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 chi (2) (S-chi (2)) and the likelihood ratio G(2) (S-G(2)) was assessed in a simulation study and compared with two fit indices similar to those currently in use (Q(1)-X-2 and Q(1)-G(2)). The simulations included three conditions in which the simulating and fitting models were identical and three conditions involving model misspecification. S-X-2 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(2) tended to reject the null hypothesis too often, as did Q(1)-X-2 and Q(1)-G(2) The power of S-X-2 appeared to be similar for all test lengths, but varied depending on the type of model misspecification.