention the problem of factor score indeterminacy (FSI). Thus, many students and contemporary researchers are unaware of an important fact. Namely, for any common factor model with known (or estimated) model parameters, infinite sets of factor scores can be constructed to fit the model. Because all sets are mathematically exchangeable, factor scores are indeterminate. Our professional silence on this topic is difficult to explain given that FSI was first noted almost 100 years ago by E. B. Wilson, the 24th president (1929) of the American Statistical Association. To help disseminate Wilson's insights, we demonstrate the underlying mathematics of FSI using the language of finite-dimensional vector spaces and well-known ideas of regression theory. We then illustrate the numerical implications of FSI by describing new and easily implemented methods for transforming factor scores into alternative sets of factor scores. An online supplement (and the fungible R library) includes R functions for illustrating FSI. (As Provided).
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Erfasst von	ERIC (Education Resources Information Center), Washington, DC
Update	2024/1/01