The MIMIC Model as a Tool for Differential Bundle Functioning Detection

Increasingly, researchers interested in identifying potentially biased test items are encouraged to use a confirmatory, rather than exploratory, approach. One such method for confirmatory testing is rooted in differential bundle functioning (DBF), where hypotheses regarding potential differential item functioning (DIF) for sets of items (bundles) are developed based on the substantive nature of the items and expected differences in group performance. Most often, analyses of these bundles for DBF have been conducted using simultaneous item bias test (SIBTEST). The goal of the current study was to introduce an alternative methodology for DBF detection based on the multiple indicators multiple cause (MIMIC) model and to compare this alternative with the traditional SIBTEST-based approach using a Monte Carlo simulation study. The results of this study showed that the MIMIC model performed as well as SIBTEST in ideal conditions, and better when the reference and focal groups had different means on the primary latent trait being measured. In addition, the MIMIC model was more accurate at detecting the presence of DBF for two bundles simultaneously than was SIBTEST. The discussion focuses on recommendations for practitioners.

Establishing Effect Size Guidelines for Interpreting the Results of Differential Bundle Functioning Analyses Using SIBTEST

The purpose of this simulation study was to establish general effect size guidelines for interpreting the results of differential bundle functioning (DBF) analyses using simultaneous item bias test (SIBTEST). Three factors were manipulated: number of items in a bundle, test length, and magnitude of uniform differential item functioning (DIF) against the focal group in each item in a bundle. A secondary purpose was to validate the current effect size guidelines for interpreting the results of single-item DIF analyses using SIBTEST. The results of this study clearly demonstrate that ability estimation bias can only be attributed to DIF or DBF when a large number of items in a bundle are functioning differentially against focal examinees in a small way or a small number of items are functioning differentially against focal examinees in a large way. In either of these situations, the presence of DIF or DBF should be a cause for concern because it would lead one to erroneously believe that distinct groups differ in ability when in fact they do not.