Tools to support interpreting multiple regression in the face of multicollinearity

Area of Science:

• Statistics
• Econometrics
• Psychometrics

Background:

• Multicollinearity presents challenges in interpreting multiple regression (MR) results.
• Existing research often focuses on single techniques for addressing multicollinearity.
• A comprehensive understanding of predictor contributions requires a multi-faceted approach.

Purpose of the Study:

• To advocate for the use of multiple indices for interpreting multiple regression results in the presence of multicollinearity.
• To guide researchers in understanding predictor contributions to the regression model and to each other.
• To review and identify statistical software supporting these interpretation techniques.

Main Methods:

• Review of various techniques for interpreting MR effects, including correlation coefficients, beta weights, structure coefficients, all possible subsets regression, commonality coefficients, dominance weights, and relative importance weights.
• Identification of the specific data elements each interpretation method focuses on.
• Survey of statistical software capable of supporting these analyses.

Main Results:

• Multiple interpretation techniques provide a more robust understanding of predictor roles in MR models than single methods.
• Different techniques highlight distinct aspects of predictor contributions and their interdependencies.
• Specific statistical software packages can facilitate the application of these diverse interpretation methods.

Conclusions:

• Knowledgeable researchers can effectively manage multicollinearity by employing a suite of interpretation techniques.
• A multi-index approach enhances the depth of understanding regarding predictor influence and relationships within MR models.
• The judicious selection and application of appropriate statistical software are crucial for implementing these advanced interpretation strategies.