Multiple group measurement alignment of the bifactor model within the IRT framework

Measurement alignment places all item parameters across multiple groups on the same scale simultaneously. The item parameters aligned by measurement alignment are used to evaluate the presence of biased items across multiple groups. These features of measurement alignment are necessary to compare test or item properties across multiple groups. Although measurement alignment is used in various fields, applicable models are somewhat limited. Considering the increasing popularity of bifactor models, this study introduced the procedures of measurement alignment for the bifactor model. A technical description of measurement alignment for the bifactor model was provided. The extended model was evaluated through empirical data analysis by comparing it with a commonly used method, Wald-2. In addition, this study evaluated the quality of estimates through a simulation manipulating several conditions.

The empirical data analysis showed that the measurement alignment provided similar results to ones of Wald-2 approach in terms of identifying biased items while the two methods produced different estimates of parameters. The simulation study highlighted that measurement alignment for the bifactor model recovered the parameters well in general. The accuracy of estimation of measurement alignment for the bifactor model was high although the stability of estimation was slightly low. These verified results of measurement alignment for the bifactor model would be utilized for research using the bifactor model. In addition, this study would be beneficial to future studies, which aim to extend measurement alignment into other multidimensional models, because this study provided the details of the procedure as an initial study of measurement alignment for a multidimensional model.