Missing data: Our view of the state of the art.
TL;DR: 2 general approaches that come highly recommended: maximum likelihood (ML) and Bayesian multiple imputation (MI) are presented and may eventually extend the ML and MI methods that currently represent the state of the art.
Abstract: Statistical procedures for missing data have vastly improved, yet misconception and unsound practice still abound. The authors frame the missing-data problem, review methods, offer advice, and raise issues that remain unresolved. They clear up common misunderstandings regarding the missing at random (MAR) concept. They summarize the evidence against older procedures and, with few exceptions, discourage their use. They present, in both technical and practical language, 2 general approaches that come highly recommended: maximum likelihood (ML) and Bayesian multiple imputation (MI). Newer developments are discussed, including some for dealing with missing data that are not MAR. Although not yet in the mainstream, these procedures may eventually extend the ML and MI methods that currently represent the state of the art.
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01 Jan 2006TL;DR: In this article, the authors present a detailed, worked-through example drawn from psychology, management, and sociology studies illustrate the procedures, pitfalls, and extensions of CFA methodology.
Abstract: "With its emphasis on practical and conceptual aspects, rather than mathematics or formulas, this accessible book has established itself as the go-to resource on confirmatory factor analysis (CFA). Detailed, worked-through examples drawn from psychology, management, and sociology studies illustrate the procedures, pitfalls, and extensions of CFA methodology. The text shows how to formulate, program, and interpret CFA models using popular latent variable software packages (LISREL, Mplus, EQS, SAS/CALIS); understand the similarities and differences between CFA and exploratory factor analysis (EFA); and report results from a CFA study. It is filled with useful advice and tables that outline the procedures. The companion website offers data and program syntax files for most of the research examples, as well as links to CFA-related resources. New to This Edition *Updated throughout to incorporate important developments in latent variable modeling. *Chapter on Bayesian CFA and multilevel measurement models. *Addresses new topics (with examples): exploratory structural equation modeling, bifactor analysis, measurement invariance evaluation with categorical indicators, and a new method for scaling latent variables. *Utilizes the latest versions of major latent variable software packages"--
7,620 citations
TL;DR: This review presents a practical summary of the missing data literature, including a sketch of missing data theory and descriptions of normal-model multiple imputation (MI) and maximum likelihood methods, and strategies for reducing attrition bias.
Abstract: This review presents a practical summary of the missing data literature, including a sketch of missing data theory and descriptions of normalmodel multiple imputation (MI) and maximum likelihood methods. Practical missing data analysis issues are discussed, most notably the inclusion of auxiliary variables for improving power and reducing bias. Solutions are given for missing data challenges such as handling longitudinal, categorical, and clustered data with normal-model MI; including interactions in the missing data model; and handling large numbers of variables. The discussion of attrition and nonignorable missingness emphasizes the need for longitudinal diagnostics and for reducing the uncertainty about the missing data mechanism under attrition. Strategies suggested for reducing attrition bias include using auxiliary variables, collecting follow-up data on a sample of those initially missing, and collecting data on intent to drop out. Suggestions are given for moving forward with research on missing data and attrition.
5,095 citations
Cites background or methods from "Missing data: Our view of the state..."
...Schafer & Graham (2002) suggested that forming a scale score based on partial data can cause problems in some situations, but may be fine in others....
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...Researchers should use MI and ML procedures (see Schafer & Graham 2002)....
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...MCAR is a special case of MAR in which missingness does not depend on the observed data either (Schafer & Graham 2002)....
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TL;DR: Recent progress about link prediction algorithms is summarized, emphasizing on the contributions from physical perspectives and approaches, such as the random-walk-based methods and the maximum likelihood methods.
Abstract: Link prediction in complex networks has attracted increasing attention from both physical and computer science communities. The algorithms can be used to extract missing information, identify spurious interactions, evaluate network evolving mechanisms, and so on. This article summaries recent progress about link prediction algorithms, emphasizing on the contributions from physical perspectives and approaches, such as the random-walk-based methods and the maximum likelihood methods. We also introduce three typical applications: reconstruction of networks, evaluation of network evolving mechanism and classification of partially labeled networks. Finally, we introduce some applications and outline future challenges of link prediction algorithms.
2,530 citations
Cites background from "Missing data: Our view of the state..."
...Social network analysis also comes up against the missing data problem [13,14,15], where link prediction algorithms may play a role....
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TL;DR: It is recommended that researchers using MI should perform many more imputations than previously considered sufficient, based on γ, and take into consideration one’s tolerance for a preventable power falloff due to using too few imputations.
