A Comparison of the Separate and Concurrent Calibration Methods for the Full-Information Bifactor model

When calibrating items using multidimensional item response theory (MIRT) models, item response theory (IRT) calibration programs typically set the probability density of latent variables to a multivariate standard normal distribution to handle three types of indeterminacies: (a) the location of the origin, (b) the unit of measurement along each coordinate axis, and (c) the orientation of the coordinate axes. However, by doing so, item parameter estimates obtained from two independent calibration runs on nonequivalent groups are on two different coordinate systems. To handle this issue and place all the item parameter estimates on a common coordinate system, a process called linking is necessary. Although various linking methods have been introduced and studied for the full MIRT model, little research has been conducted on linking methods for the bifactor model. Thus, the purpose of this study was to provide detailed descriptions of two separate calibration methods and the concurrent calibration method for the bifactor model and to compare the three linking methods through simulation. In general, the concurrent calibration method provided more accurate linking results than the two separate calibration methods, demonstrating better recovery of the item parameters, item characteristic surfaces, and expected score distribution.