Improved Degrees of Freedom for Multivariate Significance Tests Obtained from Multiply Imputed, Small-Sample Data

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 equ...

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Bibliographic Details
Published in:The Stata journal 2009-09, Vol.9 (3), p.388-397
Main Authors: Marchenko, Yulia V., Reiter, Jerome P.
Format: Article
Language:English
Subjects:
Degrees of freedom (Statistics)
Hypotheses (Scientific method)
Methods
Multivariate analysis
Testing
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Summary: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.
ISSN:1536-867X
1536-8734
DOI:10.1177/1536867X0900900303