Investigating bias in squared regression structure coefficients

Area of Science:

• Statistics
• Psychometrics
• Quantitative Psychology

Background:

• Structure coefficients and regression weights are crucial for general linear model (GLM) analysis.
• Bias in squared structure coefficients can affect the interpretation of multiple regression results.

Purpose of the Study:

• To investigate bias in squared structure coefficients within multiple regression.
• To evaluate Pratt's formula for correcting bias in squared regression structure coefficients, analogous to its use for correlation coefficients and coefficients of determination.

Main Methods:

• A Monte Carlo simulation was employed to generate data for the study.
• Squared regression structure coefficients were analyzed with and without corrections from Pratt's formula.

Main Results:

• Pratt's formula significantly reduced bias in squared regression structure coefficients.
• Corrected estimates demonstrated greater accuracy and stability compared to uncorrected estimates.
• Multicollinearity, predictive power, number of predictors, and sample size were identified as contributors to bias.

Conclusions:

• Pratt's formula provides a viable method for correcting bias in squared regression structure coefficients.
• The findings highlight the impact of various factors on the accuracy of structure coefficient estimates in multiple regression.