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## Missing data: Our view of the state of the art (2002)

Venue: | Psychological Methods |

Citations: | 688 - 1 self |

### Citations

3036 |
A reformulation of linear models
- Nelder
- 1977
(Show Context)
Citation Context ... covariates. Ibrahim (1990) developed a weighted estimation method for generalized linear models, a class that encompasses traditional linear regression, logistic regression, and log-linear modeling (=-=McCullagh & Nelder, 1989-=-). Ibrahim’s method is an EM algorithm under a generic model for the joint distribution of the predictors. This method requires the predictors to be discrete and does not take relationships among them... |

2642 | Statistical Analysis with Missing Data
- Little, Rubin
- 1987
(Show Context)
Citation Context ... is no way to test whether MAR holds in a data set, except by obtaining followup data from nonrespondents (Glynn, Laird, & Rubin, 1993; Graham & Donaldson, 1993) or by imposing an unverifiable model (=-=Little & Rubin, 1987-=-, chapter 11). In most cases we should expect departures from MAR, but whether these departures are serious enough to cause the performance of MAR-based methods to be seriously degraded is another iss... |

2114 | Bayesian data analysis
- Gelman, Carlin, et al.
- 2003
(Show Context)
Citation Context ...radigm we combine a likelihood function with a prior distribution for the parameters. As the sample size grows, the likelihood dominates the prior, and Bayesian and likelihood answers become similar (=-=Gelman, Rubin, Carlin, & Stern, 1995-=-). Missing Values That Are Not MAR What happens when the missing data are not MAR? It is then not appropriate to use Equation 2 either as a sampling distribution or as a likelihood. From a likelihood ... |

1781 |
Multiple Imputation for Nonresponse in Surveys
- Rubin
- 1987
(Show Context)
Citation Context ...y to test whether MAR holds in a data set, except by obtaining followup data from nonrespondents (Glynn, Laird, & Rubin, 1993; Graham & Donaldson, 1993) or by imposing an unverifiable model (Little & =-=Rubin, 1987-=-, chapter 11). In most cases we should expect departures from MAR, but whether these departures are serious enough to cause the performance of MAR-based methods to be seriously degraded is another iss... |

1430 | The EM Algorithm and Extensions - McLachlan, Krishnan - 2008 |

947 |
Analysis of Incomplete Multivariate Data
- Schafer
- 1997
(Show Context)
Citation Context ...h missing value is replaced with m > 1 simulated values prior to analysis. Creation of MIs was facilitated by computer technology and new methods for Bayesian simulation discovered in the late 1980s (=-=Schafer, 1997-=-). ML and MI are now becoming standard because of implementations in free and commercial software. The 1990s have seen many new developments. Reweighting, long used by survey methodologists, has been ... |

898 |
The common structure of statistical models of truncation, sample selection, and limited dependent variables and a simple estimator for such models
- Heckman
- 1976
(Show Context)
Citation Context ...dels. Selection models were first used by econometricians to describe how the probability of response to a sensitive questionnaire item (e.g., personal income) may depend on that item (Amemiya, 1984; =-=Heckman, 1976-=-). In a selection model, we first specify a distribution for the complete data, then propose a manner in which the probability of missingness depends on the data. For example, we could assume that the... |

884 |
Statistical analysis of finite mixture distributions
- Titterington, Smith, et al.
- 1985
(Show Context)
Citation Context ...sures data, where not all participants are measured at all time points (Jennrich & Schluchter, 1986; Laird & Ware, 1982); latent class analysis (Clogg & Goodman, 1984) and other finitemixture models (=-=Titterington, Smith, & Makov, 1985-=-); and factor analysis (Rubin & Thayer, 1983). For some of these problems, non-EM methods are also available. Newton–Raphson and Fisher scoring are now considered by many to be the preferred method fo... |

731 |
Theoretical Statistics
- Cox, Hinkley
- 1974
(Show Context)
Citation Context ...roximately unbiased in large samples. It is also highly efficient; as the sample size grows, its variance approaches the theoretical lower bound of what is achievable by any unbiased estimator (e.g., =-=Cox & Hinkley, 1974-=-). Confidence intervals and regions are often computed by appealing to the fact that, in regular problems with large samples, ˆ is approximately normally distributed about the true parameter with a... |

695 |
Random-effects models for longitudinal data
- Laird, Ware
- 1982
(Show Context)
Citation Context ...g-data problems but can be formulated as such: multilevel linear models for unbalanced repeated measures data, where not all participants are measured at all time points (Jennrich & Schluchter, 1986; =-=Laird & Ware, 1982-=-); latent class analysis (Clogg & Goodman, 1984) and other finitemixture models (Titterington, Smith, & Makov, 1985); and factor analysis (Rubin & Thayer, 1983). For some of these problems, non-EM met... |

