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Multiple Imputation of Missing Values
Open accessAbstract
Following the seminal publications of Rubin about thirty years ago, statisticians have become increasingly aware of the inadequacy of “complete-case” analysis of datasets with missing observations. In medicine, for example, observations may be missing in a sporadic way for different covariates, and a complete-case analysis may omit as many as half of the available cases. Hotdeck imputation was implemented in Stata in 1999 by Mander and Clayton. However, this technique may perform poorly when many rows of data have at least one missing value. This article describes an implementation for Stata of the MICE method of multiple multivariate imputation described by van Buuren, Boshuizen, and Knook (1999). MICE stands for multivariate imputation by chained equations. The basic idea of data analysis with multiple imputation is to create a small number (e.g., 5–10) of copies of the data, each of which has the missing values suitably imputed, and analyze each complete dataset independently. Estimates of parameters of interest are averaged across the copies to give a single estimate. Standard errors are computed according to the “Rubin rules”, devised to allow for the between- and within-imputation components of variation in the parameter estimates. This article describes five ado-files. mvis creates multiple multivariate imputations. uvis imputes missing values for a single variable as a function of several covariates, each with complete data. micombine fits a wide variety of regression models to a multiply imputed dataset, combining the estimates using Rubin's rules, and supports survival analysis models (stcox and streg), categorical data models, generalized linear models, and more. Finally, misplit and mijoin are utilities to intercon-vert datasets created by mvis and by the miset program from John Carlin and colleagues. The use of the routines is illustrated with an example of prognostic modeling in breast cancer.
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“Missing data were imputed through multiple imputation with Stata using the MICE (multivariate imputation by chained equations) module (Royston, 2004).Five imputed data sets were generated.”
From Culture and Identity‐Protective Cognition: Explaining the White‐Male Effect in Risk Perception (2007) · cites this paper as Royston, 2004
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- 10.1177/1536867X0300300302 · DOI
- 10.1016/S0895-4356(02)00539-5 · DOI
- Mander A., 1999, Stata Technical Bulletin, 51, 32
- 10.1093/biomet/63.3.581 · DOI · Paper page
- 10.1111/1467-985X.00122 · DOI
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“puted using multiple imputation method with five data sets (27).”
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“The application in Stata was developed by Patrick Royston (2004).”
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“We imputed missing information on covariates and outcomes (n = 22 to n = 84) using chained equations ("mi impute chained" in STATA) [24].”
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“Ten imputed data sets were generated and analyzed separately, and the results were combined using the Rubin's method (Supplementary Tables 1 and 2) (Royston, 2004).”
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Family Events and the Timing of Intergenerational Transfers
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“For the imputation and the estimation of our models we use the Stata commands ice and mim (”
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“Missing data were imputed using the univariate imputation procedure in Stata (Royston, 2004, 2005).”
BackgroundMethodInfluentialHodsoll, J., Rhind, C., Micali, N., Hibbs, R., Goddard, E., Nazar, B. P., Schmidt, U., Gowers, S., Macdonald, P., Todd, G., et al. (2017) · European eating disorders review · doi:10.1002/erv.2540 · Cited by 59
“Missing data were imputed with the user written commands ‘mi’ and ‘ice’ in STATA (Royston, 2004).”
MethodInfluentialChildren’s Education and Parents’ Trajectories of Depressive Symptoms
Lee, C., Glei, D. A., Goldman, N., & Weinstein, M. (2017) · Journal of Health and Social Behavior · doi:10.1177/0022146517690200 · Cited by 66
Schmidt, U., Ryan, E., Bartholdy, S., Renwick, B., Keyes, A., O’Hara, C. B., McClelland, J., Lose, A., Kenyon, M., DeJong, H., et al. (2016) · International Journal of Eating Disorders · doi:10.1002/eat.22523 · Cited by 59
Borgonovi, F., & Pokropek, A. (2016) · PLoS ONE · doi:10.1371/journal.pone.0149716 · Cited by 103
“All our analyses are based on estimates obtained using multiple imputation of missing information [82] using ten imputation datasets, each generated with one literacy plausible value score.”
MethodSettlement Intentions of Recently Arrived Immigrants and Refugees in the Netherlands
de Vroome, T., & van Tubergen, F. (2014) · doi:10.1080/15562948.2013.810798 · Cited by 59
“6%), we have used multiple imputation with the program ICE in Stata 11 to impute the missing values (Royston, 2004).”
MethodKoury, A. S., & Votruba-Drzal, E. (2014) · Journal of Educational Psychology · doi:10.1037/a0034374 · Cited by 59
Luntamo, M., Kulmala, T., Cheung, Y. B., Maleta, K. M., & Ashorn, P. (2013) · Tropical Medicine & International Health · doi:10.1111/tmi.12074 · Cited by 56
“1% of newborns were recorded to weigh exactly 2500 g): one defined LBW as 2500 g, another considered a birthweight of 2500 g a missing value and used a multiple imputation method to replace the value (van Buuren et al. 1999; Royston 2004).”
