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    Latent variables in structural equation modeling are indeterminate, even with identified parameters. This indeterminacy, stemming from estimating latent variables via observed ones, impacts real-world analyses and depends on data characteristics.

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    Area of Science:

    • Statistics
    • Econometrics
    • Psychometrics

    Background:

    • Structural equation modeling (SEM) is widely used in various fields.
    • The Lisrel (Linear Structural Relations) model is a common SEM framework.
    • Understanding the properties of latent variables is crucial for valid SEM results.

    Purpose of the Study:

    • To investigate the indeterminacy of latent variables and errors in the Lisrel model.
    • To explain the source of this indeterminacy.
    • To assess the practical implications of latent variable indeterminacy.

    Main Methods:

    • Analysis of the Lisrel model's mathematical structure.
    • Examination of the relationship between latent and observed variables.
    • Investigation of parameter identification and estimation.

    Main Results:

    • Latent variables and errors in the Lisrel model are indeterminate, irrespective of parameter identification.
    • Indeterminacy arises from estimating latent variables using observed variables.
    • Empirical examples show negative minimum correlations between equivalent latent variables.
    • The degree of indeterminacy is data-dependent.

    Conclusions:

    • The indeterminacy of latent variables in Lisrel is a fundamental issue.
    • This indeterminacy has practical consequences for interpreting SEM results.
    • Researchers must consider data characteristics when assessing latent variable reliability.