Using Mixture Modeling to Make Meaning of Differential Item Functioning

• In Event: Issues of Measurement Invariance in Mixture Models for Educational Data

Abstract

This paper discusses theoretical frameworks for using the combination of differential item functioning (DIF) and mixture model findings for validity arguments. Additionally, it discusses the philosophical consequences of invoking the notion of measurement invariance when using mixture models, namely causal theories of measurement (Hood, 2009). While some researchers are explicitly working on the statistical aspects of measurement invariance in mixture modelling including covariate inclusion and DIF within mixture models (c.f. Cohen & Bolt, 2005; Cole, Bauer, & Hussong, 2019; Masyn, 2017), certain theoretical and philosophical problems remain. For use-cases, identifying reasons for DIF is important. Mixture models may help with understanding aspects of measure and test fairness (and describing possible causes of DIF in non-mixture settings), especially as DIF researchers increasingly acknowledge that person groupings are not as simple as the categories often assigned (Mislevy, 2018). Emergence of latent classes indicate that the data generation process exists differently for some respondents to a test or survey. A more complicated vision exists when measurement non-invariance is invoked within a finite mixture model where model parameters differ across classes for manifest person groupings (Lubke & Luningham, 2017).

Author

• Daniel Katz, University of California - Santa Barbara