The use of latent variable mixture models to identify invariant items in test construction

Richard Sawatzky, Lara B. Russell, Tolulope T. Sajobi, Lisa M. Lix, Jacek Kopec, Bruno D. Zumbo

Patient-reported outcome measures (PROMs) are frequently used in heterogeneous patient populations. PROM scores may lead to biased inferences when sources of heterogeneity (e.g., gender, ethnicity, and social factors) are ignored. Latent variable mixture models (LVMMs) can be used to examine measurement invariance (MI) when sources of heterogeneity in the population are not known a priori. The goal of this article is to discuss the use of LVMMs to identify invariant items within the context of test construction. The Draper-Lindely-de Finetti (DLD) framework for the measurement of latent variables provides a theoretical context for the use of LVMMs to identify the most invariant items in test construction. In an expository analysis using 39 items measuring daily activities, LVMMs were conducted to compare 1- and 2-class item response theory models (IRT). If the 2-class model had better fit, item-level logistic regression differential item functioning (DIF) analyses were conducted to identify items that were not invariant. These items were removed and LVMMs and DIF testing repeated until all remaining items showed MI. The 39 items had an essentially unidimensional measurement structure. However, a 1-class IRT model resulted in many statistically significant bivariate residuals, indicating suboptimal fit due to remaining local dependence. A 2-class LVMM had better fit. Through subsequent rounds of LVMMs and DIF testing, nine items were identified as being most invariant. The DLD framework and the use of LVMMs have significant potential for advancing theoretical developments and research on item selection and the development of PROMs for heterogeneous populations.