Examining Measurement Invariance in Bayesian Item Response Theory Models: A Simulation Study

The aim of the study is to determine a measurement invariance cut-off point based on item parameter differences in Bayesian Item Response Theory Models. Within this scope, Bayes factor estimated for testing invariance. For purpose, simulation conducted. data were generated R software each condition under one-parameter logistic model 10 binary (1-0 scored) items. test was performed various group sizes (n=500, 1000, 1500 and 2000) difficulty parameters (dk=0, dk=0.1, dk=0.3, dk=0.5 dk=0.7). analyzes WINBUGS using codes written R. A that provides evidence calculated depending differences. Savage–Dickey density ratio, one MCMC sampling schemas, used calculate factor. As result, if difference dk=0.3 are or larger, cannot be achieved. However, small sample (n=1000 less) interpretation should done carefully. When dk=0.5, there invariant items only n=500. According results, has been produced when dk=0.7