Measurement invariance (MI) is typically framed as a psychometric prerequisite for valid group comparisons in psychological research. However, this view treats MI as a statistical property rather than a substantive research question, and leaves researchers unaware of its implicit causal assumptions. Recent literature has integrated causal inference perspectives into MI research. In this thesis, we extend this work by examining the causal implications of MI testing from both conceptual and methodological perspectives. We clarify the causal interpretation of MI by integrating different theoretical developments. We also propose the use of a Bayesian moderated nonlinear factor analysis (MNLFA) approach for investigating MI violations under the specific extension. Last, we demonstrate with a real-world application how conclusions may differ substantially when MI is approached through a causal angle rather than treated purely as a statistical requirement.