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    Area of Science:

    • Statistics
    • Psychometrics
    • Quantitative Psychology

    Background:

    • Fitting propensity (FP) is crucial for model selection.
    • In structural equation modeling (SEM), FP is often simplified to solely consider the number of free parameters.
    • Other structural aspects influencing FP are frequently overlooked.

    Purpose of the Study:

    • To examine the relevance of fitting propensity (FP) in structural equation modeling (SEM) for model selection.
    • To demonstrate that SEMs with identical parameter counts but differing structures can exhibit distinct FPs.
    • To advocate for enhanced quantification and consideration of FP in SEM.

    Main Methods:

    • Conceptual analysis of fitting propensity within SEM.
    • Illustrative examples using diverse data patterns.
    • Examination of models from published SEM research.

    Main Results:

    • Models with the same number of free parameters can possess different fitting propensities due to structural variations.
    • This difference in FP can significantly impact model selection outcomes.
    • Current SEM practices may neglect important facets of FP.

    Conclusions:

    • Fitting propensity is a multifaceted concept in SEM, not solely determined by parameter count.
    • Quantifying and incorporating diverse aspects of FP is essential for robust model selection in SEM.
    • Further research and practical methods are needed to better assess FP in SEM.