Multiple Imputation for Multivariate Missing-Data Problems: A Data Analyst's Perspective
Abstract
Analyses of multivariate data are frequently hampered by missing values. Until recently, the only missing-data methods available to most data analysts have been relatively ad1 hoc practices such as listwise deletion. Recent dramatic advances in theoretical and computational statistics, however, have produced anew generation of flexible procedures with a sound statistical basis. These procedures involve multiple imputation (Rubin, 1987), a simulation technique that replaces each missing datum with a set of m > 1 plausible values. The rn versions of the complete data are analyzed by standard complete-data methods, and the results are combined using simple rules to yield estimates, standard errors, and p-values that formally incorporate missing-data uncertainty. New computational algorithms and software described in a recent book (Schafer, 1997a) allow us to create proper multiple imputations in complex multivariate settings. This article reviews the key ideas of multiple imputation, discusses the software programs currently available, and demonstrates their use on data from the Adolescent Alcohol Prevention Trial (Hansen & Graham, 199 I).
Integrity signals
Registry
Cites
Statistics
Claims the paper makes
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
Missing values were imputed using the expectation-maximization (EM) procedure.
“Missing values were imputed using the expectation–maximization (EM) procedure (Schafer & Olsen, 1998).”
From Measuring Decentering – Development and Validation of the French Version of the Experiences Questionnaire (EQ-F) (2024) · cites this paper as Schafer & Olsen, 1998
Missing data will be estimated using a multiple imputation procedure described by Schafer and Olsen.
“Missing data will be estimated using a multiple imputation procedure described by Schafer and Olsen [40].”
Cites
Maximum Likelihood from Incomplete Data Via the <i>EM</i> Algorithm
Dempster, A. P., Laird, N. M., & Rubin, D. B. (1977) · Journal of the Royal Statistical Society Series B: Statistical Methodology · doi:10.1111/j.2517-6161.1977.tb01600.x · Cited by 50,444 · see citing works
Multiple Imputation for Nonresponse in Surveys
Rubin, D. B. (1987) · Wiley Series in Probability and Statistics · doi:10.1002/9780470316696 · Cited by 20,701 · see citing works
Statistical Analysis With Missing Data
Lahiff, M., Little, R. J. A., & Rubin, D. B. (1989) · Journal of the American Statistical Association · doi:10.2307/2289883 · Cited by 17,384 · see citing works
Littell, R. C. (1996) · Medical Entomology and Zoology · Cited by 10,345 · see citing works
RUBIN, D. B. (1976) · Biometrika · doi:10.1093/biomet/63.3.581 · Cited by 9,925 · see citing works
Markov Chain Monte Carlo in Practice
Gilks, W. R., Richardson, S. T., & Spiegelhalter, D. J. (1995) · Chapman & Hall/CRC eBooks · doi:10.1201/b14835 · Cited by 7,927 · see citing works
Analysis of Incomplete Multivariate Data
Schafer, J. L. (1997) · doi:10.1201/9781439821862 · Cited by 6,012 · see citing works
Self-citationAnalysis of Incomplete Multivariate Data
Booth, D. E., & Schafer, J. L. (2000) · Technometrics · doi:10.2307/1271466 · Cited by 5,627 · see citing works
Self-citationMultiple imputation after 18+ years
Rubin, D. B. (1996) · Journal of the American Statistical Association · doi:10.1080/01621459.1996.10476908 · Cited by 4,072 · see citing works
The Calculation of Posterior Distributions by Data Augmentation
Tanner, M. A., & Wong, W. H. (1987) · Journal of the American Statistical Association · doi:10.1080/01621459.1987.10478458 · Cited by 3,929 · see citing works
Multiple Imputation After 18+ Years
Rubin, D. B. (1996) · Journal of the American Statistical Association · doi:10.2307/2291635 · Cited by 2,686 · see citing works
Maximum likelihood estimation via the ECM algorithm: A general framework
Meng, X., & Rubin, D. B. (1993) · Biometrika · doi:10.1093/biomet/80.2.267 · Cited by 1,835 · see citing works
Hansen, W. B., & Graham, J. A. (1991) · Preventive Medicine · doi:10.1016/0091-7435(91)90039-7 · Cited by 560 · see citing works
Arbuckle, J. (2008) · DSpace Biblioteca Universidad de Talca (Universidad de Talca) · Cited by 453 · see citing works
Analysis with missing data in prevention research.
