ERIC Number: EJ1371508
Record Type: Journal
Publication Date: 2023-Apr
Pages: 18
Abstractor: As Provided
ISBN: N/A
ISSN: ISSN-1076-9986
EISSN: EISSN-1935-1054
Available Date: N/A
Breaking Our Silence on Factor Score Indeterminacy
Waller, Niels G.
Journal of Educational and Behavioral Statistics, v48 n2 p244-261 Apr 2023
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.
Descriptors: Statistics Education, Multivariate Analysis, Factor Analysis, Factor Structure, Scores, Equations (Mathematics), Computation, Algorithms
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Publication Type: Journal Articles; Reports - Descriptive
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Language: English
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