Breaking Our Silence on Factor Score Indeterminacy

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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.

Original languageEnglish (US)
Pages (from-to)244-261
Number of pages18
JournalJournal of Educational and Behavioral Statistics
Issue number2
StatePublished - Apr 2023

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  • factor analysis
  • factor score indeterminacy
  • multivariate statistics
  • statistics education


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