Abstract: Multiple imputation (MI) and full information maximum likelihood (FIML) are the two most common approaches to missing data analysis. In theory, MI and FIML are equivalent when identical models are tested using the same variables, and when m, the number of imputations performed with MI, approaches infinity. However, it is important to know how many imputations are necessary before MI and FIML are sufficiently equivalent in ways that are important to prevention scientists. MI theory suggests that small values of m, even on the order of three to five imputations, yield excellent results. Previous guidelines for sufficient m are based on relative efficiency, which involves the fraction of missing information (γ) for the parameter being estimated, and m. In the present study, we used a Monte Carlo simulation to test MI models across several scenarios in which γ and m were varied. Standard errors and p-values for the regression coefficient of interest varied as a function of m, but not at the same rate as relative efficiency. Most importantly, statistical power for small effect sizes diminished as m became smaller, and the rate of this power falloff was much greater than predicted by changes in relative efficiency. Based our findings, we recommend that researchers using MI should perform many more imputations than previously considered sufficient. These recommendations are based on γ, and take into consideration one’s tolerance for a preventable power falloff (compared to FIML) due to using too few imputations.
2,253 citations
Cites background from "Missing data: Our view of the state..."
...Technical articles, books, and multiple imputation software abound (e.g., Collins et al. 2001; Graham et al. 2003; King et al. 2001; Schafer, 1997; Schafer and Graham 2002; Schafer and Olsen 1998)....
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...Missing data theorists (e.g., Collins et al. 2001; Schafer and Graham 2002; Graham et al. 2003) have argued that MI and FIML are equivalent....
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Book•
29 Mar 2012
TL;DR: The problem of missing data concepts of MCAR, MAR and MNAR simple solutions that do not (always) work multiple imputation in a nutshell and some dangers, some do's and some don'ts are covered.
Abstract: Basics Introduction The problem of missing data Concepts of MCAR, MAR and MNAR Simple solutions that do not (always) work Multiple imputation in a nutshell Goal of the book What the book does not cover Structure of the book Exercises Multiple imputation Historic overview Incomplete data concepts Why and when multiple imputation works Statistical intervals and tests Evaluation criteria When to use multiple imputation How many imputations? Exercises Univariate missing data How to generate multiple imputations Imputation under the normal linear normal Imputation under non-normal distributions Predictive mean matching Categorical data Other data types Classification and regression trees Multilevel data Non-ignorable methods Exercises Multivariate missing data Missing data pattern Issues in multivariate imputation Monotone data imputation Joint Modeling Fully Conditional Specification FCS and JM Conclusion Exercises Imputation in practice Overview of modeling choices Ignorable or non-ignorable? Model form and predictors Derived variables Algorithmic options Diagnostics Conclusion Exercises Analysis of imputed data What to do with the imputed data? Parameter pooling Statistical tests for multiple imputation Stepwise model selection Conclusion Exercises Case studies Measurement issues Too many columns Sensitivity analysis Correct prevalence estimates from self-reported data Enhancing comparability Exercises Selection issues Correcting for selective drop-out Correcting for non-response Exercises Longitudinal data Long and wide format SE Fireworks Disaster Study Time raster imputation Conclusion Exercises Extensions Conclusion Some dangers, some do's and some don'ts Reporting Other applications Future developments Exercises Appendices: Software R S-Plus Stata SAS SPSS Other software References Author Index Subject Index
2,156 citations
Cites background from "Missing data: Our view of the state..."
...Complete case analysis can perform quite badly under MAR and some MNAR cases (Schafer and Graham, 2002), but there are two special cases where it can outperform multiple imputation....
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References
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49,597 citations
Book•
01 Jan 1983TL;DR: In this paper, a generalization of the analysis of variance is given for these models using log- likelihoods, illustrated by examples relating to four distributions; the Normal, Binomial (probit analysis, etc.), Poisson (contingency tables), and gamma (variance components).
Abstract: The technique of iterative weighted linear regression can be used to obtain maximum likelihood estimates of the parameters with observations distributed according to some exponential family and systematic effects that can be made linear by a suitable transformation. A generalization of the analysis of variance is given for these models using log- likelihoods. These generalized linear models are illustrated by examples relating to four distributions; the Normal, Binomial (probit analysis, etc.), Poisson (contingency tables) and gamma (variance components).
23,215 citations
Book•
01 Jan 1987
TL;DR: This work states that maximum Likelihood for General Patterns of Missing Data: Introduction and Theory with Ignorable Nonresponse and large-Sample Inference Based on Maximum Likelihood Estimates is likely to be high.
Abstract: Preface.PART I: OVERVIEW AND BASIC APPROACHES.Introduction.Missing Data in Experiments.Complete-Case and Available-Case Analysis, Including Weighting Methods.Single Imputation Methods.Estimation of Imputation Uncertainty.PART II: LIKELIHOOD-BASED APPROACHES TO THE ANALYSIS OF MISSING DATA.Theory of Inference Based on the Likelihood Function.Methods Based on Factoring the Likelihood, Ignoring the Missing-Data Mechanism.Maximum Likelihood for General Patterns of Missing Data: Introduction and Theory with Ignorable Nonresponse.Large-Sample Inference Based on Maximum Likelihood Estimates.Bayes and Multiple Imputation.PART III: LIKELIHOOD-BASED APPROACHES TO THE ANALYSIS OF MISSING DATA: APPLICATIONS TO SOME COMMON MODELS.Multivariate Normal Examples, Ignoring the Missing-Data Mechanism.Models for Robust Estimation.Models for Partially Classified Contingency Tables, Ignoring the Missing-Data Mechanism.Mixed Normal and Nonnormal Data with Missing Values, Ignoring the Missing-Data Mechanism.Nonignorable Missing-Data Models.References.Author Index.Subject Index.
