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A Dual-Purpose Rasch Model with Joint Maximum Likelihood Estimation.

Xiao Luo, John T Willse

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    This study introduces the Rasch model with subdimensions (RMS) for reporting overall and diagnostic scores. The joint maximum likelihood estimation (JMLE) procedure efficiently estimates parameters, showing good performance across various conditions.

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    Area of Science:

    • Psychometrics
    • Statistical modeling

    Background:

    • Growing need for reporting both overall scores for decision-making and subscores for diagnostics.
    • Existing models may not adequately address the dual reporting requirement.

    Purpose of the Study:

    • To introduce and evaluate the Rasch model with subdimensions (RMS).
    • To propose a joint maximum likelihood estimation (JMLE) procedure for computationally efficient estimation within the RMS framework.
    • To assess the performance of the RMS model with JMLE under varying simulation conditions.

    Main Methods:

    • Application of the Rasch model with subdimensions (RMS).
    • Development and implementation of a joint maximum likelihood estimation (JMLE) procedure.
    • Conducting a simulation study with variations in sample size, test length, and subdimension loading structure.

    Main Results:

    • The JMLE procedure provided generally accurate parameter estimations for the RMS model.
    • Item and overall ability parameters estimated using RMS with JMLE were consistent with those from the standard Rasch model.
    • The model demonstrated good performance across different simulated conditions.

    Conclusions:

    • The Rasch model with subdimensions (RMS) effectively addresses the need for both overall and diagnostic scoring.
    • The proposed JMLE procedure offers a computationally efficient and reliable method for estimating RMS parameters.
    • The findings support the utility of RMS with JMLE in practical assessment scenarios.