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Improved degrees of freedom for multivariate significance tests obtained from multiply imputed, small-sample data

Author

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  • Yulia V. Marchenko

    (StataCorp)

  • Jerome P. Reiter

    (Duke University)

Abstract

We propose improvements to existing degrees of freedom used for significance testing of multivariate hypotheses in small samples when missing data are handled using multiple imputation. The improvements are for 1) tests based on unrestricted fractions of missing information and 2) tests based on equal fractions of missing information with M (p − 1) ≤ 4, where M is the number of imputations and p is the number of tested parameters. Using the mi command available as of Stata 11, we demonstrate via simulation that using these adjustments can result in a more sensible degrees of freedom (and hence closer-to-nominal rejection rates) than existing degrees of freedom. Copyright 2009 by StataCorp LP.

Suggested Citation

  • Yulia V. Marchenko & Jerome P. Reiter, 2009. "Improved degrees of freedom for multivariate significance tests obtained from multiply imputed, small-sample data," Stata Journal, StataCorp LP, vol. 9(3), pages 388-397, September.
    • Handle: RePEc:tsj:stataj:v:9:y:2009:i:3:p:388-397
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    References listed on IDEAS

    as
    1. Reiter, Jerome P. & Raghunathan, Trivellore E., 2007. "The Multiple Adaptations of Multiple Imputation," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 1462-1471, December.
    2. Jerome P. Reiter, 2007. "Small-sample degrees of freedom for multi-component significance tests with multiple imputation for missing data," Biometrika, Biometrika Trust, vol. 94(2), pages 502-508.
    3. Patrick Royston & John B. Carlin & Ian R. White, 2009. "Multiple imputation of missing values: New features for mim," Stata Journal, StataCorp LP, vol. 9(2), pages 252-264, June.
    4. Patrick Royston, 2004. "Multiple imputation of missing values," Stata Journal, StataCorp LP, vol. 4(3), pages 227-241, September.
    5. John B. Carlin & John C. Galati & Patrick Royston, 2008. "A new framework for managing and analyzing multiply imputed data in Stata," Stata Journal, StataCorp LP, vol. 8(1), pages 49-67, February.
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