640 |
Inference and missing data
- Rubin
- 1976
(Show Context)
Citation Context ..., with elements of R set to 1 or 0 according to whether the corresponding data values are observed or missing. In modern missing-data procedures missingness is regarded as a probabilistic phenomenon (=-=Rubin, 1976-=-). We treat R as a set of random variables having a joint probability distribution. We may not have to specify a particular distribution for R, but we must agree that it has a distribution. In statist... |

625 |
SAS system for mixed models
- Littell, Milliken, et al.
- 1996
(Show Context)
Citation Context ...al models with structured covariance matrices. Multilevel linear models can be fit with HLM (Bryk, Raudenbush, & Congdon, 1996), MLWin (Multilevel Models Project, 1996), the SAS procedure PROC MIXED (=-=Littell, Milliken, Stroup, & Wolfinger, 1996-=-), Stata (Stata, 2001), and the lme function in S-PLUS (Insightful, 2001). Any of these may be used for repeated measures data. In some cases, the documentation and accompanying literature do not ment... |

594 |
Maximum likelihood estimation from incomplete data via the EM algorithm
- Dempster, Laird, et al.
- 1977
(Show Context)
Citation Context ...Until the 1970s, missing values were handled primarily by editing. Rubin (1976) developed a framework of inference from incomplete data that remains in use today. The formulation of the EM algorithm (=-=Dempster, Laird, & Rubin, 1977-=-) made it feasible to compute ML estimates in many missing-data problems. Rather than deleting or filling in incomplete cases, ML treats the missing data as random variables to be removed from (i.e., ... |

550 |
Linear Mixed Models for Longitudinal Data
- Verbeke, Molenberghs
- 2000
(Show Context)
Citation Context ...sons closely related to the outcomes being measured (Little, 1995). Researchers are now beginning to assess the sensitivity of results to alternative hypotheses about the distribution of missingness (=-=Verbeke & Molenberghs, 2000-=-). Goals and Criteria With or without missing data, the goal of a statistical procedure should be to make valid and efficient inferences about a population of interest—not to estimate, predict, or rec... |

389 | Analyzing Incomplete Political Science Data: An Alternative Algorithm for Multiple Imputation
- King, Honaker, et al.
- 2001
(Show Context)
Citation Context ...P Statistical Software, 1992), now incorporated into the missing-data module of SPSS (Version 10.0). The procedure is also found in EMCOV (Graham & Hofer, 1991), NORM, SAS (Y. C. Yuan, 2000), Amelia (=-=King et al., 2001-=-), SPLUS (Schimert, Schafer, Hesterberg, Fraley, & Clarkson, 2001), LISREL (Jöreskog & Sörbom, 2001), and Mplus (L. K. Muthén & Muthén, 1998). ML is also available for normal models with structure... |

369 | On the problem of the most efficient tests of statistical hypotheses,” Philosophical Transactions of the Royal Society of London Series A Containing Papers of a Mathematical or - Neyman, Pearson - 1933 |

332 | Multiple imputation after 18+ years - Rubin - 1996 |

261 |
Corrections to Test Statistics and Standard Errors in Covariance Structure Analysis." in Latent Variable Analysis: Applications for Developmental Research, edited by
- Satorra, Bentler
- 1994
(Show Context)
Citation Context ...m model assumptions. Sometimes (e.g., in structural equation models) departures might not have a serious effect on estimates but could cause standard errors and test statistics to be very misleading (=-=Satorra & Bentler, 1994-=-). If one dispenses with the full parametric model, estimation procedures with incomplete data are still possible, but they typically require the missing values to be MCAR rather than MAR (K. H. Yuan ... |

237 |
Tobit models: a survey
- Amemiya
- 1984
(Show Context)
Citation Context ...s. Selection models. Selection models were first used by econometricians to describe how the probability of response to a sensitive questionnaire item (e.g., personal income) may depend on that item (=-=Amemiya, 1984-=-; Heckman, 1976). In a selection model, we first specify a distribution for the complete data, then propose a manner in which the probability of missingness depends on the data. For example, we could ... |

185 |
Estimation of Regression Coefficients when some Regressors are not Always Observed
- Robins, Rotnitzky, et al.
- 1994
(Show Context)
Citation Context ...h missing covariates (Ibrahim, 1990). SCHAFER AND GRAHAM148 New lines of research focus on how to handle missing values while avoiding the specification of a full parametric model for the population (=-=Robins, Rotnitzky, & Zhao, 1994-=-). New methods for nonignorable modeling, in which the probabilities of nonresponse are allowed to depend on the missing values themselves, are proliferating in biostatistics and public health. The pr... |

176 |
Model for longitudinal data: a generalized estimating equation approach
- Zeger, Liang
- 1988
(Show Context)
Citation Context ...es with the full parametric model, estimation procedures with incomplete data are still possible, but they typically require the missing values to be MCAR rather than MAR (K. H. Yuan & Bentler, 2000; =-=Zeger, Liang, & Albert, 1988-=-). For an evaluation of these new procedures for structural equation models, see the recent article by Enders (2001). Finally, the likelihood methods described in this section assume MAR. When missing... |

