Monte Carlo Based Null Distribution for an Alternative Goodness‐of‐Fit Test Statistic in IRT Models

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Nonparametric Item Response Function Estimation for Assessing Parametric Model Fit (2001, methodology): “The distribution of a χ2 statistic for the null hypothesis of model fit has been studied (Stone, 2000) using monte carlo simulation.”
Nonparametric Item Response Theory in Action: An Overview of the Special Issue (2001, methodology): “Their bootstrapped hypothesis test might be less biased in favor of the PIRT model than other parametric bootstrap techniques (e.g., Gelman, Meng, & Stern, 1996; Stone, 2000).”
An Investigation of the Performance of the Generalized S-X2 Item-Fit Index for Polytomous IRT Models (2007, methodology): “According to Hambleton, Swaminathan and Rogers (1991), and Stone (2000), a common strategy for assessing item-fit of an IRT model can be summarized as follows: (1) estimate the item and ability parameters under the chosen model, (2) classify examinees into K homogeneous groups in terms of their…”
Performance of the generalized S-X2 item fit index for the graded response model (2011, background): “According to Stone (2000) and Lee et al. (2002), two main causes of lack of fit between observed data and model predictions are (1) violations to the model assumptions (e.g., unidimensionality) and (2) inadequacies in estimation procedures (i.e., a huge discrepancy between the expected item…”