Selecting the model for multiple imputation of missing data: Just use an IC!

Area of Science:

• Statistics
• Data Analysis

Background:

• Missing data analysis commonly employs multiple imputation and maximum likelihood estimation (expectation-maximization).
• These methods are often viewed as distinct, but improper multiple imputation approximates stochastic expectation-maximization.
• Improper imputation model choice can bias statistical inference.

Purpose of the Study:

• To demonstrate that likelihood-based model selection criteria can select appropriate imputation models.
• To show that the Bayesian Information Criterion (BIC) can consistently identify the correct imputation model with missing data.
• To highlight the importance of model complexity in imputation to avoid bias.

Main Methods:

• Exploiting the equivalence between improper multiple imputation and stochastic expectation-maximization.
• Applying likelihood-based model selection criteria, specifically Akaike's Information Criterion (AIC) and BIC, to choose imputation models.
• Conducting simulation studies and analyzing real-world missing data examples.

Main Results:

• Model selection criteria (AIC, BIC) can effectively choose imputation models that best fit observed data.
• BIC demonstrates consistency in selecting the correct imputation model in the presence of missing data.
• Both misspecification and overfitting of the imputation model can bias parameter estimates.

Conclusions:

• Conventional model selection tools offer a data-driven approach to choosing imputation models, reducing reliance on sensitivity analysis alone.
• BIC provides a consistent method for selecting imputation models, improving the reliability of analyses with missing data.
• Selecting the appropriate complexity of the imputation model is crucial for accurate statistical inference.