135 |
Informative drop-out in longitudinal data-analysis (with discussion
- Diggle, Kenward
- 1994
(Show Context)
Citation Context ...eans that it depends on the unseen responses after the participant drops out. In this specialized setting, MAR has been called noninformative or ignorable dropout, whereas MNAR is called informative (=-=Diggle & Kenward, 1994-=-). 1 In Rubin’s (1976) definition, Equation 1 is not required to hold for all possible values of R, but only for the R that actually appeared in the sample. This technical point clarifies certain issu... |

129 |
Modeling the drop-out mechanism in repeated-measures studies
- Little
- 1995
(Show Context)
Citation Context ...public health. The primary focus of these nonignorable models is dropout in clinical trials, in which participants may be leaving the study for reasons closely related to the outcomes being measured (=-=Little, 1995-=-). Researchers are now beginning to assess the sensitivity of results to alternative hypotheses about the distribution of missingness (Verbeke & Molenberghs, 2000). Goals and Criteria With or without ... |

127 |
Pattern-mixture models for multivariate incomplete data
- Little
- 1993
(Show Context)
Citation Context ... effects is possible only through identifying restrictions, and the observed data provide no evidence whatsoever to support or contradict these assumptions. Proponents of patternmixture models (e.g., =-=Little, 1993-=-) have suggested using these methods for sensitivity analysis, varying the identifying restrictions to see how the results change. Detailed examples of pattern-mixture modeling were given by Verbeke a... |

123 | Semiparametric Efficiency in Multivariate Regression Models with Missing - Robins, Rotnitzky - 1995 |

119 |
A comparison of inclusive and restrictive strategies in modern missing data procedures
- Collins, Schafer, et al.
(Show Context)
Citation Context ...kely that MAR is precisely satisfied. In many realistic applications, however, we believe that departures from MAR are not large enough to effectively invalidate the results of an MAR-based analysis (=-=Collins et al., 2001-=-). When the reasons for missingness seem strongly related to the data, one can formulate a likelihood or Table 4 Performance of Maximum Likelihood for Parameter Estimates and Confidence Intervals Over... |

117 | Outline of a theory of statistical estimation based on the classical theory of probability - Neyman - 1937 |

113 | Multiple imputation for multivariate missing-data problems: A data analyst’s perspective - Schafer, Olsen - 1998 |

111 |
Newton-Raphson and EM algorithms for linear mixed-effects models for repeated-measures data
- Lindstrom, Bates
- 1988
(Show Context)
Citation Context ...er, 1983). For some of these problems, non-EM methods are also available. Newton–Raphson and Fisher scoring are now considered by many to be the preferred method for fitting multilevel linear models (=-=Lindstrom & Bates, 1988-=-). However, in certain classes of models—finite mixtures, for example—EM is still the method of choice (McLachlan & Peel, 2000). Software for ML Estimation in Missing-Data Problems An EM algorithm for... |

95 |
NORM: Multiple imputation of incomplete multivariate data under a normal model
- Schafer
- 1999
(Show Context)
Citation Context ...ohn W. Graham (http:// methodology.psu.edu/resources.html) will provide timely updates on missing-data applications and utilities as they evolve, along with step-by-step instructions on MI with NORM (=-=Schafer, 1999-=-b). Fundamentals What Is a Missing Value? Data contain various codes to indicate lack of response: “Don’t know,” “Refused,” “Unintelligible,” and so on. Before applying a missing-data procedure, one s... |

94 |
Unbalanced Repeated-Measures Models With Structured Covariance Matrices
- Jennrich, Schluchter
- 1986
(Show Context)
Citation Context ...essarily thought of as missing-data problems but can be formulated as such: multilevel linear models for unbalanced repeated measures data, where not all participants are measured at all time points (=-=Jennrich & Schluchter, 1986-=-; Laird & Ware, 1982); latent class analysis (Clogg & Goodman, 1984) and other finitemixture models (Titterington, Smith, & Makov, 1985); and factor analysis (Rubin & Thayer, 1983). For some of these ... |

85 | Multiple-Imputation Inferences with Uncongenial Sources of input.” Statistical Science 9(4):538–573 - Meng - 1994 |

84 | Application of random-effects pattern-mixture models for missing data in longitudinal studies - Hedeker, Gibbons - 1997 |

84 | IVEware: Imputation and variance estimation software user guide - Raghunathan, Solenberger, et al. - 2002 |

84 | Longitudinal and multi-group modeling with missing data - Wothke - 1998 |

83 | Multiple Imputation for Missing Data: A Cautionary Tale
- Allison
(Show Context)
Citation Context ...estimates of the distribution of a single outcome, not to preserve the relationship between the outcome and other items. Imputations created by this method may seriously distort covariance structure (=-=Allison, 2000-=-). An alternative procedure in SOLAS, called the model-based method, is described below; it is more appropriate for situations in which postimputation analyses will involve covariances and correlation... |

