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Multiple imputation, when improperly used, is equivalent to stochastic expectation-maximization. Likelihood-based model selection criteria like BIC can consistently choose the best imputation model for missing data analysis, preventing biased inference.

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imputation model selectioninformation criteriamissing data analysisstochastic EM algorithm

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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.