Graham, J. A., Hofer, S. M., Donaldson, S. I., MacKinnon, D. P., & Schafer, J. L. (1997) · American Psychological Association eBooks · doi:10.1037/10222-010 · Cited by 280 · see citing works
Self-citationOn the performance of multiple imputation for multivariate data with small sample size
Graham, J. A., Schafer, J. L., & Hoyle, R. H. (1999) · Cited by 235 · see citing works
Self-citation
Flagged first, then by citations
Cited by
Sorted by citations
Missing data: our view of the state of the art
Schafer, J. L., & Graham, J. W. (2002) · Psychological Methods · doi:10.1037/1082-989x.7.2.147 · Cited by 11,638 · see citing works
Self-citationMissing data analysis: making it work in the real world
Graham, J. W. (2009) · Annual Review of Psychology · doi:10.1146/annurev.psych.58.110405.085530 · Cited by 6,163 · see citing works
How Many Imputations are Really Needed? Some Practical Clarifications of Multiple Imputation Theory
Graham, J. W., Olchowski, A. E., & Gilreath, T. D. (2007) · Prevention Science · doi:10.1007/s11121-007-0070-9 · Cited by 2,795 · see citing works
A comparison of inclusive and restrictive strategies in modern missing data procedures.
Collins, L. M., Schafer, J. L., & Kam, C.-M. (2001) · Psychological Methods · doi:10.1037/1082-989x.6.4.330 · Cited by 2,389 · see citing works
Self-citationPrincipled missing data methods for researchers
Dong, Y., & Peng, C.-Y. J. (2013) · SpringerPlus · doi:10.1186/2193-1801-2-222 · Cited by 2,208 · see citing works
Cheung, M. W.-L. (2014) · Psychological Methods · doi:10.1037/a0032968 · Cited by 1,342 · see citing works
A Primer on Maximum Likelihood Algorithms Available for Use With Missing Data
Enders, C. K. (2001) · Structural Equation Modeling: A Multidisciplinary Journal · doi:10.1207/s15328007sem0801_7 · Cited by 1,027 · see citing works
What to do about missing values in time series cross- section data
Honaker, J., & King, G. (2010) · American Journal of Political Science · doi:10.1111/j.1540-5907.2010.00447.x · Cited by 966 · see citing works
The use of multiple imputation for the analysis of missing data.
Sinharay, S., Stern, H. S., & Russell, D. (2001) · Psychological Methods · doi:10.1037/1082-989x.6.4.317 · Cited by 560 · see citing works
Ladd, G. W. (2006) · Child Development · doi:10.1111/j.1467-8624.2006.00905.x · Cited by 494 · see citing works
Church-Based Social Support and Health in Old Age: Exploring Variations by Race
Krause, N. (2002) · The Journals of Gerontology Series B: Psychological Sciences and Social Sciences · doi:10.1093/geronb/57.6.s332 · Cited by 469 · see citing works
Swami, V., & Barron, D. (2019) · Body Image · doi:10.1016/j.bodyim.2018.08.014 · Cited by 454 · see citing works
Organizational stressors and police performance
Shane, J. M. (2010) · Journal of Criminal Justice · doi:10.1016/j.jcrimjus.2010.05.008 · Cited by 389 · see citing works
Culturally Grounded Substance Use Prevention: An Evaluation of the keepin' it R.E.A.L. Curriculum
Hecht, M. L., Marsiglia, F. F., Elek, E., Wagstaff, D. A., Kulis, S., Dustman, P., & Miller-Day, M. (2003) · Prevention Science · doi:10.1023/a:1026016131401 · Cited by 383 · see citing works
Analyzing longitudinal data with missing values
Enders, C. K. (2011) · Rehabilitation Psychology · doi:10.1037/a0025579 · Cited by 321 · see citing works
A Primer on the Use of Modern Missing-Data Methods in Psychosomatic Medicine Research
Enders, C. K. (2006) · Psychosomatic Medicine · doi:10.1097/01.psy.0000221275.75056.d8 · Cited by 274 · see citing works
A comparison of item-level and scale-level multiple imputation for questionnaire batteries
