The DOI matches its Crossref record.
Analysis of Incomplete Multivariate Data
Abstract
The last two decades have seen enormous developments in statistical methods for incomplete data. The EM algorithm and its extensions, multiple imputation, and Markov Chain Monte Carlo provide a set of flexible and reliable tools from inference in large classes of missing-data problems. Yet, in practical terms, those developments have had surprisingly little impact on the way most data analysts handle missing values on a routine basis. Analysis of Incomplete Multivariate Data helps bridge the gap between theory and practice, making these missing-data tools accessible to a broad audience. It presents a unified, Bayesian approach to the analysis of incomplete multivariate data, covering datasets in which the variables are continuous, categorical, or both. The focus is applied, where necessary, to help readers thoroughly understand the statistical properties of those methods, and the behavior of the accompanying algorithms.All techniques are illustrated with real data examples, with extended discussion and practical advice. All of the algorithms described in this book have been implemented by the author for general use in the statistical languages S and S Plus. The software is available free of charge on the Internet.
Overview
Integrity signals
Registry
Cites
Statistics
Verification
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?
In the citing paper
“Methods to deal with data missing at random (MAR) fall into three broad classes [ 108 , 111 ]: likelihood-based approaches [ 112 ], weighted estimation [ 113 ] and multiple imputation [ 111 , 114 ].”
From Strengthening the Reporting of Observational Studies in Epidemiology (STROBE): Explanation and Elaboration (2007) · cites this paper as [111]
In the citing paper
“The percentage of missing values in the WAI-TECH-SF, PHQ-9, and CEQ scores ranged from 0% to 1.6%. After testing that the values were missing at random using Little’s MCAR test (p > 0.05), they were imputed using the Expectation–Maximization Algorithm method [40].”
In the citing paper
“Parallel Analysis [40] showed that one factor had to be retained because only one factor had an eigenvalue (raw data eigenvalue = 9.08) greater than the eigenvalue at the 95th percentile for randomly generated data (95th percentile eigenvalue = 1.53) [48].”
In the citing paper
“For the remaining part of the survey, we utilized a planned missing data design or “matrix sampling” (Schafer, 1997; Graham et al., 2006) to keep the burden on participants to a minimum, and used multiple imputations to deal with the uncertainty related to missing data (as described in detail in Section Multiple Imputation Procedure below).”
From Using Genetic Algorithms in a Large Nationally Representative American Sample to Abbreviate the Multidimensional Experiential Avoidance Questionnaire (2016) · cites this paper as Schafer, 1997
In the citing paper
“Missing data for outcomes at six weeks, six months and 12 months were imputed using multiple imputation based upon the Markov chain Monte Carlo method (Schafer, 1997) and maximum likelihood imputation based upon the Expectation-Maximization (EM) algorithm.”
From A randomised clinical trial to evaluate the acceptability and efficacy of an early phase, online, guided augmentation of outpatient care for adults with anorexia nervosa (2020) · cites this paper as Schafer, 1997
Citations
Cited by
Sorted by citations
Items 801–900 of 1,077
Troop‐Gordon, W., & Kopp, J. (2011) · Social Development · doi:10.1111/j.1467-9507.2011.00604.x · Cited by 124
Randomized controlled evaluation of an early intervention to prevent post-rape psychopathology
Resnick, H. S., Acierno, R. E., Waldrop, A. E., King, L. A., King, D. W., Danielson, C. K., Ruggiero, K. J., & Kilpatrick, D. G. (2007) · Behaviour Research and Therapy · doi:10.1016/j.brat.2007.05.002 · Cited by 111
Parish, S. L., Magaña, S., Rose, R. A., Timberlake, M. T., & Swaine, J. G. (2012) · American Journal on Intellectual and Developmental Disabilities · doi:10.1352/1944-7558-117.4.304 · Cited by 119
Zhang, D., Landmark, L. J., Reber, A., Hsu, H.-Y. M., Kwok, O., & Benz, M. R. (2009) · Remedial and Special Education · doi:10.1177/0741932509338348 · Cited by 129
Multiple imputation techniques in small sample clinical trials
Barnes, S. A., Lindborg, S. R., & Seaman, J. W. (2005) · Statistics in Medicine · doi:10.1002/sim.2231 · Cited by 112
A randomized controlled bicenter trial of yoga for patients with colorectal cancer
Cramer, H., Pokhrel, B., Fester, C., Meier, B., Gaß, F., Lauche, R., Eggleston, B., Walz, M. K., Michalsen, A., Kunz, R., et al. (2015) · Psycho-Oncology · doi:10.1002/pon.3927 · Cited by 111
The Impact of Regime Type on Health: Does Redistribution Explain Everything?
