1557-0657/asset/MPR_left.gif?v=1&s=c936e780fe15aef542fbfadab38a26c22e0a186c)
1557-0657/asset/MPR_right.gif?v=1&s=e57cf8e939e0257a0a785c85fb295e952ced8e4f)
Research Article
You have free access to this content
Multiple imputation by chained equations: what is it and how does it work?
Article first published online: 24 FEB 2011
DOI: 10.1002/mpr.329
Copyright © 2011 John Wiley & Sons, Ltd.
Issue
International Journal of Methods in Psychiatric Research
Volume 20, Issue 1, pages 40–49, March 2011
Additional Information
How to Cite
Azur, M. J., Stuart, E. A., Frangakis, C. and Leaf, P. J. (2011), Multiple imputation by chained equations: what is it and how does it work?. Int. J. Methods Psychiatr. Res., 20: 40–49. doi: 10.1002/mpr.329
Publication History
- Issue published online: 24 FEB 2011
- Article first published online: 24 FEB 2011
- Manuscript Accepted: 13 OCT 2010
- Manuscript Revised: 26 JUL 2010
- Manuscript Received: 16 FEB 2010
Funded by
- National Institute of Mental Health. Grant Number: 1R01MH075828-01A1
References
- , , (2008) Diagnostics for multivariate imputations. Journal of the Royal Statistical Society: Series C (Applied Statistics), 57, 273–291, DOI: 10.1111/j.1467-9876.2007.00613.x
- , , , (2007) Incomplete hierarchical data. Statistical Methods in Medical Research, 16, 457–492, DOI: 10.1177/0962280206075310
- (1999) Development, implementation and evaluation of multiple imputation strategies for the statistical analysis of incomplete data sets, unpublished, Erasmus University, Rotterdam.
- , , (2001) A comparison of inclusive and restrictive strategies in modern missing data procedures. Psychological Methods, 6, 330–351, DOI: 10.1037/1082-989X.6.4.330
- , (2008) An imputation strategy for incomplete longitudinal ordinal data. Statistics in Medicine, 27, 4086–4093, DOI: 10.1002/sim.3239
- , , , , (2011) mi: Missing Data Imputation and Model Checking. Package for the R statistical software. http://lib.stat.cmu.edu/R/CRAN/ [27 January 2011]
- (2003) Adding missing-data relevant variables to FIML-based structural equation models. Structural Equation Modeling, 10, 80–100, DOI: 10.1207/S15328007SEM1001_4
- (2009) Missing data analysis: making it work in the real world. Annual Review of Psychology, 60, 549–576, DOI: 10.1146/annurev.psych.58.110405.085530
- , , (2007) How many imputations are really needed? Some practical clarifications of multiple imputation theory. Prevention Science, 8, 206–213, DOI: 10.1007/s11121-007-0070-9
- , (1995) A critical look at methods for handling missing covariates in epidemiologic regression analyses. American Journal of Epidemiology, 142, 1255–1264.
- , (2007) Multiple imputation: review of theory, implementation and software. Statistics in Medicine, 26, 3057–3077, DOI: 10.1002/sim.2787
- , , , , (2009) Multiple imputation in a large-scale complex survey: a practical guide. Statistical Methods in Medical Research, 1–18, DOI: 10.1177/0962280208101273
- , (2007) Much ado about nothing: a comparison of missing data methods and software to fit incomplete data regression models. The American Statistician, 61, 79–90, DOI: 10.1198/000313007X172556
- (2005) WinMICE User's Manual for WinMICE Prototype Version 0.1, The Hague, TNO Quality of Life.
- , (2010) Multiple imputation for missing data: fully conditional specification versus multivariate normal imputation. American Journal of Epidemiology, 171, 624–632, DOI: 10.1093/aje/kwp425
- , , (2006) An analysis of incomplete longitudinal binary data using multiple imputation. Statistics in Medicine, 25, 2107–2124, DOI: 10.1002/sim.2343
- (2008) Mitools: tools for multiple imputation of missing data. Package for the R statistical software package. http://cran.r-project.org/web/packages/mitools/ [14 May 2008].
