Don't let MI be misunderstood: Measurement invariance is more than a statistical assumption

Measurement invariance (MI) is often treated as a statistical prerequisite for meaningful comparisons of constructs across groups or time points. However, this perspective overlooks the substantive implications (a lack of) MI can have for psychological theories of constructs. In this paper, we frame MI as a causal concept with theoretical significance. We present a causal framework based on directed acyclic graphs (DAGs) that allows researchers to reason about potential causes of non-invariance and include them in their modeling strategy. We argue that non-invariance should not be seen as prohibitive for further exploration and analyses but as an opportunity to generate new insights about constructs and their measurement. That is, under non-invariance, data need a different treatment than simply comparing constructs between groups and causal reasoning can guide researchers in this regard. We demonstrate the causal framework through an application to the study of acquiescent response style. We further discuss an extension of the causal framework to longitudinal designs. When investigating the invariance of measurements over time, the framework can help to take into account expected or desired non-invariance; for example, when constructs evolve over time or certain interventions might change measurement models. By presenting MI as a substantive finding with theoretical implications, we aim to bridge the gap between methodological rigor and applied research reality.