Wigley, S., & Akkoyunlu-Wigley, A. (2011) · World Politics · doi:10.1017/s0043887111000177 · Cited by 110
Kelley, M. L., & Fals-Stewart, W. S. (2002) · Journal of Consulting and Clinical Psychology · doi:10.1037/0022-006x.70.2.417 · Cited by 111
“However, listwise deletion produces biased parameter estimates, particularly in instances in which more than 5% of cases have missing data (Schafer, 1997).”
BackgroundCystatin C, Albuminuria, and 5-Year All-Cause Mortality in HIV-Infected Persons
Choi, A. I., Scherzer, R., Bacchetti, P., Tien, P. C., Saag, M. S., Gibert, C. L., Szczech, L. A. M., Grünfeld, C., & Shlipak, M. G. (2010) · American Journal of Kidney Diseases · doi:10.1053/j.ajkd.2010.05.019 · Cited by 110
The Dark Side of Chinese Growth: Declining Social Capital and Well-Being in Times of Economic Boom
Bartolini, S., & Sarracino, F. (2015) · World Development · doi:10.1016/j.worlddev.2015.05.010 · Cited by 109
Kropko, J., Goodrich, B., Gelman, A., & Hill, J. (2014) · Political Analysis · doi:10.1093/pan/mpu007 · Cited by 111
Non-Hierarchical Multilevel Models
Rasbash, J., & Browne, W. J. (2007) · Springer eBooks · doi:10.1007/978-0-387-73186-5_8 · Cited by 110
“Data augmentation has been reviewed by Schafer [19].”
MethodBirthweight, childhood growth, and blood pressure at 43 years in a British birth cohort
Hardy, R. (2004) · International Journal of Epidemiology · doi:10.1093/ije/dyh027 · Cited by 110
Nested multiple imputation of NMES via partially incompatible MCMC
Rubin, D. B. (2003) · Statistica Neerlandica · doi:10.1111/1467-9574.00217 · Cited by 108
Circulating serum xenoestrogens and mammographic breast density
Sprague, B. L., Trentham‐Dietz, A., Hedman, C. J., Wang, J., Hemming, J. D. C., Hampton, J. M., Buist, D. S. M., Bowles, E. J. A., Sisney, G. S., & Burnside, E. S. (2013) · Breast Cancer Research · doi:10.1186/bcr3432 · Cited by 109
Cottrell, D. J., Wright-Hughes, A., Collinson, M., Boston, P., Eisler, I., Fortune, S., Graham, E. H., Green, J., House, A. O., Kerfoot, M., et al. (2018) · The Lancet Psychiatry · doi:10.1016/s2215-0366(18)30058-0 · Cited by 109
School-Based Drug Prevention Among At-Risk Adolescents: Effects of ALERT Plus
Longshore, D. L., Ellickson, P. L., McCaffrey, D. F., & Clair, P. A. S. (2007) · Health Education & Behavior · doi:10.1177/1090198106294895 · Cited by 108
Dhont, K., Hiel, A. V., & Hewstone, M. (2013) · Group Processes & Intergroup Relations · doi:10.1177/1368430213497064 · Cited by 126
A SVM Regression Based Approach to Filling in Missing Values
Honghai, F., Guoshun, C., Cheng, Y., et al. (2005) · Lecture notes in computer science · doi:10.1007/11553939_83 · Cited by 109
“Means and regression imputation [2,3,4] are widely used, due to their quickness and simplicity and lack of easy-to-use software packages that implement more advanced methods, such as EM imputation [2,3,4].”
