Understanding linear interaction analysis with causal graphs

Interaction analysis using linear regression is widely employed in psychology and related fields, yet it often induces confusion among applied researchers and students. This paper aims to address this confusion by developing intuitive visual explanations based on causal graphs. By leveraging causal graphs with distinct interaction nodes, we provide clear insights into interpreting main effects in the presence of interaction, the rationale behind centering to reduce multicollinearity, and other pertinent topics. The proposed graphical approach could serve as a useful complement to existing algebraic explanations, fostering a more comprehensive understanding of the mechanics of linear interaction analysis.