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Model Selection with Missing Data Embedded in Missing-at-Random Data

Author

Listed:
  • Keiji Takai

    (Faculty of Commerce, Kansai University, Yamatecho 3-3-35, Osaka 564-8680, Japan)

  • Kenichi Hayashi

    (Department of Mathematics, Keio University, Hiyoshi 3-14-1, Kohokuku, Yokohama 223-0061, Japan)

Abstract

When models are built with missing data, an information criterion is needed to select the best model among the various candidates. Using a conventional information criterion for missing data may lead to the selection of the wrong model when data are not missing at random. Conventional information criteria implicitly assume that any subset of missing-at-random data is also missing at random, and thus the maximum likelihood estimator is assumed to be consistent; that is, it is assumed that the estimator will converge to the true value. However, this assumption may not be practical. In this paper, we develop an information criterion that works even for not-missing-at-random data, so long as the largest missing data set is missing at random. Simulations are performed to show the superiority of the proposed information criterion over conventional criteria.

Suggested Citation

  • Keiji Takai & Kenichi Hayashi, 2023. "Model Selection with Missing Data Embedded in Missing-at-Random Data," Stats, MDPI, vol. 6(2), pages 1-11, April.
    • Handle: RePEc:gam:jstats:v:6:y:2023:i:2:p:31-505:d:1120512
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    References listed on IDEAS

    as
    1. Ibrahim, Joseph G. & Zhu, Hongtu & Tang, Niansheng, 2008. "Model Selection Criteria for Missing-Data Problems Using the EM Algorithm," Journal of the American Statistical Association, American Statistical Association, vol. 103(484), pages 1648-1658.
    2. Chang, Wan-Ying & Richards, Donald St.P., 2009. "Finite-sample inference with monotone incomplete multivariate normal data, I," Journal of Multivariate Analysis, Elsevier, vol. 100(9), pages 1883-1899, October.
    3. Ran Tao & Donglin Zeng & Dan-Yu Lin, 2020. "Optimal Designs of Two-Phase Studies," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 115(532), pages 1946-1959, December.
    4. Gerda Claeskens & Fabrizio Consentino, 2008. "Variable Selection with Incomplete Covariate Data," Biometrics, The International Biometric Society, vol. 64(4), pages 1062-1069, December.
    5. Chang, Wan-Ying & Richards, Donald St. P., 2010. "Finite-sample inference with monotone incomplete multivariate normal data, II," Journal of Multivariate Analysis, Elsevier, vol. 101(3), pages 603-620, March.
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