MethodMethods for Addressing Missing Data in Psychiatric and Developmental Research
Croy, C. D., & Novins, D. K. (2005) · Journal of the American Academy of Child & Adolescent Psychiatry · doi:10.1097/01.chi.0000181044.06337.6f · Cited by 109
“Fourth, the researcher should generate an adequate number of imputed values to replace the missing data; we recommend at least five (Allison, 2003; Rubin, 1996; Schafer, 1997).”
BackgroundMethodWeinfurt, K. P., Castel, L. D., Li, Y., et al. (2003) · Cancer · doi:10.1002/cncr.11483 · Cited by 109
“Statistical Analysis Missing data were handled using multiple imputation by means of a full Bayes multivariate normal imputation model containing all study variables.(23) That is, a full Bayes multivariate normal model of the data with noninformative priors was used to generate posterior densities from which values we…”
MethodInfluentialGervai, J., Novák, A., Lakatos, K., Tóth, I., Danis, I., Rónai, Z., Nemoda, Z., Sasvári‐Székely, M., Bureau, J.-F., Bronfman, E. T., et al. (2007) · Social Neuroscience · doi:10.1080/17470910701391893 · Cited by 113
Substance use and community violence: A test of the relation at the daily level.
Mulvey, E. P., Odgers, C. L., Skeem, J. L., Gardner, W. P., Schubert, C. A., & Lidz, C. W. (2006) · Journal of Consulting and Clinical Psychology · doi:10.1037/0022-006x.74.4.743 · Cited by 110
Echinacea for Treating the Common Cold
Barrett, B. P., Brown, R., Rakel, D., Mundt, M. P., Bone, K. M., Barlow, S., & Ewers, T. (2010) · Annals of Internal Medicine · doi:10.7326/0003-4819-153-12-201012210-00003 · Cited by 109
Swanson, K. A., Bastani, R., Rubenstein, L. V., Meredith, L. S., & Ford, D. E. (2007) · Medical Care Research and Review · doi:10.1177/1077558707299479 · Cited by 110
“Three datasets were imputed using a procedure called the Markov Chain Monte Carlo (MCMC) method, which is prescribed for datasets with randomly missing data (Schafer 1997).”
MethodErler, N. S., Rizopoulos, D., van Rosmalen, J., Jaddoe, V. W. V., Franco, O. H., & Lesaffre, E. M. E. H. (2016) · Statistics in Medicine · doi:10.1002/sim.6944 · Cited by 103
Nadelson, L. S., & Southerland, S. A. (2012) · International Journal of Science Education · doi:10.1080/09500693.2012.702235 · Cited by 110
Newgard, C. D. (2006) · Academic Emergency Medicine · doi:10.1197/j.aem.2005.09.011 · Cited by 111
Effects of Legal BAC Limits on Fatal Crash Involvement: Analyses of 28 States from 1976 through 2002
Wagenaar, A. C., Maldonado‐Molina, M. M., Ma, L., et al. (2007) · Journal of Safety Research · doi:10.1016/j.jsr.2007.06.001 · Cited by 108
Cui, M., & Conger, R. D. (2008) · Journal of Research on Adolescence · doi:10.1111/j.1532-7795.2008.00560.x · Cited by 107
Imputation of missing values of tumour stage in population-based cancer registration
Eisemann, N., Waldmann, A., & Katalinic, A. (2011) · BMC Medical Research Methodology · doi:10.1186/1471-2288-11-129 · Cited by 107
Heinrichs, A. J., Heinrichs, B. S., Harel, O., Rogers, G. W., & Place, N. T. (2005) · Journal of Dairy Science · doi:10.3168/jds.s0022-0302(05)72963-5 · Cited by 108
“Reviews (Allison, 2002; Schafer, 1999; Schafer and Olsen, 1998) and a detailed application of the method (Schafer, 1997) have been published.”
