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Model Selection Criteria for Missing-Data Problems Using the EM Algorithm.

Joseph G Ibrahim1, Hongtu Zhu, Niansheng Tang

  • 1Joseph G. Ibrahim is Alumni Distinguished Professor (E-mail: ibrahim@bios.unc.edu ), Department of Biostatistics, University of North Carolina, Chapel Hill.

Journal of the American Statistical Association
|August 21, 2009
PubMed
Summary
This summary is machine-generated.

This study introduces novel information criteria (IC(H)(,)(Q)) for model selection with missing data using the EM algorithm. These criteria, including IC(H̃)((k)(),)(Q) and IC(Q), offer versatile and computationally efficient solutions for incomplete data problems.

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Area of Science:

  • Statistics
  • Computational Statistics
  • Data Science

Background:

  • Missing data poses significant challenges in statistical modeling.
  • The Expectation-Maximization (EM) algorithm is a common approach for handling incomplete datasets.
  • Existing model selection criteria may not be directly applicable or computationally efficient in missing-data scenarios.

Purpose of the Study:

  • To develop novel, generalizable methods for computing model selection criteria in the presence of missing data.
  • To introduce a new class of information criteria, IC(H)(,)(Q), derived from EM algorithm outputs.
  • To propose computationally simplified approximations, IC(H̃)((k)(),)(Q) and IC(Q), for enhanced usability.

Main Methods:

  • Utilizing the output of the EM algorithm for maximum likelihood estimation.
  • Developing an analytic approximation for the H-function to derive IC(H)(,)(Q).
  • Proposing IC(Q) as a computationally simpler alternative dependent only on the Q-function of the EM algorithm.

Main Results:

  • The proposed IC(H)(,)(Q) framework encompasses established criteria like AIC and BIC.
  • Theoretical properties, including consistency, of IC(H̃)((k)(),)(Q) were rigorously investigated.
  • Simulations demonstrated the methodology's effectiveness and the performance of the proposed criteria in various missing-data settings.

Conclusions:

  • The developed information criteria provide robust and flexible tools for model selection with incomplete data.
  • IC(Q) offers a computationally advantageous alternative for practical applications.
  • The methodology is broadly applicable across diverse regression models and missing data mechanisms.