Interpreting moderated multiple regression: A comment on Van Iddekinge, Aguinis, Mackey, and DeOrtentiis (2018)

Area of Science:

• Organizational Psychology
• Quantitative Psychology
• Management Science

Background:

• The additive versus multiplicative nature of performance determinants (ability and motivation) is a key theoretical debate.
• Previous meta-analytic conclusions suggesting additive effects may be flawed due to analytical misinterpretations.
• Moderated multiple regression (MMR) is commonly used but can lead to incorrect inferences about interaction effects.

Purpose of the Study:

• To identify and illustrate a common error in interpreting MMR results regarding additive versus multiplicative effects.
• To demonstrate the limitations of MMR in distinguishing independent (additive) from joint (multiplicative) effects.
• To propose methodological improvements for validly testing multiplicative performance models.

Main Methods:

• A Monte Carlo simulation study was conducted to examine the interpretation of MMR.
• The study simulated data to assess the ability of MMR to differentiate between additive and multiplicative relationships.
• The appropriateness of using incremental R-squared as an effect size for interaction terms was evaluated.

Main Results:

• MMR is effective for detecting moderation but often insufficient for determining the degree of additive versus multiplicative effects.
• Interpreting the incremental contribution of interaction terms as effect sizes in MMR is generally inappropriate due to statistical artifact.
• The simulation highlights how MMR can erroneously suggest additive effects when multiplicative effects are present.

Conclusions:

• The common practice of interpreting MMR results can lead to invalid conclusions about the functional form of performance determinants.
• Researchers should exercise caution when interpreting MMR, particularly regarding additive versus multiplicative effects.
• Fitting the entire MMR model simultaneously is recommended to prevent misinterpretations and ensure valid theoretical conclusions.