When estimating causal effects using observational data, it is desirable to replicate a randomized experiment as closely as possible by obtaining treated and control groups with similar covariate distributions. This goal can often be achieved by choosing well-matched samples of the original treated and control groups, thereby reducing bias due to the covariates. Since the 1970's, work on matching methods has examined how to best choose treated and control subjects for comparison. Matching methods are gaining popularity in fields such as economics, epidemiology, medicine, and political science. However, until now the literature and related advice has been scattered across disciplines. Researchers who are interested in using matching methods-or developing methods related to matching-do not have a single place to turn to learn about past and current research. This paper provides a structure for thinking about matching methods and guidance on their use, coalescing the existing research (both old and new) and providing a summary of where the literature on matching methods is now and where it should be headed.

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Matching Methods for Causal Inference: A Review and a Look Forward

Principles for reporting analyses using structural equation modeling are reviewed, with the goal of supplying readers with complete and accurate information. It is recommended that every report give a detailed justification of the model used, along with plausible alternatives and an account of identifiability. Nonnormality and missing data problems should also be addressed. A complete set of parameters and their standard errors is desirable, and it will often be convenient to supply the correlation matrix and discrepancies, as well as goodness-of-fit indices, so that readers can exercise independent critical judgment. A survey of fairly representative studies compares recent practice with the principles of reporting recommended here. Structural equation modeling (SEM), also known as path analysis with latent variables, is now a regularly used method for representing dependency (arguably “causal”) relations in multivariate data in the behavioral and social sciences. Following the seminal

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Principles and practice in reporting structural equation analyses.

Although published works rarely include causal estimates from more than a few model specifications, authors usually choose the presented estimates from numerous trial runs readers never see. Given the often large variation in estimates across choices of control variables, functional forms, and other modeling assumptions, how can researchers ensure that the few estimates presented are accurate or representative? How do readers know that publications are not merely demonstrations that it is possible to find a specification that fits the author's favorite hypothesis? And how do we evaluate or even define statistical properties like unbiasedness or mean squared error when no unique model or estimator even exists? Matching methods, which offer the promise of causal inference with fewer assumptions, constitute one possible way forward, but crucial results in this fast-growing methodological literature are often grossly misinterpreted. We explain how to avoid these misinterpretations and propose a unified approach that makes it possible for researchers to preprocess data with matching (such as with the easy-to-use software we offer) and then to apply the best parametric techniques they would have used anyway. This procedure makes parametric models produce more accurate and considerably less model-dependent causal inferences.

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Matching as Nonparametric Preprocessing for Reducing Model Dependence in Parametric Causal Inference

Multiple imputation was designed to handle the problem of missing data in public-use data bases where the data-base constructor and the ultimate user are distinct entities. The objective is valid frequency inference for ultimate users who in general have access only to complete-data software and possess limited knowledge of specific reasons and models for nonresponse. For this situation and objective, I believe that multiple imputation by the data-base constructor is the method of choice. This article first provides a description of the assumed context and objectives, and second, reviews the multiple imputation framework and its standard results. These preliminary discussions are especially important because some recent commentaries on multiple imputation have reflected either misunderstandings of the practical objectives of multiple imputation or misunderstandings of fundamental theoretical results. Then, criticisms of multiple imputation are considered, and, finally, comparisons are made to alt...

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Multiple Imputation After 18+ Years

Much medical research is observational. The reporting of observational studies is often of insufficient quality. Poor reporting hampers the assessment of the strengths and weaknesses of a study and the generalizability of its results. Taking into account empirical evidence and theoretical considerations, a group of methodologists, researchers, and editors developed the Strengthening the Reporting of Observational Studies in Epidemiology (STROBE) recommendations to improve the quality of reporting of observational studies. The STROBE Statement consists of a checklist of 22 items, which relate to the title, abstract, introduction, methods, results, and discussion sections of articles. Eighteen items are common to cohort studies, case-control studies, and cross-sectional studies, and 4 are specific to each of the 3 study designs. The STROBE Statement provides guidance to authors about how to improve the reporting of observational studies and facilitates critical appraisal and interpretation of studies by reviewers, journal editors, and readers. This explanatory and elaboration document is intended to enhance the use, understanding, and dissemination of the STROBE Statement. The meaning and rationale for each checklist item are presented. For each item, 1 or several published examples and, where possible, references to relevant empirical studies and methodological literature are provided. Examples of useful flow diagrams are also included. The STROBE Statement, this document, and the associated Web site (www.strobe-statement.org) should be helpful resources to improve reporting of observational research.

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Strengthening the Reporting of Observational Studies in Epidemiology (STROBE): Explanation and Elaboration

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.

C. D. Kershaw

Papers

Multiple Imputation for Nonresponse in Surveys.