TY - JOUR

T1 - Breaking Our Silence on Factor Score Indeterminacy

AU - Waller, Niels G.

N1 - Publisher Copyright:
© 2022 The Author(s).

PY - 2022

Y1 - 2022

N2 - 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.

AB - 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.

KW - factor analysis

KW - factor score indeterminacy

KW - multivariate statistics

KW - statistics education

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U2 - 10.3102/10769986221128810

DO - 10.3102/10769986221128810

M3 - Article

AN - SCOPUS:85141792353

SN - 1076-9986

JO - Journal of Educational and Behavioral Statistics

JF - Journal of Educational and Behavioral Statistics

ER -