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    Area of Science:

    • Statistics
    • Quantitative Psychology
    • Econometrics

    Background:

    • Model evaluation is crucial in Structural Equation Modeling (SEM).
    • Numerous model fit indices are reported in SEM publications.
    • Interpretation often assumes test statistics follow chi-square distributions.

    Purpose of the Study:

    • Investigate properties of SEM fit indices when chi-square assumptions are violated.
    • Propose methods for approximating fit index distributions.
    • Clarify the influence of various conditions on fit index values.

    Main Methods:

    • Examined commonly used fit indices under relaxed distributional assumptions.
    • Identified sensible statistics for fit index evaluation involving degrees of freedom.
    • Proposed linear approximation of fit index distributions based on conditions like sample size and data distribution.

    Main Results:

    • Commonly used fit indices show substantial changes in linear relationships when conditions vary.
    • The slope and intercept of these relationships are sensitive to sample size, data distribution, and base statistics.
    • A fit index showing minimal change may be artificially influenced.

    Conclusions:

    • Fit index values reflect more than just model fit, including uncontrollable factors.
    • Recommends a nuanced approach to using fit indices in SEM.
    • Highlights the need for careful consideration of underlying assumptions and conditions during SEM analysis.