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    Area of Science:

    • Quantitative Psychology
    • Psychometrics
    • Behavioral Genetics

    Background:

    • The one-factor model is a foundational structure in psychometrics.
    • Latent variable models are widely used to represent unobserved constructs.
    • Comparing competing models is crucial for scientific advancement.

    Purpose of the Study:

    • To demonstrate the equivalence between the one-factor model and the quasi-simplex model.
    • To introduce a general nonstationary autoregressive moving average (NARMA) model.
    • To illustrate the application of the NARMA model in comparing different latent variable models.

    Main Methods:

    • Rewriting the one-factor model as a quasi-simplex model.
    • Applying addition theorems from time series analysis.
    • Deriving NARMA representations for specific growth curve models.

    Main Results:

    • The one-factor model can be expressed as a quasi-simplex model.
    • The nonstationary autoregressive moving average (NARMA) model unifies various latent variable models.
    • Equivalent NARMA representations were found for the hybrid behavior genetics model and the quasi-simplex model.

    Conclusions:

    • The NARMA model provides a unifying framework for latent variable models with continuous indicators and latent variables.
    • Rewriting models into a common framework, like NARMA, facilitates direct comparison.
    • The equivalence of NARMA representations for different models highlights their underlying structural similarities.