Measurement Invariance in Mixture Modeling: Issues and Current Practices

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

Abstract

While many researchers are conversant with measurement invariance testing in a factor analytic context, procedures of invariance testing in mixture modeling is less commonly discussed. Further, best practices for undertaking a study of measurement invariance are very limited. Measurement invariance in latent class analysis, similar to approaches in factor analysis, involves stringent equality constraints which, in practice, are often not fulfilled. Therefore, it is important to first ask whether group comparisons are vital to the research question.
Measurement invariance in the latent class analysis context considers group differences across unconstrained and constrained models, rather than across configural, metric, scalar and strict invariance as in a factor analytic model. This paper explains the procedures used in the literature (Lanza & Collins, 2010; Finch, 2015; Kankaraš, Moors & Vermunt, 2011; Olivera-Aguilar & Rikoon, 2018) to determine invariance in an LCA context and draws comparisons between these and factor analytic procedures.
The first test of invariariance in LCA is the unconditional model where parameters are freely estimated, and may be compared to the factor analytic configural model. This determines the structural part of the model by freely estimating the number of classes in each group to ensure their equivalence (Masyn, 2017). The next level of invariance, a semi-constrained model holding means and variances of the indicators equal across groups, is the measurement aspect of the model (Masyn, 2017). This may be compared to a combination of scalar and metric invariance in factor analysis. The final test of invariance is the fully constrained model holding the probability of class membership equal across groups (Olivera-Aguilar & Rikoon, 2018), which can be compared to strict invariance in a factor analytic context. Fit indices and their interpretations are also discussed (Finch, 2015, Olivera-Aguilar & Rikoon, 2018).
Current practices in measurement invariance in mixture models suggest adherence to the fully constrained model to compare groups (Olivera-Aguilar & Rikoon, 2018), meaning that full measurement invariance is rarely found. This may induce researchers to treat the group membership variable as a covariate rather than as a grouping variable. Doing this assumes the covariate is equal between groups, which, if incorrect, can bias the findings (Kuha & Moustaki, 2015). Researchers might first consider whether they believe the groups are fundamentally different in some way. If the answer is yes then invariance testing is key to the study, however if not researchers may prefer to treat the variable as a covariate and undergo differential item functioning testing in accordance with Masyn (2017). One workaround for the strict invariance of LCA is a type of partial invariance where several classes are compared across groups while allowing one or more classes to differ (Collins & Lanza, 2010). The implications of this for researchers are that conceptual differences need to be considered carefully, as researchers must consider whether there are qualitative differences between groups that are being ignored by holding the groups equal. Measurement invariance in mixture models is a fast developing area of research, with procedures and recommendations of when to allow noninvariance yet to be determined.

Authors

• Odelia Simon, University of California - Santa Barbara

• Karen L. Nylund-Gibson, University of California - Santa Barbara