Gottschall, A. C., West, S. G., & Enders, C. K. (2012) · Multivariate Behavioral Research · doi:10.1080/00273171.2012.640589 · Cited by 225 · see citing works
Psychological Distress and Cancer Survival: A Follow-Up 10 Years After Diagnosis
Brown, K. W., Levy, A. R., Rosberger, Z., & Edgar, L. (2003) · Psychosomatic Medicine · doi:10.1097/01.psy.0000077503.96903.a6 · Cited by 213 · see citing works
Blankers, M., Koeter, M. W. J., & Schippers, G. M. (2010) · Journal of Medical Internet Research · doi:10.2196/jmir.1448 · Cited by 194 · see citing works
Cheung, M. W.-L. (2008) · Psychological Methods · doi:10.1037/a0013163 · Cited by 175 · see citing works
Iterative stepwise regression imputation using standard and robust methods
Templ, M., Kowarik, A., & Filzmoser, P. (2011) · Computational Statistics & Data Analysis · doi:10.1016/j.csda.2011.04.012 · Cited by 169 · see citing works
Broderick, J. E., Schneider, S., Junghaenel, D. U., Schwartz, J. E., & Stone, A. A. (2013) · Arthritis Care & Research · doi:10.1002/acr.22025 · Cited by 158 · see citing works
Delgadillo, J., de Jong, K., Lucock, M., Lutz, W., Rubel, J., Gilbody, S., Ali, S., Aguirre, E., Appleton, M., Nevin, J., et al. (2018) · The Lancet Psychiatry · doi:10.1016/s2215-0366(18)30162-7 · Cited by 152 · see citing works
Dinov, I. D., Heavner, B., Tang, M., Glusman, G., Chard, K., Darcy, M., Madduri, R., Pa, J., Spino, C., Kesselman, C., et al. (2016) · PLOS ONE · doi:10.1371/journal.pone.0157077 · Cited by 145 · see citing works
Bureau, J.-F., Easterbrooks, M. A., & Lyons-Ruth, K. (2009) · Development and Psychopathology · doi:10.1017/s0954579409000285 · Cited by 132 · see citing works
Frost, D. M., Fine, M., Torre, M. E., & Cabana, A. (2019) · American Journal of Community Psychology · doi:10.1002/ajcp.12326 · Cited by 129 · see citing works
Smerillo, N. E., Reynolds, A. J., Temple, J. A., & Ou, S.-R. (2018) · Journal of School Psychology · doi:10.1016/j.jsp.2017.11.001 · Cited by 125 · see citing works
Impact of diabetes on cognitive function among older Latinos
Wu, J. H., Haan, M. N., Liang, J., Ghosh, D., Gonzalez, H. M., & Herman, W. H. (2003) · Journal of Clinical Epidemiology · doi:10.1016/s0895-4356(03)00077-5 · Cited by 104 · see citing works
Sullivan, T. R., Salter, A. B., Ryan, P., & Lee, K. J. (2015) · American Journal of Epidemiology · doi:10.1093/aje/kwv100 · Cited by 86 · see citing works
Understanding infidelity: Correlates in a national random sample.
Atkins, D. C., Baucom, D. H., & Jacobson, N. S. (2001) · Journal of Family Psychology · doi:10.1037/0893-3200.15.4.735 · Cited by 458 · see citing works
Shilton, A. L., Laycock, R., & Crewther, S. G. (2017) · Frontiers in Psychology · doi:10.3389/fpsyg.2017.00567 · Cited by 76 · see citing works
Ekkers, W., Korrelboom, K., Huijbrechts, I., Smits, N., Cuijpers, P., & van der Gaag, M. (2011) · Behaviour Research and Therapy · doi:10.1016/j.brat.2011.05.010 · Cited by 75 · see citing works
A framework and a measurement instrument for sustainability of work practices in long-term care
Slaghuis, S. S., Strating, M. M., Bal, R. A., & Nieboer, A. P. (2011) · BMC Health Services Research · doi:10.1186/1472-6963-11-314 · Cited by 71 · see citing works
Wu, J. H., Haan, M. N., Liang, J., Ghosh, D., Gonzalez, H. M., & Herman, W. H. (2003) · Annals of Epidemiology · doi:10.1016/s1047-2797(02)00464-7 · Cited by 68 · see citing works
Ansari, A., & Winsler, A. (2014) · Journal of Educational Psychology · doi:10.1037/a0036799 · Cited by 65 · see citing works
