The Impact of Multidimensionality on the Detection of Differential Bundle Functioning Using Simultaneous Item Bias Test

Douglas, Roussos, and Stout introduced the concept of differential bundle functioning (DBF) for identifying the underlying causes of differential item functioning (DIF). In this study, reference group was simulated to have higher mean ability than the focal group on a nuisance dimension, resulting in DIF for each of the multidimensional items that, when examined together, produced DBF. The empirical power and the Type I error of the Simultaneous Item Bias Test for DBF analysis were examined under various sample sizes, ratios of reference to focal group sizes, correlations between target and nuisance dimensions, magnitudes of DIF/DBF, test lengths, percentages of test items in the bundle, and item discriminations. Power was generally high in cells with larger DIF magnitudes, higher percentages of items in the bundle, larger sample sizes, and with the nuisance dimension having a higher discrimination than the target dimension. Type I error rates approximated the nominal alpha rate for all conditions.