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    Area of Science:

    • Statistics
    • Psychometrics

    Background:

    • The factor analysis model is widely used in various scientific disciplines.
    • Indeterminacy in factor analysis has been a long-standing debate with two main interpretations.

    Purpose of the Study:

    • To clarify the issue of indeterminacy in the factor analysis model.
    • To evaluate the two main positions on factor analysis indeterminacy: the alternative solution position and the posterior moment position.

    Main Methods:

    • Conceptual analysis of the criteria for defining latent common factors.
    • Examination of the mathematical and statistical underpinnings of factor analysis indeterminacy.

    Main Results:

    • The debate on factor analysis indeterminacy hinges on the criterion for identifying latent common factors.
    • The alternative solution position is deemed correct, defining latent common factors as random variates determined by model constraints.
    • The posterior moment position is identified as a conflation of the model's criterion with external concepts.

    Conclusions:

    • The criterion for latent common factors is derived from the factor analysis model's equations.
    • The alternative solution position provides a valid interpretation of indeterminacy.
    • Implications for applied factor analysis research are discussed, emphasizing the correct interpretation of latent common factors.