Interaction, Nonlinearity, and Multicollinearity: implications for Multiple Regression

Key Points

• This research investigates how multicollinearity and nonlinearity in variables affect the validity of interaction terms in multiple regression analysis.
• Used moderated hierarchical multiple regression to analyze interactions among correlated variables.
• Recommended including squared terms as covariates to address confounding effects.
• Assessed the implications of using squared terms on the power of significance tests.
• Found that interaction terms may appear significant due to unmeasured nonlinear relationships.
• Demonstrated that incorporating squared terms minimally impacts power due to loss of degrees of freedom.
• Indicated that using squared terms is a viable method to mitigate confounding without substantial power loss.