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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.
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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
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“Although it cannot be tested whether the MAR assumption holds (Schafer, 1997, p. 22), multiple imputation will still give less biased results than listwise deletion (Schafer, 1997, p. 26) when this assumption is violated.”
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“…incorporate nested data; (b) it uses restricted maximum likelihood procedures to estimate effects; (c) it does not require equal spacing between observations; and (d) it can accommodate data that are unbalanced or missing at random (Raudenbush & Bryk, 2002; Schafer, 1997; Singer & Willett, 2003).”
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“Therefore, the expectation-maximization (EM) algorithm was used for data imputation, a robust method to obtain maximum likelihood estimates (Schafer, 1997).”
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“For a detailed description of missing data within surveys, see, for example, Little and Rubin (2002) or Schafer (1997).”
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“However, there is growing consensus that ad hoc ITT analyses are not the most appropriate for a variety of studies, including population-based intervention trials (eg, Hall et al,, 2001; Schafer, 1997; Schafer & Graham, 2002).”
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“Data imputation was conducted using NORM (Schafer, 1997a, 1997b).”
Multiple Imputation for General Missing Data Patterns in the Presence of High-dimensional Data
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Methods for Handling Missing Data
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Risky Lifestyles, Low Self-control, and Violent Victimization Across Gendered Pathways to Crime
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“errors observed in single imputation procedures (Schafer 1997).”
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“Due to the potential for bias from nonresponse, analyses were conducted on data subjected to multiple imputation [ 43 ].”
MethodA Household-Based Human Development Index
Harttgen, K., & Klasen, S. (2011) · World Development · doi:10.1016/j.worlddev.2011.09.011 · Cited by 128
“It has been shown that multiple imputation performs favorably (see, e.g. Schaefer and Graham, 2002; Schaefer, 1997; Wayman 2003).”
MethodSkaalvik, E. M., & Skaalvik, S. (2019) · Creative Education · doi:10.4236/ce.2019.107104 · Cited by 165
Lutfey, K., Link, C. L., Rosen, R. C., Wiegel, M., & McKinlay, J. B. (2008) · Archives of Sexual Behavior · doi:10.1007/s10508-007-9290-0 · Cited by 134
“Multiple imputation (MI) was used to impute missing values using the MI procedure in SAS version 9.1 (Rubin, 1987; SAS Institute, 2003; Schafer, 1997 ).”
MethodInfluentialNeed-service matching in substance abuse treatment: Racial/ethnic differences
Marsh, J. C., Cao, D., Guerrero, E. G., & Shin, H.-C. (2008) · Evaluation and Program Planning · doi:10.1016/j.evalprogplan.2008.09.003 · Cited by 130
“In the multiple imputation procedure, each missing value was replaced with five plausible values using the Markov Chain Monte Carlo (MCMC) method (Schafer, 1997).”
Subthreshold Depression and Successful Aging in Older Women
Vahia, I. V., Meeks, T. W., Thompson, W. K., Depp, C. A., Zisook, S., Allison, M., Judd, L. L., & Jeste, D. V. (2010) · American Journal of Geriatric Psychiatry · doi:10.1097/jgp.0b013e3181b7f10e · Cited by 128
Residential Radon and Lung Cancer Risk in a High-exposure Area of Gansu Province, China
Wang, Z. (2002) · American Journal of Epidemiology · doi:10.1093/aje/155.6.554 · Cited by 128
Serum androgen levels in black, Hispanic, and white men
Litman, H. J., Bhasin, S., Link, C. L., Araujo, A. B., & McKinlay, J. B. (2006) · The Journal of Clinical Endocrinology & Metabolism · doi:10.1210/jc.2006-0037 · Cited by 127
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
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