18,201 citations
Book•
01 Jan 1995TL;DR: Detailed notes on Bayesian Computation Basics of Markov Chain Simulation, Regression Models, and Asymptotic Theorems are provided.
Abstract: FUNDAMENTALS OF BAYESIAN INFERENCE Probability and Inference Single-Parameter Models Introduction to Multiparameter Models Asymptotics and Connections to Non-Bayesian Approaches Hierarchical Models FUNDAMENTALS OF BAYESIAN DATA ANALYSIS Model Checking Evaluating, Comparing, and Expanding Models Modeling Accounting for Data Collection Decision Analysis ADVANCED COMPUTATION Introduction to Bayesian Computation Basics of Markov Chain Simulation Computationally Efficient Markov Chain Simulation Modal and Distributional Approximations REGRESSION MODELS Introduction to Regression Models Hierarchical Linear Models Generalized Linear Models Models for Robust Inference Models for Missing Data NONLINEAR AND NONPARAMETRIC MODELS Parametric Nonlinear Models Basic Function Models Gaussian Process Models Finite Mixture Models Dirichlet Process Models APPENDICES A: Standard Probability Distributions B: Outline of Proofs of Asymptotic Theorems C: Computation in R and Stan Bibliographic Notes and Exercises appear at the end of each chapter.
16,079 citations
Book•
01 Jan 1987
TL;DR: In this article, a survey of drinking behavior among men of retirement age was conducted and the results showed that the majority of the participants reported that they did not receive any benefits from the Social Security Administration.
Abstract: Tables and Figures. Glossary. 1. Introduction. 1.1 Overview. 1.2 Examples of Surveys with Nonresponse. 1.3 Properly Handling Nonresponse. 1.4 Single Imputation. 1.5 Multiple Imputation. 1.6 Numerical Example Using Multiple Imputation. 1.7 Guidance for the Reader. 2. Statistical Background. 2.1 Introduction. 2.2 Variables in the Finite Population. 2.3 Probability Distributions and Related Calculations. 2.4 Probability Specifications for Indicator Variables. 2.5 Probability Specifications for (X,Y). 2.6 Bayesian Inference for a Population Quality. 2.7 Interval Estimation. 2.8 Bayesian Procedures for Constructing Interval Estimates, Including Significance Levels and Point Estimates. 2.9 Evaluating the Performance of Procedures. 2.10 Similarity of Bayesian and Randomization--Based Inferences in Many Practical Cases. 3. Underlying Bayesian Theory. 3.1 Introduction and Summary of Repeated--Imputation Inferences. 3.2 Key Results for Analysis When the Multiple Imputations are Repeated Draws from the Posterior Distribution of the Missing Values. 3.3 Inference for Scalar Estimands from a Modest Number of Repeated Completed--Data Means and Variances. 3.4 Significance Levels for Multicomponent Estimands from a Modest Number of Repeated Completed--Data Means and Variance--Covariance Matrices. 3.5 Significance Levels from Repeated Completed--Data Significance Levels. 3.6 Relating the Completed--Data and Completed--Data Posterior Distributions When the Sampling Mechanism is Ignorable. 4. Randomization--Based Evaluations. 4.1 Introduction. 4.2 General Conditions for the Randomization--Validity of Infinite--m Repeated--Imputation Inferences. 4.3Examples of Proper and Improper Imputation Methods in a Simple Case with Ignorable Nonresponse. 4.4 Further Discussion of Proper Imputation Methods. 4.5 The Asymptotic Distibution of (Qm,Um,Bm) for Proper Imputation Methods. 4.6 Evaluations of Finite--m Inferences with Scalar Estimands. 4.7 Evaluation of Significance Levels from the Moment--Based Statistics Dm and Dm with Multicomponent Estimands. 4.8 Evaluation of Significance Levels Based on Repeated Significance Levels. 5. Procedures with Ignorable Nonresponse. 5.1 Introduction. 5.2 Creating Imputed Values under an Explicit Model. 5.3 Some Explicit Imputation Models with Univariate YI and Covariates. 5.4 Monotone Patterns of Missingness in Multivariate YI. 5.5 Missing Social Security Benefits in the Current Population Survey. 5.6 Beyond Monotone Missingness. 6. Procedures with Nonignorable Nonresponse. 6.1 Introduction. 6.2 Nonignorable Nonresponse with Univariate YI and No XI. 6.3 Formal Tasks with Nonignorable Nonresponse. 6.4 Illustrating Mixture Modeling Using Educational Testing Service Data. 6.5 Illustrating Selection Modeling Using CPS Data. 6.6 Extensions to Surveys with Follow--Ups. 6.7 Follow--Up Response in a Survey of Drinking Behavior Among Men of Retirement Age. References. Author Index. Subject Index. Appendix I. Report Written for the Social Security Administration in 1977. Appendix II. Report Written for the Census Bureau in 1983.
14,574 citations