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    Assessing structural equation model fit is crucial for small sample sizes. Simulation studies reveal how sample size, estimation, and model misspecification impact fit indices, guiding their use in research.

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    Area of Science:

    • Statistics
    • Psychometrics
    • Quantitative Psychology

    Background:

    • Structural Equation Modeling (SEM) is widely used in various scientific disciplines.
    • Accurate assessment of model fit is essential for valid SEM applications, especially with limited sample sizes.
    • Numerous fit indices exist, but their performance under different conditions is not fully understood.

    Purpose of the Study:

    • To critically evaluate the behavior of various structural equation model fit indices.
    • To investigate the influence of sample size, estimation method, and model misspecification on fit index performance.
    • To provide evidence-based recommendations for using fit indices in SEM.

    Main Methods:

    • Review of existing literature on structural equation model fit indices.
    • Conducting simulation studies with varying sample sizes, estimation methods, and degrees of model misspecification.
    • Analysis of a confirmatory factor analysis model with a known population.
    • Analysis of an empirical dataset with an approximately known population.

    Main Results:

    • Fit indices demonstrate varying sensitivity to sample size, estimation methods, and model misspecification.
    • Simulation results highlight specific conditions under which certain fit indices perform more reliably or unreliably.
    • The choice of estimation method and the degree of model misspecification significantly affect the observed fit index values.

    Conclusions:

    • The selection and interpretation of structural equation model fit indices require careful consideration of study conditions.
    • Researchers should be aware of the limitations and performance characteristics of different fit indices when assessing model fit.
    • Recommendations are provided for the appropriate use of fit indices to enhance the rigor of SEM applications.