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

Abstract

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