Testing for Nonuniform Differential Item Functioning With Multiple Indicator Multiple Cause Models

Abstract

In extant literature, multiple indicator multiple cause (MIMIC) models have been presented for identifying items that display uniform differential item functioning (DIF) only, not nonuniform DIF. This article addresses, for apparently the first time, the use of MIMIC models for testing both uniform and nonuniform DIF with categorical indicators. A latent variable interaction is added to the MIMIC model to test for nonuniform DIF. The approach is tested in simulations with small focal-group N and illustrated with an empirical example using a scale about agoraphobic cognitions. MIMIC-interaction models are compared with MIMIC models without the interaction as well as likelihood ratio DIF testing using item response theory (IRT-LR-DIF). The most important finding is that when the latent moderated structural equations approach is used to estimate the interaction, the Type I error in MIMIC-interaction DIF models is severely inflated.

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

“…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.…”

“…As a result of DIF, a biased item provides either a constant advantage for a particular group (i.e., uniform DIF) or an advantage varying in magnitude and/or in direction across the latent trait continuum (i.e., non-uniform DIF). Although uniform DIF is more frequently observed than non-uniform DIF in practice, several studies indicated that non-uniform DIF can also be present in real data sets from educational and psychological assessments (e.g., Mazor et al, 1994;De Beer, 2004;Le, 2006;Woods and Grimm, 2011;Teresi and Fleishman, 2017). Therefore, when conducting DIF analyses, the type of DIF (i.e., uniform or non-uniform) is crucial because different DIF methods can be more appropriate for each type of DIF (Penfield and Camilli, 2007).…”

“…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. Previous studies compared the unidimensional forms of MIMIC, IRT-LR, and logistic regression with each other as well as with other DIF detection methods (e.g., Finch, 2005;Woods, 2009a;Atar and Kamata, 2011;Woods and Grimm, 2011;Kan and Bulut, 2014). However, the relative performances of these approaches are still unknown in the context of multidimensional tests.…”

“…Early forms of the MIMIC model were only used for examining uniform DIF for dichotomously or polytomously scored item responses (e.g., Finch, 2005Finch, , 2012Shih and Wang, 2009;Woods et al, 2009). To examine uniform and non-uniform DIF simultaneously, Woods and Grimm (2011) introduced the MIMICinteraction model, which is similar to restricted factor analysis models with an interaction term (Ferrando and Lorenzo-Seva, 2000;Barendse et al, 2010). The MIMIC-interaction model can be written as follows:…”

“…The LMS method relies on a full-information maximum-likelihood estimation that gives an important efficiency and power advantage in analyzing nonnormally distributed interaction effects between latent variables and observed variables [for more details on the LMS method, see Klein and Moosbrugger (2000)]. 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.…”