A Comparison of Item Fit Statistics for Mixed IRT Models

Kyong Hee Chon · Won‐Chan Lee · Stephen B. Dunbar

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Psychometric Methodologies and Testing Educational Assessment and Pedagogy Statistical Methods and Bayesian Inference

Abstract

In this study we examined procedures for assessing model‐data fit of item response theory (IRT) models for mixed format data. The model fit indices used in this study include PARSCALE's G2, Orlando and Thissen's S − X2 and S − G2, and Stone's χ2* and G2*. To investigate the relative performance of the fit statistics at the item level, we conducted two simulation studies: Type I error and power studies. We evaluated the performance of the item fit indices for various conditions of test length, sample size, and IRT models. Among the competing measures, the summed score‐based indices S − X2 and S − G2 were found to be the sensible and efficient choice for assessing model fit for mixed format data. These indices performed well, particularly with short tests. The pseudo‐observed score indices, χ2* and G2*, showed inflated Type I error rates in some simulation conditions. Consistent with the findings of current literature, the PARSCALE's G2 index was rarely useful, although it provided reasonable results for long tests.

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References

1982A Rasch Model for Partial Credit Scoring 1992A Generalized Partial Credit Model: Application of an EM Algorithm 1972Estimating Item Parameters and Latent Ability when Responses are Scored in Two or More Nominal Categories 2000Likelihood-Based Item-Fit Indices for Dichotomous Item Response Theory Models 1990BILOG 3 : item analysis and test scoring with binary logistic models 2003Further Investigation of the Performance of S - X2: An Item Fit Index for Use With Dichotomous Item Response Theory Models 1981Using Simulation Results to Choose a Latent Trait Model 2008Performance of the Generalized S‐X2 Item Fit Index for Polytomous IRT Models

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2017Practical Consequences of Item Response Theory Model Misfit in the Context of Test Equating with Mixed-Format Test Data

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