Fit Indices for Measurement Invariance Tests in the Thurstonian IRT Model

This study examined whether cutoffs in fit indices suggested for traditional formats with maximum likelihood estimators can be utilized to assess model fit and to test measurement invariance when a multiple group confirmatory factor analysis was employed for the Thurstonian item response theory (IRT) model. Regarding the performance of the evaluation criteria, detection of measurement non-invariance and Type I error rates were examined. The impact of measurement non-invariance on estimated scores in the Thurstonian IRT model was also examined through accuracy and efficiency in score estimation. The fit indices used for the evaluation of model fit performed well. Among six cutoffs for changes in model fit indices, only Delta CFI > .01 and Delta NCI > .02 detected metric non-invariance when the medium magnitude of non-invariance occurred and none of the cutoffs performed well to detect scalar non-invariance. Based on the generated sampling distributions of fit index differences, this study suggested Delta CFI > .001 and Delta NCI > .004 for scalar non-invariance and Delta CFI > .007 for metric non-invariance. Considering Type I error rate control and detection rates of measurement non-invariance, Delta CFI was recommended for measurement non-invariance tests for forced-choice format data. Challenges in measurement non-invariance tests in the Thurstonian IRT model were discussed along with the direction for future research to enhance the utility of forced-choice formats in test development for cross-cultural and international settings.