<abstract xmlns="http://www.w3.org/1999/xhtml"><p> Multiple imputation is a popular approach to handling missing data. Although it was originally motivated by survey nonresponse problems, it has been readily applied to other data settings. However, its general behavior still remains unclear when applied to survey data with complex sample designs, including clustering. Recently, Lewis et al. (2014) compared single- and multiple-imputation analyses for certain incomplete variables in the 2008 National Ambulatory Medicare Care Survey, which has a nationally representative, multistage, and clustered sampling design. Their study results suggested that the increase of the variance estimate due to multiple imputation compared with single imputation largely disappears for estimates with large design effects. We complement their empirical research by providing some theoretical reasoning. We consider data sampled from an equally weighted, single-stage cluster design and characterize the process using a balanced, one-way normal random-effects model. Assuming that the missingness is completely at random, we derive analytic expressions for the within- and between-multiple-imputation variance estimators for the mean estimator, and thus conveniently reveal the impact of design effects on these variance estimators. We propose approximations for the fraction of missing information in clustered samples, extending previous results for simple random samples. We discuss some generalizations of this research and its practical implications for data release by statistical agencies.</p></abstract>

Multiple imputation is a popular approach to handling missing data. Although it was originally motivated by survey nonresponse problems, it has been readily applied to other data settings. However, its general behavior still remains unclear when applied to survey data with complex sample designs, including clustering. Recently, Lewis et al. (2014) compared single- and multiple-imputation analyses for certain incomplete variables in the 2008 National Ambulatory Medicare Care Survey, which has a nationally representative, multistage, and clustered sampling design. Their study results suggested that the increase of the variance estimate due to multiple imputation compared with single imputation largely disappears for estimates with large design effects. We complement their empirical research by providing some theoretical reasoning. We consider data sampled from an equally weighted, single-stage cluster design and characterize the process using a balanced, one-way normal random-effects model. Assuming that the missingness is completely at random, we derive analytic expressions for the within- and between-multiple-imputation variance estimators for the mean estimator, and thus conveniently reveal the impact of design effects on these variance estimators. We propose approximations for the fraction of missing information in clustered samples, extending previous results for simple random samples. We discuss some generalizations of this research and its practical implications for data release by statistical agencies.

A Note on the Effect of Data Clustering on the Multiple-Imputation Variance Estimator: A Theoretical Addendum to the Lewis et al. article in JOS 2014

National Center for Health Statistics, Centers for Disease Control and Prevention, Hyattsville, MD, 20782, U.S.A.

Journal of Official Statistics

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Multiple imputation is a popular approach to handling missing data. Although it was originally motivated by survey nonresponse problems, it has been readily...

A Note on the Effect of Data Clustering on the Multiple-Imputation Variance Estimator: A Theoretical Addendum to the Lewis et al. article in JOS 2014

Published Online: Mar 10, 2016

Page range: 147 - 164

Received: Oct 01, 2014

Accepted: Jun 01, 2015

DOI: https://doi.org/10.1515/jos-2016-0007

Keywords
Bayesian, complex survey design, data release, exploratory data analysis, fraction of missing information, missing data

© by Yulei He

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

A Note on the Effect of Data Clustering on the Multiple-Imputation Variance Estimator: A Theoretical Addendum to the Lewis et al. article in JOS 2014

Published Online: Mar 10, 2016

Page range: 147 - 164

Received: Oct 01, 2014

Accepted: Jun 01, 2015

DOI: https://doi.org/10.1515/jos-2016-0007

KeywordsBayesian, complex survey design, data release, exploratory data analysis, fraction of missing information, missing data

© by Yulei He

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Keywords
Bayesian, complex survey design, data release, exploratory data analysis, fraction of missing information, missing data