MethodModelling relative survival in the presence of incomplete data: a tutorial
Nur, U., Shack, L., Rachet, B., Carpenter, J. R., & Coleman, M. P. (2009) · International Journal of Epidemiology · doi:10.1093/ije/dyp309 · Cited by 107
Proper and Improper Multiple Imputation
Nielsen, S. F. (2003) · International Statistical Review · doi:10.1111/j.1751-5823.2003.tb00214.x · Cited by 106
Bayesian perspectives for epidemiologic research: III. Bias analysis via missing-data methods
Greenland, S. (2009) · International Journal of Epidemiology · doi:10.1093/ije/dyp278 · Cited by 107
Becerra, A. Z., Probst, C. P., Tejani, M. A., et al. (2016) · Annals of Surgical Oncology · doi:10.1245/s10434-015-5014-1 · Cited by 107
Long-Term Mortality Effect of Early Pacemaker Implantation After Surgical Aortic Valve Replacement
Greason, K. L., Lahr, B. D., Stulak, J. M., Cha, Y., Rea, R. F., Schaff, H. V., & Dearani, J. A. (2017) · The Annals of Thoracic Surgery · doi:10.1016/j.athoracsur.2017.01.083 · Cited by 108
Gender differences in the impact of comprehensive services in substance abuse treatment
Marsh, J. C., Cao, D., & D’Aunno, T. A. (2004) · Journal of Substance Abuse Treatment · doi:10.1016/j.jsat.2004.08.004 · Cited by 107
“In the multiple imputation procedure, each missing value was replaced with five plausible values using Markov Chain Monte Carlo method ( Schafer, 1997 ).”
MethodWinters, J. J., Fals-Stewart, W., O'Farrell, T., Birchler, G., & Kelley, M. (2002) · Journal of Consulting and Clinical Psychology · doi:10.1037/0022-006x.70.2.344 · Cited by 111
“Listwise deletion produces biased parameter estimates, particularly in instances where more than 5% of cases have missing data and when data are not missing completely at random (Schafer, 1997).”
BackgroundKennedy, B. S., Kasl, S. V., & Vaccarino, V. (2001) · American Journal of Epidemiology · doi:10.1093/aje/153.3.232 · Cited by 107
“In all multivariate models, the issue of having subjects with missing covariate information was handled by using the method of multiple imputation as previously described by Rubin (50) and Schafer ( 51 ) and implemented by using macro programs in the SAS/IML language based upon the work of Allison (52).”
MethodKupelian, V. A., Link, C. L., & McKinlay, J. B. (2007) · European Urology · doi:10.1016/j.eururo.2007.03.015 · Cited by 106
Sehl, M. E., Lu, X., Silliman, R. A., & Ganz, P. A. (2012) · Journal of Cancer Survivorship · doi:10.1007/s11764-012-0239-5 · Cited by 107
Anstey, K. J., Hofer, S. M., & Luszcz, M. A. (2003) · Journal of Experimental Psychology General · doi:10.1037/0096-3445.132.3.470 · Cited by 107
Culpin, I., Stapinski, L. A., Miles, Ö. B., Araya, R., & Joinson, C. J. (2015) · Journal of Affective Disorders · doi:10.1016/j.jad.2015.05.030 · Cited by 108
Survival after bidirectional cavopulmonary anastomosis: Analysis of preoperative risk factors
Scheurer, M. A., Hill, E. G., Vasuki, N., Maurer, S. H., Graham, E. M., Bandisode, V. M., Shirali, G. S., Atz, A. M., & Bradley, S. M. (2007) · Journal of Thoracic and Cardiovascular Surgery · doi:10.1016/j.jtcvs.2007.02.017 · Cited by 106
Multivariate missing data in hydrology – Review and applications
Aissia, M. ‐. B., Chebana, F., & Ouarda, T. B. M. J. (2017) · Advances in Water Resources · doi:10.1016/j.advwatres.2017.10.002 · Cited by 107
The path from social origins to top jobs: social reproduction via education
Sullivan, A., Parsons, S., Green, F., Wiggins, R. D., & Ploubidis, G. B. (2017) · British Journal of Sociology · doi:10.1111/1468-4446.12314 · Cited by 105
