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    Area of Science:

    • Statistics
    • Psychometrics
    • Categorical Data Analysis

    Background:

    • The likelihood ratio test statistic G(2)(dif) is commonly used for nested model comparison in categorical data.
    • Its validity relies on the correct specification of the least restrictive model, especially in large samples.

    Purpose of the Study:

    • To investigate the impact of least restrictive model misspecification on the G(2)(dif) statistic.
    • To determine the robustness of G(2)(dif) under varying degrees of model misspecification.

    Main Methods:

    • A simulation study was conducted using nested item response theory models.
    • The G(2)(dif) statistic was evaluated under different levels of least restrictive model misspecification.

    Main Results:

    • The G(2)(dif) statistic demonstrated robustness only when the least restrictive model was only slightly misspecified.
    • Significant misspecification of the least restrictive model invalidated the chi-square approximation for G(2)(dif).

    Conclusions:

    • Assessing the absolute goodness of fit for the least restrictive model is crucial before utilizing G(2)(dif) for relative model fit assessment.
    • Incorrect conclusions may arise from using G(2)(dif) without validating the base model's adequacy.