75 |
Multiple imputation: A primer
- Schafer
- 1999
(Show Context)
Citation Context ... over the likelihood-based intervals in the bottom panel of Table 4; in most cases the coverage is closer to 95%. Good performance of MI intervals in small samples has been previously noted (Graham & =-=Schafer, 1999-=-). Increasing the sample size to 250, we found that the results from MI became nearly indistinguishable from the ML results with the same sample size. General Comments on MI MI is a relative newcomer,... |

72 |
Ignorability and coarse data
- Heitjan, Rubin
- 1991
(Show Context)
Citation Context ...ng values are part of the more general concept of coarsened data, which includes numbers that have been grouped, aggregated, rounded, censored, or truncated, resulting in partial loss of information (=-=Heitjan & Rubin, 1991-=-). Latent variables, a concept familiar to psychologists, are also closely related to missing data. Latent variables are unobservable quantities (e.g., intelligence, assertiveness) that are only imper... |

71 | On structural equation modeling with data that are not missing completely at random - Muth¶en, Kaplan, et al. - 1987 |

67 |
LEM: A general program for the analysis of categorical data [Computer software
- Vermunt
- 1997
(Show Context)
Citation Context ...ysis (LCA) is a missing-data problem in the sense that the latent classification is missing for all participants. A variety of software packages for LCA are available; one of the most popular is LEM (=-=Vermunt, 1997-=-). Latent transition analysis (LTA), an extension of LCA to longitudinal studies with a modest number of time points, is available in WinLTA (Collins, Flaherty, Hyatt, & Schafer, 1999). The EM algorit... |

61 | Maximum likelihood estimates for a multivariate normal dis tribution when some observations are missing - Anderson - 1957 |

59 | Multiple Imputation in Practice: Comparison of Software Packages for Regression Models With Missing Variables - Horton, Lipsitz - 2001 |

56 | Imputation of the 1989 Survey of Consumer Finances: Stochastic Relaxation and Multiple - Kennickell - 1991 |

54 |
Latent structure analysis of a set of multidimensional contingency tables
- Clogg, Goodman
- 1984
(Show Context)
Citation Context ...ire items. Computational methods for missing data may simplify parameter estimation in latent-variable models; a good example is the expectation-maximization (EM) algorithm for latent class analysis (=-=Clogg & Goodman, 1984-=-). Psychologists have sometimes made a distinction between missing values on independent variables (predictors) and missing values on dependent variables (outcomes). From our perspective, these two do... |

48 | A multiple imputation strategy for clinical trials with truncation of patient data. Statistics in medicine - Lavori, Dawson, et al. - 1913 |

46 | The impact of nonnormality on full information maximum-likelihood estimation for structural equation models with missing data - Enders - 2001 |

46 |
Three likelihoodbased methods for mean and covariance structure analysis with nonnormal missing data
- Yuan, Bentler
- 2000
(Show Context)
Citation Context ... 1994). If one dispenses with the full parametric model, estimation procedures with incomplete data are still possible, but they typically require the missing values to be MCAR rather than MAR (K. H. =-=Yuan & Bentler, 2000-=-; Zeger, Liang, & Albert, 1988). For an evaluation of these new procedures for structural equation models, see the recent article by Enders (2001). Finally, the likelihood methods described in this se... |

45 |
Incomplete data in generalized linear models
- Ibrahim
- 1990
(Show Context)
Citation Context ...rcial software. The 1990s have seen many new developments. Reweighting, long used by survey methodologists, has been proposed for handling missing values in regression models with missing covariates (=-=Ibrahim, 1990-=-). SCHAFER AND GRAHAM148 New lines of research focus on how to handle missing values while avoiding the specification of a full parametric model for the population (Robins, Rotnitzky, & Zhao, 1994). N... |

42 |
Estimation of linear models with incomplete data
- Allison
- 1987
(Show Context)
Citation Context ...al studies with dropout, see Little (1995) or Verbeke and Molenberghs (2000). Pattern-mixture models are closely related to multiple-group procedures for missing data in structural equation modeling (=-=Allison, 1987-=-; Duncan & Duncan, 1994; Muthén, Kaplan, & Hollis, 1987). In the multiple-groups approach, observational units are sorted by missingness pattern and each pattern is assumed to provide information abo... |

38 |
Hierarchical linear and nonlinear modeling with the HLM/2L and HLM/3L programs. Chicago: Scienti¯c
- Bryk, Raudenbush, et al.
- 1996
(Show Context)
Citation Context ...ISREL (Jöreskog & Sörbom, 2001), and Mplus (L. K. Muthén & Muthén, 1998). ML is also available for normal models with structured covariance matrices. Multilevel linear models can be fit with HLM (=-=Bryk, Raudenbush, & Congdon, 1996-=-), MLWin (Multilevel Models Project, 1996), the SAS procedure PROC MIXED (Littell, Milliken, Stroup, & Wolfinger, 1996), Stata (Stata, 2001), and the lme function in S-PLUS (Insightful, 2001). Any of ... |

