The Comparison Study Of Three Measurement Invariance Methods

There are three methods in the study of measurement invariance, MCFA, IRT-LR and DFIT. The purpose of this study was to compare the differences among three Measurement Invariance Methods. Simulated and empirical data were employed to understand the sensitivity and consistency of three methods. The power and Type I error were calculated in the simulated study.In the first study, given the item parameters and ability parameter, simulated data were generated under several conditions: two ability distributions, two sample sizes and three DIF types. The sensitivity of three methods are compared based on the power and Type I error. In the second study, the consistency of three methods was examined in the empirical data, collected by the Interpersonal Reactivity Index (IRI). The conclusions of this study were summarized as follows.(1) The simulation study showed that DFIT perform best, next MCFA, last IRT-LR.(2) The simulation study showed that the difference in the ability distributions across focal and reference groups had little adverse effect on the accuracy of three methods.(3) The simulation study showed that the power of three methods increased as the sample size grew.(4) The simulation study showed that while the three methods were sensitive to the uniform DIF items, they were not sensitive to the nonuniform DIF items(5) The results from empirical data showed that the three methods yielded low consistency on detecting DIF items.