Direction of Effects in Multiple Linear Regression Models.

Area of Science:

• Statistics
• Econometrics
• Psychometrics

Background:

• Previous methods for determining variable direction of dependence were limited to bivariate regression.
• Asymmetric properties of the Pearson correlation coefficient, using higher-order moments, were previously used for bivariate analysis.
• Existing techniques lack applicability in multiple linear regression settings with observational data.

Purpose of the Study:

• To extend direction of dependence methodology to multiple linear regression.
• To analyze distributional properties of residuals from competing multiple regression models.
• To establish which variable is more likely to be on the outcome side in a multiple regression context.

Main Methods:

• Analysis of the third central moments of estimated regression residuals.
• Application of statistical inference approaches: D'Agostino normality test, skewness difference test, and bootstrap difference test.
• Monte Carlo simulations to assess Type I error and power of the proposed procedures.

Main Results:

• Demonstration that third central moments of regression residuals can indicate direction of effects under specific conditions.
• Evaluation of the performance of three statistical inference methods.
• Identification of the effectiveness of the proposed methodology in multiple regression settings.

Conclusions:

• The proposed method effectively extends direction of dependence analysis to multiple linear regression.
• The third central moment of residuals offers a viable approach for determining effect direction.
• Further research could explore extensions to the fourth central moment and applications in psychological data analysis.