38 |
Maximizing the usefulness of data obtained with planned missing value patterns: An application of maximum likelihood procedures
- Graham, Hofer, et al.
- 1996
(Show Context)
Citation Context ...gns for longitudinal studies (McArdle & Hamagami, 1991; Nesselroade & Baltes, 1979) and the use of multiple questionnaire forms containing different subsets of items (Graham, Hofer, & Piccinin, 1994; =-=Graham, Hofer, & MacKinnon, 1996-=-). Planned missingness in a study may have important advantages in terms of efficiency and cost (Graham, Taylor, & Cumsille, 2001). Planned missing values are usually MCAR, but MAR situations sometime... |

38 |
The use of multiple imputation for the analysis of missing data
- Sinharay, Stern, et al.
- 2001
(Show Context)
Citation Context ..., especially its convergence behavior. A gentle introduction and tutorial on the use of MI under a multivariate normal model was provided by Schafer and Olsen (1998; also see Graham et al., in press; =-=Sinharay et al., 2001-=-). Choosing the Imputation Model Notice that the MI procedure described above is based on a joint normality assumption for Y1, Y2, and Y3. This model makes no distinctions between response (dependent)... |

38 | Flexible Multivariate Imputation by MICE - Buuren, CGM - 1999 |

36 | Multiple imputation in multivariate research - Graham, Hoffer - 2000 |

32 |
Longitudinal research in the study of behavior and development
- Nesselroade, Baltes
- 1979
(Show Context)
Citation Context ...hold. These include planned missingness in which the missing data were never intended to be collected in the first place: cohort-sequential designs for longitudinal studies (McArdle & Hamagami, 1991; =-=Nesselroade & Baltes, 1979-=-) and the use of multiple questionnaire forms containing different subsets of items (Graham, Hofer, & Piccinin, 1994; Graham, Hofer, & MacKinnon, 1996). Planned missingness in a study may have importa... |

31 |
Multiple Imputation for Missing Data: Concepts and New Development
- Yuan
(Show Context)
Citation Context ...released by BMDP (BMDP Statistical Software, 1992), now incorporated into the missing-data module of SPSS (Version 10.0). The procedure is also found in EMCOV (Graham & Hofer, 1991), NORM, SAS (Y. C. =-=Yuan, 2000-=-), Amelia (King et al., 2001), SPLUS (Schimert, Schafer, Hesterberg, Fraley, & Clarkson, 2001), LISREL (Jöreskog & Sörbom, 2001), and Mplus (L. K. Muthén & Muthén, 1998). ML is also available for ... |

30 |
On the performance of multiple imputation for multivariate data with small sample size
- Graham, Schafer
- 1999
(Show Context)
Citation Context ...provement over the likelihood-based intervals in the bottom panel of Table 4; in most cases the coverage is closer to 95%. Good performance of MI intervals in small samples has been previously noted (=-=Graham & Schafer, 1999-=-). Increasing the sample size to 250, we found that the results from MI became nearly indistinguishable from the ML results with the same sample size. General Comments on MI MI is a relative newcomer,... |

30 |
Modeling incomplete longitudinal and cross-sectional data using latent growth structural models
- McArdle, Hamagami
- 1992
(Show Context)
Citation Context ...settings, MAR is known to hold. These include planned missingness in which the missing data were never intended to be collected in the first place: cohort-sequential designs for longitudinal studies (=-=McArdle & Hamagami, 1991-=-; Nesselroade & Baltes, 1979) and the use of multiple questionnaire forms containing different subsets of items (Graham, Hofer, & Piccinin, 1994; Graham, Hofer, & MacKinnon, 1996). Planned missingness... |

29 | Analysis with missing data in prevention research The science of prevention: Methodological advances from alcohol and substance abuse research (pp
- Graham, Hofer, et al.
- 1997
(Show Context)
Citation Context .... In most cases we should expect departures from MAR, but whether these departures are serious enough to cause the performance of MAR-based methods to be seriously degraded is another issue entirely (=-=Graham, Hofer, Donaldson, MacKinnon, & Schafer, 1997-=-). Recently, Collins, Schafer, and Kam (2001) demonstrated that in many realistic cases, an erroneous assumption of MAR (e.g., failing to take into account a cause or correlate of missingness) may oft... |

26 | Semiparametric regression for repeated outcomes with non-ignorable non-response - Robins, Rotnitzky, et al. - 1998 |

25 |
Evaluating interventions with differential attrition: The importance of nonresponse mechanisms and follow-up data
- Graham, Donaldson
- 1993
(Show Context)
Citation Context ...tion is unknown and MAR is only an assumption. In general, there is no way to test whether MAR holds in a data set, except by obtaining followup data from nonrespondents (Glynn, Laird, & Rubin, 1993; =-=Graham & Donaldson, 1993-=-) or by imposing an unverifiable model (Little & Rubin, 1987, chapter 11). In most cases we should expect departures from MAR, but whether these departures are serious enough to cause the performance ... |