The costs of social anxiety disorder: the role of symptom severity and comorbidities
Stuhldreher, N., Leibing, E., Leichsenring, F., Beutel, M. E., Herpertz, S., Hoyer, J., Konnopka, A., Salzer, S., Strauss, B., Wiltink, J., et al. (2014) · Journal of Affective Disorders · doi:10.1016/j.jad.2014.04.039 · Cited by 63 · see citing works
Rhode, M. P., & Arriaza, B. T. (2006) · American Journal of Physical Anthropology · doi:10.1002/ajpa.20333 · Cited by 61 · see citing works
Missing data techniques for multilevel data: implications of model misspecification
Black, A. C., Harel, O., & Betsy McCoach, D. (2011) · Journal of Applied Statistics · doi:10.1080/02664763.2010.529882 · Cited by 55 · see citing works
Lustyk, M. K. B., Olson, K. C., Gerrish, W. G., Holder, A., & Widman, L. (2010) · Biological Psychology · doi:10.1016/j.biopsycho.2009.11.003 · Cited by 53 · see citing works
Examining language and early numeracy skills in young Latino dual language learners
Méndez, L. I., Hammer, C. S., Lopez, L. M., & Blair, C. (2019) · Early Childhood Research Quarterly · doi:10.1016/j.ecresq.2018.02.004 · Cited by 51 · see citing works
Bücker, L., Bierbrodt, J., Hand, I., Wittekind, C., & Moritz, S. (2018) · PLoS ONE · doi:10.1371/journal.pone.0198859 · Cited by 50 · see citing works
Chronic Fatigue Self-Management in Primary Care: A Randomized Trial
Friedberg, F., Napoli, A., Coronel, J., Adamowicz, J., Seva, V., Caikauskaite, I., Ngan, M. C., Chang, J., & Meng, H. (2013) · Psychosomatic Medicine · doi:10.1097/psy.0b013e31829dbed4 · Cited by 30 · see citing works
“Missing data were assumed to be missing at random (33).”
BackgroundGuerrini Usubini, A., Varallo, G., Giusti, E. M., Cattivelli, R., Granese, V., Consoli, S., Bastoni, I., Volpi, C., & Castelnuovo, G. (2022) · Frontiers in Psychology · doi:10.3389/fpsyg.2022.861341 · Cited by 22 · see citing works
Prigerson, H. G., Viola, M., Brewin, C. R., Cox, C., Ouyang, D., Rogers, M., Pan, C. X., Rabin, S., Xu, J., Vaughan, S., et al. (2019) · Trials · doi:10.1186/s13063-019-3515-0 · Cited by 23 · see citing works
Handling missing data in single-case studies
Peng, C.-Y. J., & Chen, L.-T. (2018) · Journal of Modern Applied Statistical Methods · doi:10.22237/jmasm/1525133280 · Cited by 22 · see citing works
Gamaiunova, L., Shankland, R., Moore, M., Mayor, E., Dessart, G., Kotsou, I., & Fresco, D. (2024) · Psychological Test Adaptation and Development · doi:10.1027/2698-1866/a000083 · Cited by 1 · see citing works
- Authors
- Schafer, J. L., & Olsen, M. K.
- Affiliations
- Pennsylvania State University (US)
- ORCID
- Olsen, Maren K.
- Venue
- Multivariate Behavioral Research
- Publisher
- Informa UK Limited
- Published
- 1998-10
- Volume
- 33
- Issue
- 4
- Pages
- 545-571
- ISSN
- 0027-3171 (ISSN-L)
- 1532-7906
- OpenAlex
- W2031668066
- Cited by
- 1,518
- References
- 16
- Citations by year
- 2026: 21 · 2025: 35 · 2024: 51 · 2023: 42 · 2022: 70 · 2021: 81 · 2020: 63 · 2019: 78 · 2018: 81 · 2017: 83 · 2016: 76 · 2015: 73 · 2014: 85 · 2013: 82 · 2012: 80
- FWCI
- 16.42
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Multivariate Behavioral Research (publishedVersion)
- PubMed (publishedVersion)
- Topics
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Bayesian Inference
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Applications
- Social Sciences › Decision Sciences › Management Science and Operations Research › Psychometric Methodologies and Testing
- Keywords
- multiple imputation, missing data, listwise deletion
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
