Dynamic measurement invariance cutoffs for longitudinal and dyadic data

Measurement invariance is a common interest in behavioral research to ensure that scores are comparable across groups or time. Evidence for measurement invariance is traditionally evaluated by comparing fit index differences between constrained and unconstrained models to cutoffs like ΔCFI > - 0.01. However, traditional fit index difference cutoffs have been noted to have limited generalizability and potentially poor performance outside of conditions used to derive cutoffs. Dynamic measurement invariance (DMI) cutoffs were proposed to address generalizability concerns by re-simulating cutoffs for each model so that the cutoffs are custom-tailored to the researcher's model and data characteristics. However, a notable limitation of the extant fit index difference cutoff literature is that only multiple-group factor models for two-group comparisons have been considered. These models are appropriate for evaluating invariance of independent groups (e.g., demographic characteristics, countries, languages), but they cannot accommodate dependent groups with correlated responses across groups. Common examples of dependent groups include longitudinal data (i.e., groups are timepoints) or dyadic data (e.g., romantic partners, parents, and children). In such cases, models outside the multiple-group framework that incorporate between-group correlations are needed to evaluate invariance, but there is currently no guidance for interpreting fit index difference cutoffs in these models. Therefore, this paper proposes extending DMI cutoffs for dependent groups (DG-DMI). After describing the method, three empirical examples are provided to show how DG-DMI can inform conclusions about dyadic or longitudinal measurement invariance (including data with three or more timepoints). Open-source software is provided to facilitate the application of the method.