From Path Diagrams to Causal Graphs: A Structural Causal Perspective on Cross-Sectional Multilevel Models

Causal graphs provide a rigorous framework for encoding causal assumptions. Yet, their integration with multilevel models remains limited. We review common path diagram conventions in multilevel modeling and show, through a bivariate regression example, that these function as statistical model visualizations rather than causal graphs. We formalize parametric cross-sectional multilevel models as parametric structural causal models with linear causal effects (conditional on possible moderators) and Gaussian error terms. We then translate them into acyclic directed mixed graphs. We illustrate this framework using a well-known empirical example, the High School and Beyond study. This work provides a systematic bridge between cross-sectional parametric multilevel models and modern causal graph theory.