“As list-wise deletion/complete case analysis returns biased estimates, we use multiple imputation with chained equations (20 imputed datasets) to ‘fill-in’ values of any missing items in the variables selected for our analysis adopting Schafer’s data augmentation approach (Schafer 1997) under the assumption”
MethodPseudobulbar affect: an under-recognized and under-treated neurological disorder
Work, S. S., Colamonico, J., Bradley, W. G., & Kaye, R. E. (2011) · Advances in Therapy · doi:10.1007/s12325-011-0031-3 · Cited by 105
Marti, C. N. (2008) · Community College Journal of Research and Practice · doi:10.1080/10668920701366867 · Cited by 118
Recovery of information from multiple imputation: a simulation study
Lee, K. J., & Carlin, J. B. (2012) · Emerging Themes in Epidemiology · doi:10.1186/1742-7622-9-3 · Cited by 105
The analysis of incomplete cost data due to dropout
Oostenbrink, J. B., & Al, M. (2005) · Health Economics · doi:10.1002/hec.966 · Cited by 106
Tools for Analyzing Multiple Imputed Datasets
Carlin, J., Li, N., Greenwood, P., & Coffey, C. (2003) · The Stata Journal Promoting communications on statistics and Stata · doi:10.1177/1536867x0300300302 · Cited by 113
“For general model specifications, this in principle requires Markov Chain Monte Carlo ( MCMC ) methods, and Schafer (1997) has developed a set of reasonably flexible software that covers a range of models.”
BackgroundMethodChae, D. H., & Walters, K. L. (2009) · American Journal of Public Health · doi:10.2105/ajph.2007.126003 · Cited by 106
Guerrero, E. G., & Andrews, C. M. (2011) · Drug and Alcohol Dependence · doi:10.1016/j.drugalcdep.2011.05.020 · Cited by 110
Arsandaux, J., Montagni, I., Macalli, M., Texier, N., Pouriel, M., Germain, R., Mebarki, A., Kinouani, S., Tournier, M., Schück, S., et al. (2021) · BMJ Open · doi:10.1136/bmjopen-2021-053231 · Cited by 120
Dunton, G. F., Liao, Y., Dzubur, E., Leventhal, A. M., Huh, J., Gruenewald, T. L., Margolin, G., Koprowski, C., Tate, E. B., & Intille, S. S. (2015) · Contemporary Clinical Trials · doi:10.1016/j.cct.2015.05.007 · Cited by 103
Naghib, A., Gharehchopogh, F. S., & Zamanifar, A. (2025) · Artificial Intelligence Review · doi:10.1007/s10462-024-11101-w · Cited by 135
Ginsburg, G. S., Becker, K. D., Drazdowski, T. K., & Tein, J. (2011) · Child & Youth Care Forum · doi:10.1007/s10566-011-9156-4 · Cited by 107
Capital structure and innovation: causality and determinants
Bartoloni, E. (2011) · Empirica · doi:10.1007/s10663-011-9179-y · Cited by 107
A Parametric Approach for Dealing with Compositional Rounded Zeros
Palarea‐Albaladejo, J., Fernández, J. A. M., & Gómez-García, J. (2007) · Mathematical Geology · doi:10.1007/s11004-007-9100-1 · Cited by 105
“As stated in Schafer (1997) or Little and Rubin (2002), the EM algorithm (Dempster et al. 1977) and the multiple imputation (MI) method (Rubin 1987) are the most reliable parametric methods for missing data in a real space and represents the current state of the art.”
MethodImpact of Diabetes Screening on Quality of Life
Edelman, D. E., Olsen, M. K., Dudley, T. K., Harris, A. C., & Oddone, E. Ž. (2002) · Diabetes Care · doi:10.2337/diacare.25.6.1022 · Cited by 106
Day, D. V., Sin, H., & Chen, T. T. (2004) · Personnel Psychology · doi:10.1111/j.1744-6570.2004.00001.x · Cited by 110
“In cases of nonignorable missingness, results are robust to the extent that all data are efficiently used and the amount of missing data is relatively small (Schafer, 1997).”
