ML versus MI for Missing Data with Violation of Distribution Conditions

Area of Science:

• Statistics
• Data Analysis

Background:

• Missing data analysis is crucial in statistical modeling.
• Maximum Likelihood (ML) and Multiple Imputation (MI) are primary methods.
• Comparing their performance regarding bias and efficiency is essential.

Purpose of the Study:

• To compare ML and MI for missing data analysis.
• To evaluate bias and efficiency of parameter estimates.
• To assess standard error estimation accuracy.

Main Methods:

• Comparative analysis of ML and MI procedures.
• Evaluation of parameter estimate bias and efficiency.
• Comparison of formula-based versus empirical standard errors.

Main Results:

• MI parameter estimates are less efficient than ML.
• MI variance-covariance estimates show more bias, especially with heavy-tailed distributions.
• ML estimates can be biased at smaller sample sizes.
• Sandwich-type and observed information matrix SEs are comparable to empirical SEs for normal distributions.
• Sandwich-type SEs are more reliable for ML with heavy-tailed distributions.
• Neither formula-based SE method is consistent for MI.

Conclusions:

• ML is generally preferred over MI in practice for missing data.
• MI parameter estimates may still be consistent despite limitations.
• Accurate standard error estimation is critical and challenging with MI.