Assessing Fit of Alternative Unidimensional Polytomous IRT Models Using Posterior Predictive Model Checking

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Abstract

This article explored the application of the posterior predictive model checking (PPMC) method in assessing fit for unidimensional polytomous item response theory (IRT) models, specifically the divide-by-total models (e.g., the generalized partial credit model). Previous research has primarily focused on using PPMC in model checking for unidimensional and multidimensional IRT models for dichotomous data, and has paid little attention to polytomous models. A Monte Carlo simulation was conducted to investigate the performance of PPMC in detecting different sources of misfit for the partial credit model family. Results showed that the PPMC method, in combination with appropriate discrepancy measures, had adequate power in detecting different sources of misfit for the partial credit model family. Global odds ratio and item total correlation exhibited specific patterns in detecting the absence of the slope parameter, whereas Yen’s Q1 was found to be promising in the detection of misfit caused by the constant category intersection parameter constraint across items.

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