BackgroundML Versus MI for Missing Data With Violation of Distribution Conditions
Yuan, K., Yang‐Wallentin, F., & Bentler, P. M. (2012) · Sociological Methods & Research · doi:10.1177/0049124112460373 · Cited by 106
“50) of Schafer (1997). 8.”
BackgroundMethodInfluentialBayesian analysis for partially observed network data, missing ties, attributes and actors
Koskinen, J. H., Robins, G. L., Wang, P., & Pattison, P. E. (2013) · Social Networks · doi:10.1016/j.socnet.2013.07.003 · Cited by 101
Kins, E., Soenens, B., & Beyers, W. (2011) · Journal of Clinical Psychology · doi:10.1002/jclp.20786 · Cited by 116
“%) were estimated using the expectation maximization (EM) algorithm, a method used to obtain maximum likelihood estimates (Schafer, 1997).”
MethodCombining multiple imputation and meta‐analysis with individual participant data
Burgess, S., White, I. R., Resche‐Rigon, M., & Wood, A. (2013) · Statistics in Medicine · doi:10.1002/sim.5844 · Cited by 105
Stiffman, A. R., Hadley-Ives, E., Doré, P., Polgar, M., Horvath, V. E., Striley, C. W., & Elze, D. E. (2000) · Mental Health Services Research · doi:10.1023/a:1010189710028 · Cited by 104
“Before proceeding with data analyses, we imputed missing values in each variable by replacing those missing with a measure of central tendency (Schafer, 1997).”
MethodThe leaky mathematics pipeline for girls
Watt, H. M. G., Eccles, J. S., & Durik, A. M. (2006) · Equal Opportunities International · doi:10.1108/02610150610719119 · Cited by 104
“Sixty-five per cent of participants were present for all three occasions, 88 per cent were present for at least two, and multiple imputation was used to impute missing data (Schafer, 1997).”
MethodEconomic burden and quality of life of vulvodynia in the United States
Xie, Y., Shi, L., Xiong, X., Wu, E. Q., Veasley, C., & Dade, C. (2012) · Current Medical Research and Opinion · doi:10.1185/03007995.2012.666963 · Cited by 105
Socio‐environmental influences on adolescents’ alcohol outcome expectancies: a prospective analysis
Martino, S. C., Collins, R. L., Ellickson, P. L., Schell, T. L., & McCaffrey, D. F. (2006) · Addiction · doi:10.1111/j.1360-0443.2006.01445.x · Cited by 104
Stroke Disparities in Older Americans
Avendaño, M., & Glymour, M. M. (2008) · Stroke · doi:10.1161/strokeaha.107.490383 · Cited by 103
Chae, D. H., Lincoln, K. D., & Jackson, J. S. (2011) · American Journal of Orthopsychiatry · doi:10.1111/j.1939-0025.2011.01122.x · Cited by 104
Comparing Two Web-Based Smoking Cessation Programs: Randomized Controlled Trial
McKay, H. G., Danaher, B. G., Seeley, J. R., Lichtenstein, E., & Gau, J. M. (2008) · Journal of Medical Internet Research · doi:10.2196/jmir.993 · Cited by 99
Late presentation for HIV diagnosis and care in G ermany
Zoufaly, A., der Heiden, M. A., Marcus, U., et al. (2011) · HIV Medicine · doi:10.1111/j.1468-1293.2011.00958.x · Cited by 103
Areepattamannil, S. (2012) · The Journal of Educational Research · doi:10.1080/00220671.2010.533717 · Cited by 115
Ellis, R., Seal, M. L., Simmons, J. G., Whittle, S., Schwartz, O., Byrne, M. L., & Allen, N. B. (2016) · Child Psychiatry & Human Development · doi:10.1007/s10578-016-0682-z · Cited by 103
Tax determinants revisited. An unbalanced data panel analysis
Rodríguez, V. M. C. (2018) · Journal of Applied Economics · doi:10.1080/15140326.2018.1526867 · Cited by 108
