Using simulation results to choose a latent trait model

A latent trait model goodness-of-fit statistic was defined, and its relationships to several other commonly used fit statistics were described. Simulation data were used to examine the behavior of these fit statistics under conditions similar to those found with real data. The simulation data were generated for 36 pseudo-items and 1,000 simulees using three-, two-, and one-parameter logistic latent trait models. The data were analyzed using three-, two-, and one-parameter models. Between-model comparisons were made of the fit statistics, trait estimates, and item parameter estimates. The three generating models produced clearly different patterns of results. The simulation results were compared to results for real data involving seventh- and eighth-grade students’ performance on eight achievement tests. The achievement test results appeared most similar to the simulation results based on data generated with the three-parameter model. Some practical problems that can result from using an inappropriate model with multiple-choice tests are discussed