24 |
Development, Implementation and Evaluation of Multiple Imputation Strategies for the Statistical Analysis of Incomplete Data Sets
- Brand
- 1999
(Show Context)
Citation Context ...true joint distribution. Technically speaking, these iterative algorithms may never “converge” because the joint distribution to which they may converge does not exist. Nevertheless, simulation work (=-=Brand, 1999-=-) suggests that in some practical applications the method can indeed work well despite the theoretical problems. Some utilities are also available to simplify the task of analyzing imputed data sets. ... |

24 |
Analysis with missing data in drug prevention research
- Graham, Hofer, et al.
- 1994
(Show Context)
Citation Context ...rst place: cohort-sequential designs for longitudinal studies (McArdle & Hamagami, 1991; Nesselroade & Baltes, 1979) and the use of multiple questionnaire forms containing different subsets of items (=-=Graham, Hofer, & Piccinin, 1994-=-; Graham, Hofer, & MacKinnon, 1996). Planned missingness in a study may have important advantages in terms of efficiency and cost (Graham, Taylor, & Cumsille, 2001). Planned missing values are usually... |

22 | Efficacy of the indirect approach for estimating structural equation models with missing data: A comparison of five methods. Structural Equation Modeling 1:287–316 - Brown - 1994 |

21 | Likelihood based frequentist inference when data are missing at random - Kenward, Molenberghs - 1998 |

19 | Inferences with imputed conditional means
- Schafer, Schenker
- 2000
(Show Context)
Citation Context ...n, because Yˆ estimates the conditional mean of Y given X. Conditional mean imputation is nearly optimal for a limited class of estimation problems if special corrections are made to standard errors (=-=Schafer & Schenker, 2000-=-). The method is not recommended for analyses of covariances or correlations, because it overstates the strength of the relationship between Y and the X variables; the multiple regression R2 among the... |

14 |
Model-based approaches to analyzing incomplete longitudinal and failure-time data
- Hogan, Laird
- 1997
(Show Context)
Citation Context ...in the outcome prior to death, and response trajectories estimated under an MAR assumption may be somewhat optimistic. In those cases, joint modeling of the outcome and death events may be warranted (=-=Hogan & Laird, 1997-=-). Older Methods Case Deletion Among older methods for missing data, the most popular is to discard units whose information is incomplete. Case deletion, also known commonly as listwise deletion (LD) ... |

14 | Maximum likelihood analysis of generalized linear models with missing covariates - Horton, Laird - 1998 |

13 |
Multiple imputation in mixture models for nonignorable nonresponse with follow-ups
- Glynn, Laird, et al.
- 1993
(Show Context)
Citation Context ...rcher’s control, its distribution is unknown and MAR is only an assumption. In general, there is no way to test whether MAR holds in a data set, except by obtaining followup data from nonrespondents (=-=Glynn, Laird, & Rubin, 1993-=-; Graham & Donaldson, 1993) or by imposing an unverifiable model (Little & Rubin, 1987, chapter 11). In most cases we should expect departures from MAR, but whether these departures are serious enough... |

10 |
AMOS 4.0 user's guide [Computer software manual
- Arbukle, Wothke, et al.
- 1999
(Show Context)
Citation Context ...led nonresponse (e.g., attrition), all of these programs will assume MAR. ML estimates for structural equation models with incomplete data are available in Mx (Neale, Boker, Xie, & Maes, 1999), AMOS (=-=Arbuckle & Wothke, 1999-=-), LISREL, and Mplus, which also assume MAR. These programs provide standard errors based on expected or observed information. If offered a choice, the user should opt for observed rather than expecte... |

10 |
Planned missing data designs in analysis of change. In New methods for the analysis of change, edited by
- Graham, Taylor, et al.
- 2001
(Show Context)
Citation Context ...ontaining different subsets of items (Graham, Hofer, & Piccinin, 1994; Graham, Hofer, & MacKinnon, 1996). Planned missingness in a study may have important advantages in terms of efficiency and cost (=-=Graham, Taylor, & Cumsille, 2001-=-). Planned missing values are usually MCAR, but MAR situations sometimes arise—for example, if participants are included in a follow-up measure only if their pretest scores exceed a cutoff value. Late... |

10 |
Using the EM-Algorithm for Survival Data with Incomplete Categorical Covariates.” Lifetime Data Analysis
- Lipsitz, Ibrahim
- 1996
(Show Context)
Citation Context ...special case of EM for mixed continuous and categorical data considered by Little and Rubin (1987) and Schafer (1997). The method has also been used for survival analysis (Schluchter & Jackson, 1989; =-=Lipsitz & Ibrahim, 1996-=-, 1998). Weighting methods for ML regression with missing covariates were reviewed by Horton and Laird (1999). Although formal comparisons have not yet been made, we expect that, in many cases, these ... |