Wagenaar, A. C., Maldonado‐Molina, M. M., Erickson, D. J., Ma, L., Tobler, A. L., & Komro, K. A. (2007) · Accident Analysis & Prevention · doi:10.1016/j.aap.2007.01.003 · Cited by 102
The Moderating Effects of Maternal Psychopathology on Children's Adjustment Post–Hurricane Katrina
Spell, A. W., Kelley, M. L., Wang, J., Self-Brown, S., Davidson, K. L., Pellegrin, A., Palcic, J. L., Meyer, K., Paasch, V., & Baumeister, A. L. (2008) · Journal of Clinical Child & Adolescent Psychology · doi:10.1080/15374410802148210 · Cited by 102
Diabetes as a Predictor of Change in Functional Status Among Older Mexican Americans
Wu, J., Haan, M. N., Liang, J., Ghosh, D., González, H. M., & Herman, W. H. (2003) · Diabetes Care · doi:10.2337/diacare.26.2.314 · Cited by 103
Selby, E. A., Smith, A. R., Bulik, C. M., Olmsted, M. P., Thornton, L. M., McFarlane, T., Berrettini, W. H., Brandt, H., Crawford, S. F., Fichter, M. M., et al. (2010) · Behaviour Research and Therapy · doi:10.1016/j.brat.2010.03.016 · Cited by 103
Moens, E., Braet, C., Bosmans, G., & Rosseel, Y. (2009) · European Eating Disorders Review · doi:10.1002/erv.940 · Cited by 103
“Missing values were estimated using maximum likelihood estimation (Schafer, 1997) and the expectation maximization algorithm.”
MethodResilience in parenting among young mothers: Family and ecological risks and opportunities
Easterbrooks, M. A., Chaudhuri, J. H., Bartlett, J. D., & Copeman, A. (2010) · Children and Youth Services Review · doi:10.1016/j.childyouth.2010.08.010 · Cited by 105
Smarr, M. M., Grantz, K. L., Sundaram, R., Maisog, J. M., Kannan, K., & Louis, G. M. B. (2015) · Environmental Health · doi:10.1186/s12940-015-0060-5 · Cited by 102
Appropriate inclusion of interactions was needed to avoid bias in multiple imputation
Tilling, K. M., Williamson, E., Spratt, M., Sterne, J. A. C., & Carpenter, J. R. (2016) · Journal of Clinical Epidemiology · doi:10.1016/j.jclinepi.2016.07.004 · Cited by 99
Murayama, H., Kobayashi, E., Okamoto, S., Fukaya, T., Ishizaki, T., Liang, J., & Shinkai, S. (2020) · Archives of Gerontology and Geriatrics · doi:10.1016/j.archger.2020.104220 · Cited by 102
Presti, R. L., Barca, E., & Passarella, G. (2008) · Environmental Monitoring and Assessment · doi:10.1007/s10661-008-0653-3 · Cited by 101
“On the other hand, the MAR condition establishes that the two distributions can differ, but that the distribution of the complete dataset can be predicted starting from the observed values ( Schafer 1997 ).”
BackgroundMethodInfluentialKupelian, V. A., Rosen, R. C., Link, C. L., McVary, K. T., Aiyer, L. P., Mollon, P., Kaplan, S. A., & McKinlay, J. B. (2008) · The Journal of Urology · doi:10.1016/j.juro.2008.10.039 · Cited by 100
Identity development and peer group participation
Pugh, M. J., & Hart, D. A. (1999) · New Directions for Child and Adolescent Development · doi:10.1002/cd.23219998406 · Cited by 101
Scholtens, S., Wijga, A. H., Brunekreef, B., Kerkhof, M., Hoekstra, M. O., Gerritsen, J., Aalberse, R. C., de Jongste, J. C., & Smit, H. A. (2009) · Thorax · doi:10.1136/thx.2007.094938 · Cited by 101
PCA model building with missing data: New proposals and a comparative study
Folch‐Fortuny, A., Arteaga, F., & Ferrer, A. (2015) · Chemometrics and Intelligent Laboratory Systems · doi:10.1016/j.chemolab.2015.05.006 · Cited by 102
“Other methods rely on maximum likelihood-based estimations of missing data, like the expectation maximization (EM) algorithm [10-12].”
