Likelihood-Based Item-Fit Indices for Dichotomous Item Response Theory Models
Top Cited Papers
- 1 March 2000
- journal article
- Published by SAGE Publications in Applied Psychological Measurement
- Vol. 24 (1), 50-64
- https://doi.org/10.1177/01466216000241003
Abstract
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.Keywords
This publication has 19 references indexed in Scilit:
- Item Response Theory for Scores on Tests Including Polytomous Items with Ordered ResponsesApplied Psychological Measurement, 1995
- A Conditional Item-Fit Index for Rasch ModelsApplied Psychological Measurement, 1994
- A Monte Carlo Investigation of Several Person and Item Fit Statistics for Item Response ModelsApplied Psychological Measurement, 1987
- The Analysis of Item-Ability Regressions: An Exploratory IRT Model Fit ToolApplied Psychological Measurement, 1985
- A Comparison of Several Goodness-of-Fit StatisticsApplied Psychological Measurement, 1985
- Comparison of IRT True-Score and Equipercentile Observed-Score "Equatings"Applied Psychological Measurement, 1984
- Using Simulation Results to Choose a Latent Trait ModelApplied Psychological Measurement, 1981
- Small-Sample Comparisons of Exact Levels for Chi-Squared Goodness-of-Fit StatisticsJournal of the American Statistical Association, 1978
- An Investigation of the Restraints with Respect to Sample Size Commonly Imposed on the Use of the Chi-Square StatisticJournal of the American Statistical Association, 1971
- A Procedure for Sample-Free Item AnalysisEducational and Psychological Measurement, 1969