Using Mixed-Measurement Item Response Theory With Covariates (MM-IRT-C) to Ascertain Observed and Unobserved Measurement Equivalence

Abstract

Traditional item response theory (IRT) measurement invariance approaches examine measurement equivalence (ME) between observed groups (e.g., race, gender, culture). By contrast, mixed-measurement item response theory (MM-IRT) ascertains ME among unobserved groups (i.e., latent classes [LC] of respondents distinguished by differences in scale use). Both approaches can be integrated by using the Mixed-Measurement Item Response Theory with Covariates (MM-IRT-C) model, in which covariates (i.e., observed characteristics) are modeled in conjunction with LCs, thereby elucidating if ME is attributable to observed and/or unobserved groupings. We first show how this technique can be used to ascertain ME over multiple observed characteristics (categorical and/or continuous) concomitantly, thereby advancing a more general approach to observed ME. Next, we illustrate how the full MM-IRT-C can be used to: (a) infer underlying latent measurement classes (LCs), (b) determine associations of LC membership with observed characteristics, and (c) determine if observed measurement nonequivalence occurs predominantly within a particular latent measurement class. This method is demonstrated using a measure of union citizenship behavior, with years of work experience and gender as covariates. The proposed framework extends organizational ME research from considering a single question (i.e., Is there ME between categorical observed groups?) to addressing eight, separate questions about observed and unobserved ME. The substantive and methodological contributions of this model for rethinking ME and its use in organizational research are discussed.