- , , (2002) Overview of the national evaluation of the comprehensive community mental health services for children and their families program. Children's Services: Social Policy, Research, and Practice, 5, 3–20, DOI: 10.1207/S15326918CS0501_2
- , , , (2006) Using the outcome for imputation of missing predictor values was preferred. Journal of Clinical Epidemiology, 59, 1092–1101, DOI: 10.1016/j.jclinepi.2006.01.009
- , (1998–2007) Mplus User's Guide, 4th edition, Los Angeles, CA, Muthen & Muthen.
- , , (2009) Missing values in longitudinal dietary data: a multiple imputation approach based on a fully conditional specification. Statistics in Medicine, 28, 3657–3669, DOI: 10.1002/sim.3731
- R Development Core Team (2008) R: A Language and Environment for Statistical Computing, Vienna, R Foundation for Statistical Computing.
- , , , (2001) A multivariate technique for multiply imputing missing values using a sequence of regression models. Survey Methodology, 27, 85–95.
- , , (2002) IVEware: Imputation and Variance Estimation Software User Guide, Ann Arbor, MI, University of Michigan. http://www.isr.umich.edu/src/smp/ive/ [19 May 2008].
- (2005) Multiple imputation of missing values – update. The Stata Journal, 5, 188–201.
- , , (2009) Multiple imputation of missing values: new features for mim. The Stata Journal, 9, 252–264.
- SAS Institute Inc. (2008) SAS/STAT User's Guide 9.2, Carey, NC, SAS Institute, Inc. http://support.sas.com/documentation/cdl/en/statug/59654/HTML/default/chap0_toc.htm# [29 May 2008].
- (1999) Multiple imputation: a primer. Statistical Methods in Medical Research, 8, 3–15, DOI: 10.1177/096228029900800102
- (2003) Multiple imputation in multivariate problems when the imputation and analysis models differ. Statistica Neerlandica, 57, 19–35.
- , (2002) Missing data: our view of the state of the art. Psychological Methods, 7, 147–177, DOI: 10.1111/1467-9574.00218
- , , , , , (2006) Multiple imputation of missing income data in the National Health Interview Survey. Journal of the American Statistical Association, 101, 924–933, DOI: 10.1198/016214505000001375
- Scientific Software International (2006) Lisrel 8.8, Lincolnwood, IL, Scientific Software International, Inc.
- SPSS Inc. (2009a) Amos 18.0. SPSS Missing Values 17.0, Chicago, IL, SPSS Inc.
- SPSS Inc. (2009b) SPSS Missing Values 17.0, Chicago, IL, SPSS Inc.
- StataCorp. (2009) Stata Multiple-imputation Reference Manual, College Station, TX, StataCorp., LP.
- , , , (2009) Practical imputation with large datasets: a case study of the Children's Mental Health Initiative. American Journal of Epidemiology, 169, 1133–1139, DOI: 10.1093/aje/kwp026
- , , , (in press) Multiple imputation with diagnostics (mi) in R: Opening windows into the black box. Journal of Statistical Software. http://www.stat.columbia.edu/~gelman/research/published/mipaper.rev04.pdf.
- (2007) Multiple imputation of discrete and continuous data by fully conditional specification. Statistical Methods in Medical Research, 16, 219–242, DOI: 10.1177/0962280206074463
- , (in press) MICE: Multivariate Imputation by Chained Equations in R. Journal of Statistical Software. http://lib.stat.cmu.edu/R/CRAN/web/packages/mice/index.html
- , , (2007) Evaluation of software for multiple imputation of semi-continuous data. Statistical Methods in Medical Research, 16, 243–258, DOI: 10.1177/0962280206074464
- (2000) Multiple imputation for missing data: new concepts and development. In Proceedings of the Twenty-Fifth Annual SAS Users Group International Conference (Paper No. 267), Cary, NC, SAS Institute.
- (2008) Multiple imputation inference for multivariate multilevel continuous data with ignorable non-response. Philosophical Transactions of the Royal Society A, 366, 2389–2403, DOI: 10.1098/rsta.2008.0038