10 | A class of pattern mixture models for normal missing data - Little - 1994 |

10 | Multiple imputation and posterior simulation for multivariate missing data in longitudinal studies. Biometrics - Liu, JM, et al. |

9 |
Modeling incomplete longitudinal substance use data using latent variable growth curve methodology. Multivariate Behavioral Researdk29(4
- Duncan, Duncan
- 1994
(Show Context)
Citation Context ... dropout, see Little (1995) or Verbeke and Molenberghs (2000). Pattern-mixture models are closely related to multiple-group procedures for missing data in structural equation modeling (Allison, 1987; =-=Duncan & Duncan, 1994-=-; Muthén, Kaplan, & Hollis, 1987). In the multiple-groups approach, observational units are sorted by missingness pattern and each pattern is assumed to provide information about a subset of the mode... |

9 |
More on EM for ML factor analysis
- Rubin, Thayer
- 1983
(Show Context)
Citation Context ... time points (Jennrich & Schluchter, 1986; Laird & Ware, 1982); latent class analysis (Clogg & Goodman, 1984) and other finitemixture models (Titterington, Smith, & Makov, 1985); and factor analysis (=-=Rubin & Thayer, 1983-=-). For some of these problems, non-EM methods are also available. Newton–Raphson and Fisher scoring are now considered by many to be the preferred method for fitting multilevel linear models (Lindstro... |

9 |
Multiple imputation with
- Schafer
- 2001
(Show Context)
Citation Context ...model; however, a software implementation of this new method is not yet available. Longitudinal structure arising from repeated measurements over time has been implemented in the S-PLUS function PAN (=-=Schafer, 2001-=-; Schafer & Yucel, in press). For nonnormal imputation models, the software choices are more limited. Methods described by Schafer (1997) for multivariate categorical data, and for mixed data sets con... |

9 |
Log-linear analysis of censored survival data with partially observed covariates
- SCHLUCHTER, JACKSON
- 1989
(Show Context)
Citation Context ...e, Ibrahim’s algorithm is a special case of EM for mixed continuous and categorical data considered by Little and Rubin (1987) and Schafer (1997). The method has also been used for survival analysis (=-=Schluchter & Jackson, 1989-=-; Lipsitz & Ibrahim, 1996, 1998). Weighting methods for ML regression with missing covariates were reviewed by Horton and Laird (1999). Although formal comparisons have not yet been made, we expect th... |

8 | Estimating equations with incomplete categorical covariates in the Cox model - Lipsitz, Ibrahim - 1998 |

8 |
Mx: Statistical modeling (5th ed.) [Computer software
- Neale, Boker, et al.
- 1999
(Show Context)
Citation Context ...t by design but as a result of uncontrolled nonresponse (e.g., attrition), all of these programs will assume MAR. ML estimates for structural equation models with incomplete data are available in Mx (=-=Neale, Boker, Xie, & Maes, 1999-=-), AMOS (Arbuckle & Wothke, 1999), LISREL, and Mplus, which also assume MAR. These programs provide standard errors based on expected or observed information. If offered a choice, the user should opt ... |

5 |
BMDP statistical software manual
- Software, Inc
- 1992
(Show Context)
Citation Context ...ssing-Data Problems An EM algorithm for ML estimation of an unstructured covariance matrix is available in several programs. The first commercial implementation was released by BMDP (BMDP Statistical =-=Software, 1992-=-), now incorporated into the missing-data module of SPSS (Version 10.0). The procedure is also found in EMCOV (Graham & Hofer, 1991), NORM, SAS (Y. C. Yuan, 2000), Amelia (King et al., 2001), SPLUS (S... |

3 |
Selection models for repeated measurements for nonrandom dropout: an illustration of sensitivity
- Kenward
- 1998
(Show Context)
Citation Context ...94), results of such tests rest heavily on untestable assumptions about the population distribution, and minor changes in the assumed shape of this distribution may drastically alter the conclusions (=-=Kenward, 1998-=-). Many consider these models to be too unstable for scientific applications and to be more useful for raising questions than generating answers (Laird, 1994). Pattern-mixture models. As an alternativ... |

3 |
Discussion of “Informative drop-out in longitudinal data analysis” by P
- Laird
- 1994
(Show Context)
Citation Context ...n may drastically alter the conclusions (Kenward, 1998). Many consider these models to be too unstable for scientific applications and to be more useful for raising questions than generating answers (=-=Laird, 1994-=-). Pattern-mixture models. As an alternative to the selection model, Little (1993) described an alternative class of MNAR methods based on a pattern-mixture formulation. Pattern-mixture models do not ... |

3 |
Incomplete data in sample surveys: Vol. 1. Report and case studies
- Madow, Nisselson, et al.
- 1983
(Show Context)
Citation Context ...eserve a variable’s distribution. Survey methodologists, who have long been aware of this, have developed a wide array of singleimputation methods that more effectively preserve distributional shape (=-=Madow, Nisselson, & Olkin, 1983-=-). One popular class of procedures known as hot deck imputation fills in nonrespondents’ data with values from actual respondents. In a simple univariate hot deck, we replace each missing value by a r... |