BackgroundMethodInfluentialThe Counseling Opportunity Structure: Examining Correlates of Four-Year College-Going Rates
Engberg, M. E., & Gilbert, A. J. (2013) · Research in Higher Education · doi:10.1007/s11162-013-9309-4 · Cited by 101
COMPARISON OF ALTERNATIVE STRATEGIES FOR ANALYSIS OF LONGITUDINAL TRIALS WITH DROPOUTS
Liu, G. F., & Gould, A. L. (2002) · Journal of Biopharmaceutical Statistics · doi:10.1081/bip-120015744 · Cited by 101
Wickes, R., Hipp, J. R., Sargeant, E., & Homel, R. (2013) · American Journal of Community Psychology · doi:10.1007/s10464-013-9582-6 · Cited by 102
Evaluation of software for multiple imputation of semi-continuous data
Yu, L.-M., Burton, A., & Rivero-Arias, O. (2007) · Statistical Methods in Medical Research · doi:10.1177/0962280206074464 · Cited by 117
Heterogeneity of Diabetes Outcomes Among Asians and Pacific Islanders in the U.S.
Kanaya, A. M., Adler, N. E., Moffet, H. H., Liu, J. Y., Schillinger, D., Adams, A. S., Ahmed, A. T., & Karter, A. J. (2011) · Diabetes Care · doi:10.2337/dc10-1964 · Cited by 102
Miethe, T. D., Regoeczi, W. C., & Drass, K. A. (2004) · Cambridge University Press eBooks · doi:10.1017/cbo9780511499487 · Cited by 101
Sahdra, B. K., Ciarrochi, J., Parker, P., & Scrucca, L. (2016) · Frontiers in Psychology · doi:10.3389/fpsyg.2016.00189 · Cited by 100
García‐Aymerich, J., Benet, M., Saeys, Y., Pinart, M., Basagaña, X., Smit, H. A., Siroux, V., Just, J., Momas, I., Rancière, F., et al. (2015) · Allergy · doi:10.1111/all.12640 · Cited by 109
“We assessed the presence and patterns of missing values and, assuming the missing-at-random hypothesis (18), we used multiple imputation (20 imputed data sets) with the method of chained equations (19).”
Adiposity and Incidence of Heart Failure Hospitalization and Mortality
Levitan, E. B., Yang, A. Z., Wolk, A., & Mittleman, M. A. (2009) · Circulation Heart Failure · doi:10.1161/circheartfailure.108.794099 · Cited by 98
Metadata
- Authors
- Schafer, J. L.
- Corresponding author
- Schafer, J.L.
- Venue
- Chapman & Hall/CRC eBooks
- Publisher
- Chapman and Hall/CRC
- Published
- 1997-08-01
- Volume
- 1997
- Issue
- 1997
- Pages
- 1-99
- OpenAlex
- W4300187280
- Semantic Scholar
- d9b083d7366dc17f2a71d7799f417707c86a37d3
- Cited by
- 6,012
- References
- 0
- Citations by year
- 2026: 92 · 2025: 128 · 2024: 161 · 2023: 143 · 2022: 197 · 2021: 277 · 2020: 222 · 2019: 288 · 2018: 261 · 2017: 264 · 2016: 308 · 2015: 323 · 2014: 322 · 2013: 292 · 2012: 320
- FWCI
- 17.88
- Type
- book
- Language
- en
- Open access
- closed
- Locations
- Chapman & Hall/CRC eBooks (publishedVersion)
- Topics
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Bayesian Inference
- Physical Sciences › Mathematics › Statistics and Probability › Markov Chains and Monte Carlo Methods
- Physical Sciences › Computer Science › Artificial Intelligence › Bayesian Methods and Mixture Models
- Keywords
- missing data, Bayesian analysis, expectation-maximization algorithm, multiple imputation, Markov chain Monte Carlo
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
