Mixture Item Response Theory-Mimic Model

This study uses a new psychometric model (The mixture item response theory-MIMIC model) that simultaneously estimates differential item functioning (DIF) across manifest groups and latent classes. Current DIF detection methods investigate DIF either across manifest groups (e.g., gender, ethnicity, etc.), or across latent classes (e.g., solution strategies, speededness, etc.). Alternatively, one of these aspects is considered as the real source of DIF and the other aspect is considered as a proxy for the same source. This can only be true when manifest and latent classifications provide perfect or very high overlap. A combination of a Rasch type model for manifest group-DIF (G-DIF) and a mixture Rasch model for latent class-DIF (C-DIF) detection is applied as the mixture IRT-MIMIC model (MixIRT-MIMIC). A Markov chain Monte Carlo method called Gibbs sampler is applied for Bayesian estimation of parameters for MixIRT-MIMIC model as well as the Rasch model, and the mixture Rasch model. This study shows that in detection of DIF, when the group-class overlap is between 50% and 70%; manifest group approaches and latent class approaches can provide biased DIF, and item difficulty estimates for some test items that show G-DIF and C-DIF, simultaneously. However, for the same conditions MixIRT-MIMIC provides unbiased estimates for latent class-DIF (C-DIF) and item difficulty parameters, while the confounding is reflected as bias in G-DIF parameter estimates. Main factors of importance are group-class overlap and the overlap between DIF items. MixIRT-MIMIC contributes by; (1) estimating the unbiased magnitudes of G-DIF and C-DIF, (2) estimating the unbiased estimates of item difficulties when other approaches have biased estimates, (3) determining the overlap ratio (confounding) between groups and classes which is unknown a priori (4) true source(s) of DIF. Researchers, test developers, and state testing programs that are interested in detecting true sources of differences (e.g. cognitive, gender, ethnic) across individuals are potential users of MixIRT-MIMIC. It is important to note that this study is an initial step to detect both types of DIF simultaneously, and is limited to binary data and a special case of 2 groups by 2 classes, which can be applied to most DIF detection purposes. Its performance and extensions will be investigated for other possible situations.