3 |
A congenial overview and investigation of imputation inferences under uncongeniality
- Meng
- 1999
(Show Context)
Citation Context ...also possible to combine a fully parametric MI procedure with postimputation analysis by a robust method, and unless the imputation model is grossly misspecified the performance should be quite good (=-=Meng, 1999-=-). In structural equation modeling, for example, one could multiply impute the missing values under a normality assumption and then fit the structural model to the imputed data using the robust techni... |

2 |
WinLTA user’s guide (Version 2.0
- Collins, Flaherty, et al.
- 1999
(Show Context)
Citation Context ...e available; one of the most popular is LEM (Vermunt, 1997). Latent transition analysis (LTA), an extension of LCA to longitudinal studies with a modest number of time points, is available in WinLTA (=-=Collins, Flaherty, Hyatt, & Schafer, 1999-=-). The EM algorithm in the most recent version of LTA allows missing values to occur on the manifest variables in an arbitrary pattern. ML estimates for a wider class of latent-variable models with in... |

2 |
EMCOV.EXE users’ guide [Computer software manual]. Unpublished manuscript
- Graham, Hofer
- 1991
(Show Context)
Citation Context ...The first commercial implementation was released by BMDP (BMDP Statistical Software, 1992), now incorporated into the missing-data module of SPSS (Version 10.0). The procedure is also found in EMCOV (=-=Graham & Hofer, 1991-=-), NORM, SAS (Y. C. Yuan, 2000), Amelia (King et al., 2001), SPLUS (Schimert, Schafer, Hesterberg, Fraley, & Clarkson, 2001), LISREL (Jöreskog & Sörbom, 2001), and Mplus (L. K. Muthén & Muthén, 19... |

2 |
S-PLUS (Version 6) [Computer software
- Insightful
- 2001
(Show Context)
Citation Context ...audenbush, & Congdon, 1996), MLWin (Multilevel Models Project, 1996), the SAS procedure PROC MIXED (Littell, Milliken, Stroup, & Wolfinger, 1996), Stata (Stata, 2001), and the lme function in S-PLUS (=-=Insightful, 2001-=-). Any of these may be used for repeated measures data. In some cases, the documentation and accompanying literature do not mention missing values specifically but describe “unbalanced” data sets, in ... |

2 |
Multilevel modeling applications—A guide for users of MLn. [Computer software manual
- Project
- 1996
(Show Context)
Citation Context ... Muthén, 1998). ML is also available for normal models with structured covariance matrices. Multilevel linear models can be fit with HLM (Bryk, Raudenbush, & Congdon, 1996), MLWin (Multilevel Models =-=Project, 1996-=-), the SAS procedure PROC MIXED (Littell, Milliken, Stroup, & Wolfinger, 1996), Stata (Stata, 2001), and the lme function in S-PLUS (Insightful, 2001). Any of these may be used for repeated measures d... |

2 |
Analyzing missing values in SPLUS
- Schimert, Schafer, et al.
- 2001
(Show Context)
Citation Context ...2), now incorporated into the missing-data module of SPSS (Version 10.0). The procedure is also found in EMCOV (Graham & Hofer, 1991), NORM, SAS (Y. C. Yuan, 2000), Amelia (King et al., 2001), SPLUS (=-=Schimert, Schafer, Hesterberg, Fraley, & Clarkson, 2001-=-), LISREL (Jöreskog & Sörbom, 2001), and Mplus (L. K. Muthén & Muthén, 1998). ML is also available for normal models with structured covariance matrices. Multilevel linear models can be fit with H... |

2 | Analysis of incomplete high-dimensional normal data using a common factor model. Unpublished doctoral dissertation - Song - 1999 |

2 |
Stata user’s guide [Computer software manual
- Stata
- 2001
(Show Context)
Citation Context ...vel linear models can be fit with HLM (Bryk, Raudenbush, & Congdon, 1996), MLWin (Multilevel Models Project, 1996), the SAS procedure PROC MIXED (Littell, Milliken, Stroup, & Wolfinger, 1996), Stata (=-=Stata, 2001-=-), and the lme function in S-PLUS (Insightful, 2001). Any of these may be used for repeated measures data. In some cases, the documentation and accompanying literature do not mention missing values sp... |

2 |
SOLAS for missing data analysis (Version 1
- Solutions
- 1998
(Show Context)
Citation Context ... without covariates. Lavori, Dawson, and Shera (1995) generalized the ABB to include fully observed covariates as in Figure 1a. This method has been implemented in a program called SOLAS (Statistical =-=Solutions, 1998-=-), where it is called the propensityscore option. This procedure was designed to provide unbiased estimates of the distribution of a single outcome, not to preserve the relationship between the outcom... |