How Many Imputations are Really Needed? Some Practical Clarifications of Multiple Imputation Theory

How Many Imputations are Really Needed? Some Practical Clarifications of Multiple Imputation Theory Multiple imputation (MI) and full information maximum likelihood (FIML) are the two most common approaches to missing data analysis. In theory, MI and FIML are equivalent when identical models are tested using the same variables, and when m, the number of imputations performed with MI, approaches infinity. However, it is important to know how many imputations are necessary before MI and FIML are sufficiently equivalent in ways that are important to prevention scientists. MI theory suggests that small values of m, even on the order of three to five imputations, yield excellent results. Previous guidelines for sufficient m are based on relative efficiency, which involves the fraction of missing information (γ) for the parameter being estimated, and m. In the present study, we used a Monte Carlo simulation to test MI models across several scenarios in which γ and m were varied. Standard errors and p-values for the regression coefficient of interest varied as a function of m, but not at the same rate as relative efficiency. Most importantly, statistical power for small effect sizes diminished as m became smaller, and the rate of this power falloff was much greater than predicted by changes in relative efficiency. Based our findings, we recommend that researchers using MI should perform many more imputations than previously considered sufficient. These recommendations are based on γ, and take into consideration one’s tolerance for a preventable power falloff (compared to FIML) due to using too few imputations. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Prevention Science Springer Journals

How Many Imputations are Really Needed? Some Practical Clarifications of Multiple Imputation Theory

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Publisher
Springer US
Copyright
Copyright © 2007 by Society of Prevention Research
Subject
Medicine & Public Health; Public Health; Health Psychology; Child and School Psychology
ISSN
1389-4986
eISSN
1573-6695
D.O.I.
10.1007/s11121-007-0070-9
Publisher site
See Article on Publisher Site

Abstract

Multiple imputation (MI) and full information maximum likelihood (FIML) are the two most common approaches to missing data analysis. In theory, MI and FIML are equivalent when identical models are tested using the same variables, and when m, the number of imputations performed with MI, approaches infinity. However, it is important to know how many imputations are necessary before MI and FIML are sufficiently equivalent in ways that are important to prevention scientists. MI theory suggests that small values of m, even on the order of three to five imputations, yield excellent results. Previous guidelines for sufficient m are based on relative efficiency, which involves the fraction of missing information (γ) for the parameter being estimated, and m. In the present study, we used a Monte Carlo simulation to test MI models across several scenarios in which γ and m were varied. Standard errors and p-values for the regression coefficient of interest varied as a function of m, but not at the same rate as relative efficiency. Most importantly, statistical power for small effect sizes diminished as m became smaller, and the rate of this power falloff was much greater than predicted by changes in relative efficiency. Based our findings, we recommend that researchers using MI should perform many more imputations than previously considered sufficient. These recommendations are based on γ, and take into consideration one’s tolerance for a preventable power falloff (compared to FIML) due to using too few imputations.

Journal

Prevention ScienceSpringer Journals

Published: Jun 5, 2007

References

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