An Integrated Bayesian Model for DIF Analysis

Abstract

In this article, an integrated bayesian model for differential item functioning (DIF) analysis is proposed. The model is integrated in the sense of modeling the responses along with the DIF analysis. This approach allows DIF detection and explanation in a simultaneous setup. Previous empirical studies and/or subjective beliefs about the item parameters, including differential functioning behavior, may be conveniently expressed in terms of prior distributions. Values of indicator variables are estimated in the model, indicating which items have DIF and which do not; as a result, the data analyst may not be required to specify an “anchor set” of items that do not exhibit DIF a priori to identify the model. It reduces the iterative procedures that are commonly used for proficiency purification and DIF detection and explanation. Examples demonstrate the efficiency of this method in simulated and real situations.

Nonequivalence of measurement in latent variable modeling of multigroup data: A sensitivity analysis.

“…These conditions on identifiability can be relaxed in Bayesian modeling with informative prior distributions (e.g. Soares et al 2009, Fox 2010, and Muthén & Asparouhov 2012, 2013, but this rather hides rather than resolves the inherent limit of identifiability in partial equivalence models.…”

“…It is also possible to extend the models further to aim to explain the non-equivalence, essentially by modeling with explanatory variables the cross-group variation in measurement parameters (see e.g. Soares et al 2009;Davidov et al 2012). …”

A Penalty Approach to Differential Item Functioning in Rasch Models

“…Although the form of regularization is not given in an explicit form it typically is as efficient as regularization with corresponding penalty terms. Also mixed model methodology as used by (Soares et al, 2009) to estimate DIF can be combined with penalty terms that enforce selection. However, methodology is in its infancy, see, for example, Ni et al (2010);Bondell et al (2010).…”

“…A main contribution in this area is Thissen et al (1993), where tests are used to find items that show DIF. More recently, DIF has been embedded into the framework of mixed models (Van den Noortgate and De Boeck, 2005) and Bayesian approaches have been developed (Soares et al, 2009).…”

Bayesian item response theory models for measurement variance

“…For this purpose, random item effects models have been proposed (e.g., De Jong & Steenkamp, 2010;De Jong, Steenkamp & Fox, 2007;Fox, 2010;Fox & Verhagen, 2010) as well as mixture IRT models in which some items are classified as anchor items in the estimation process (Soares, Goncalves & Gamerman, 2009). These Bayesian models make it possible to estimate one latent underlying scale for the person parameters across countries, taking variations in country-specific item parameters into account.…”