Multidimensional Extension of Multiple Indicators Multiple Causes Models to Detect DIF

Abstract

A number of studies have found multiple indicators multiple causes (MIMIC) models to be an effective tool in detecting uniform differential item functioning (DIF) for individual items and item bundles. A recently developed MIMIC-interaction model is capable of detecting both uniform and nonuniform DIF in the unidimensional item response theory (IRT) framework. The goal of the current study is to extend the MIMIC-interaction model for detecting DIF in the context of multidimensional IRT modelling and examine the performance of the multidimensional MIMIC-interaction model under various simulation conditions with respect to Type I error and power rates. Simulation conditions include DIF pattern and magnitude, test length, correlation between latent traits, sample size, and latent mean differences between focal and reference groups. The results of this study indicate that power rates of the multidimensional MIMIC-interaction model under uniform DIF conditions were higher than those of nonuniform DIF conditions. When anchor item length and sample size increased, power for detecting DIF increased. Also, the equal latent mean condition tended to produce higher power rates than the different mean condition. Although the multidimensional MIMIC-interaction model was found to be a reasonably useful tool for identifying uniform DIF, the performance of the model in detecting nonuniform DIF appeared to be questionable.

Detecting Multidimensional Differential Item Functioning with the Multiple Indicators Multiple Causes Model, the Item Response Theory Likelihood Ratio Test, and Logistic Regression

“…The item parameters and magnitude of DIF between the focal and the reference groups in Table 1 were similar to previous multidimensional DIF studies (e.g., Oshima et al, 1997;Suh and Cho, 2014;Lee et al, 2016).…”

“…The two test lengths (12 and 22 items) were chosen to resemble the values observed in earlier DIF studies using the DIF detection methods (either unidimensional or multidimensional applications) that we considered in this study (e.g., Woods, 2009b;Woods and Grimm, 2011;Lee et al, 2016). Also, in the multidimensional application of the logistic regression by Mazor et al (1998), a fairly long test (64 items) was considered in their simulation study.…”

“…The same anchor item parameters (see Appendix) were used for reference and focal groups to generate DIF-free anchor items. These anchor item parameters were the same as the values reported in a previous study (Lee et al, 2016). DIF items were introduced in the last two items for both tests.…”

“…These approaches are typically multidimensional extensions of conventional DIF detection approaches designed for unidimensional tests, such as multidimensional SIBTEST (Stout et al, 1997), differential functioning of items and tests (Oshima et al, 1997), logistic regression (Mazor et al, 1998), item response theory likelihood ratio (IRT-LR) test (Suh and Cho, 2014), and multiple indicators multiple causes (MIMIC) model (Lee et al, 2016). Among these approaches, MIMIC, IRT-LR, and logistic regression are widely used and readily available for detecting DIF in dichotomously and polytomously scored items because of their ease of use and their connection with IRT models.…”

“…The major assumptions of the MIMIC-interaction model are independent observations and groups, locally independent items, equal latent variable variance among groups, and anchor (i.e., DIF-free) items (Woods and Grimm, 2011). Lee et al (2016) recently introduced a multidimensional extension of the MIMIC-interaction model that can handle two or more latent traits. Assuming dichotomously scored items measure two latent traits (η1 and η2), then the MIMIC-interaction model in Eq.…”