MethodInfluentialWhich patients have missing data? An analysis of missingness in a trauma registry.
O'Reilly, G., Cameron, P., & Jolley, D. (2012) · Injury · doi:10.1016/j.injury.2012.07.185 · Cited by 59
Perceptions of Collective Effcacy and Bullying Perpetration in Schools
Williams, K., & Guerra, N. (2011) · Social Problems · doi:10.1525/sp.2011.58.1.126 · Cited by 59
“Since all analyses were done in Stata/SE 10.1, imputation with chained equations was performed using the “ice” command (see Carlin, Galati, and Royston 2008; Royston 2004 for descriptions).”
MethodInfluentialJarvis, J. P., & Regoeczi, W. (2009) · doi:10.1177/1088767909331694 · Cited by 59
“The results of the logistic regression analyses on these mul tiply imputed datasets were combined using the STATA procedure MICOMBINE.”
MethodLovasi, G. S., Moudon, A. V., Smith, N. L., Lumley, T., Larson, E. B., Sohn, D. W., Siscovick, D. S., & Psaty, B. M. (2007) · Health & Place · doi:10.1016/j.healthplace.2007.09.004 · Cited by 65
“We imputed the data five times using switching regression; resulting confidence intervals reflect uncertainty due to missing data (Royston, 2004).”
MethodKirksey, J. J. (2019) · AERA Open · doi:10.1177/2332858419867692 · Cited by 69
“In the case of missing data, chained multiple imputation will be used to fill missing data for each student in the data set based on their other reported characteristics (Royston, 2004).”
MethodUtilizing Multidimensional Measures of Race in Education Research
Irizarry, Y. (2015) · Sociology of Race and Ethnicity · doi:10.1177/2332649215580350 · Cited by 63
Locally linear reconstruction based missing value imputation for supervised learning
Kang, P. (2013) · Neurocomputing · doi:10.1016/j.neucom.2013.02.016 · Cited by 58
“In contrast to single imputation methods, multiple imputation methods impute a set of possible values rather than a single value for the missing attribute of an instance [43,34].”
MethodMiller, P. L., Votruba-Drzal, E., & Coley, R. (2013) · Children and Youth Services Review · doi:10.1016/j.childyouth.2013.04.024 · Cited by 58
Michaud, K., Vera-Llonch, M., & Oster, G. (2012) · Journal of Rheumatology · doi:10.3899/jrheum.110491 · Cited by 58
McCrory, C., & Layte, R. (2011) · Social Science & Medicine (1967) · doi:10.1016/j.socscimed.2011.03.002 · Cited by 58
Michaud, K., Wallenstein, G., & Wolfe, F. (2010) · Arthritis care & research · doi:10.1002/acr.20405 · Cited by 58
Her Mother's Daughter? The Influence of Childhood Socialization on Women's Political Engagement
Gidengil, E., O’Neill, B., & Young, L. (2010) · doi:10.1080/1554477x.2010.533590 · Cited by 58
“We used the ICE method developed by Royston (2004, 2005) to impute the missing val- ues, and employed the tools developed by John B. Carlin and his colleagues (2008) to analyze the multiply imputed data in Stata.”
MethodHead Start's Comparative Advantage: Myth or Reality?
Gormley, W. T., Phillips, D. A., Adelstein, S., & Shaw, C. (2010) · Policy Studies Journal · doi:10.1111/j.1541-0072.2010.00367.x · Cited by 66
Metadata
- Authors
- Royston, P.
- Affiliations
- MRC Clinical Trials Unit at UCL (GB)
- Corresponding author
- Royston, Patrick
- ORCID
- Royston, Patrick
- Venue
- The Stata Journal: Promoting communications on statistics and Stata
- Publisher
- SAGE Publications
- Published
- 2004-08
- Volume
- 4
- Issue
- 3
- Pages
- 227-241
- ISSN
- 1536-867X (ISSN-L)
- 1536-8734
- OpenAlex
- W2161375627
- Cited by
- 2,340
- References
- 0
- Citations by year
- 2026: 40 · 2025: 49 · 2024: 42 · 2023: 67 · 2022: 99 · 2021: 106 · 2020: 100 · 2019: 107 · 2018: 103 · 2017: 109 · 2016: 123 · 2015: 129 · 2014: 137 · 2013: 179 · 2012: 178
- FWCI
- 46.61
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- The Stata Journal Promoting communications on statistics and Stata (publishedVersion)
- RePEc: Research Papers in Economics (submittedVersion)
- AgEcon Search (University of Minnesota, USA) (submittedVersion, cc-by-nc-nd)
- AgEcon Search (University of Minnesota, USA)
- Topics
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Bayesian Inference
- Physical Sciences › Mathematics › Statistics and Probability › Data Analysis with R
- Physical Sciences › Mathematics › Statistics and Probability › Advanced Causal Inference Techniques
- Keywords
- multiple imputation, chained equations, Stata ado file, missing data, complete case analysis, Rubin's rules, survival analysis, prognostic model, breast cancer
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