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

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 X2 (S-X2) and the likelihood ratio G2 (S-G2) was assessed in a simulation study and compared with two fit indices similar to those currently in use (Q1 -X2 and Q1 -G2). The simulations included three conditions in which the simulating and fitting models were identical and three conditions involving model misspecification. S-X2 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-G2 tended to reject the null hypothesis too often, as did Q1 -X2 and Q1 -G2. The power Of S-X2 appeared to be similar for all test lengths, but varied depending on the type of model misspecification.