Moderated multiple regression for interactions involving categorical variables: a statistical control for...

Area of Science:

• Statistics
• Psychometrics
• Quantitative Psychology

Background:

• Moderated multiple regression (MMR) is widely used to analyze interaction effects across groups.
• Heterogeneous error variances, a common issue, can significantly bias standard MMR analyses.
• Existing statistical corrections for heterogeneity are complex and limit in-depth interaction analysis.

Purpose of the Study:

• To address the limitations of standard MMR when dealing with heterogeneous error variances.
• To propose a statistically accurate and practical alternative for analyzing interactions in two-group studies.

Main Methods:

• The study recommends a weighted least squares (WLS) approach for two-group analyses.
• WLS is demonstrated to be statistically accurate and executable using common software packages.

Main Results:

• The weighted least squares (WLS) approach corrects for bias caused by heterogeneous error variances in MMR.
• WLS facilitates accurate analysis of regression slope differences (interactions) across groups.
• This method allows for straightforward follow-up analyses to describe interaction effects.

Conclusions:

• Weighted least squares (WLS) is a recommended, accurate, and accessible method for analyzing interactions in two-group studies with heterogeneous error variances.
• WLS overcomes the limitations of traditional MMR, enabling more robust and detailed interaction effect investigations.