Standardized Regression Coefficients and Newly Proposed Estimators for in Multiply Imputed Data

Area of Science:

• Statistics
• Biostatistics
• Data Science

Background:

• Statistical analyses on multiply imputed datasets require specific combination rules.
• Established rules exist for unstandardized coefficients and tests, but not for standardized coefficients or point estimators of R-squared.
• Lack of general agreement on combining point estimators and absence of rules for standardized coefficients hinder comprehensive analysis.

Purpose of the Study:

• To propose and discuss new combination rules for standardized regression coefficients and their confidence intervals.
• To introduce improved point estimators for R-squared in multiply imputed data.
• To evaluate the statistical properties and performance of the proposed methods.

Main Methods:

• Development of two sets of combination rules for standardized regression coefficients and confidence intervals.
• Proposal of two improved point estimators for R-squared utilizing pooled standardized coefficients.
• Conducting simulations to assess bias and confidence interval coverage.

Main Results:

• The proposed pooled standardized coefficients exhibit minimal bias.
• The 95% confidence intervals for the proposed coefficients demonstrate coverage close to the theoretical 95%.
• The newly proposed pooled estimates for R-squared are less biased than previous estimates.

Conclusions:

• The developed combination rules provide a statistically sound method for analyzing standardized regression coefficients in multiply imputed data.
• The proposed point estimators for R-squared offer enhanced accuracy.
• These advancements contribute to more reliable statistical inference in the presence of missing data.