Bayesian Interval Estimation of Multiple Correlations with Missing Data: A Gibbs Sampling Approach

Area of Science:

• Statistics
• Multivariate Analysis
• Computational Statistics

Background:

• Estimating population squared multiple correlation (SMC) is crucial in multivariate analysis.
• Incomplete data sets, with missing values on any variable, pose significant challenges.
• Existing methods often struggle with non-random missing data patterns.

Purpose of the Study:

• To develop a robust Bayesian method for interval estimation of population SMC.
• To address data sets with missing values across dependent and independent variables.
• To accommodate data missing not at random (MNAR).

Main Methods:

• A Bayesian approach utilizing Markov Chain Monte Carlo (MCMC) via Gibbs Sampling.
• The method handles incomplete multivariate normal data, regardless of missingness pattern.
• Detailed examination of Gibbs sampler convergence and prior sensitivity.

Main Results:

• The proposed Gibbs Sampling procedure effectively generates interval estimates for population SMC.
• Empirical coverage probabilities indicate accurate estimation performance.
• The method demonstrates robustness even with complex missing data scenarios.

Conclusions:

• The Bayesian method with Gibbs Sampling offers a reliable solution for SMC interval estimation with incomplete data.
• Accurate estimates are achievable despite missing values in any combination of variables.
• This approach enhances statistical inference in the presence of complex missing data.