Likelihood-Based Item-Fit Indices for Dichotomous Item Response Theory Models

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<jats:p> New goodness-of-fit indices are introduced for dichotomous item response theory (IRT) models. These indices are based on the likelihoods of number-correct scores derived from the IRT model, and they provide a direct comparison of the modeled and observed frequencies for correct and incorrect responses for each number-correct score. The behavior of Pearson’s X<jats:sup>2</jats:sup> ( S- X<jats:sup>2</jats:sup>) and the likelihood ratio G<jats:sup>2</jats:sup> ( S- G<jats:sup>2</jats:sup>) was assessed in a simulation study and compared with two fit indices similar to those currently in use ( Q1- X<jats:sup>2</jats:sup> and Q<jats:sub>1</jats:sub>- G<jats:sup>2</jats:sup>). The simulations included three conditions in which the simulating and fitting models were identical and three conditions involving model misspecification. S- X<jats:sup>2</jats:sup> performed well, with Type I error rates close to the expected .05 and .01 levels. Performance of this index improved with increased test length. S- G<jats:sup>2</jats:sup> tended to reject the null hypothesis too often, as did Q<jats:sub>1</jats:sub>- X<jats:sup>2</jats:sup> and Q<jats:sub>1</jats:sub>- G<jats:sup>2</jats:sup>. The power of S- X<jats:sup>2</jats:sup> appeared to be similar for all test lengths, but varied depending on the type of model misspecification. </jats:p>

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