Likelihood-based Item-Fit Indices for Dichotomous Item Response Theory Models
Published in: Applied Psychological Measurement, v. 24, no. 1, Mar. 2000, p. 50-64
Posted on RAND.org on January 01, 2000
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.
This report is part of the RAND Corporation External publication series. Many RAND studies are published in peer-reviewed scholarly journals, as chapters in commercial books, or as documents published by other organizations.
The RAND Corporation is a nonprofit institution that helps improve policy and decisionmaking through research and analysis. RAND's publications do not necessarily reflect the opinions of its research clients and sponsors.