Donald B. Rubin

Harvard University

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Guido W. Imbens

Stanford University

Roderick J. A. Little

University of Michigan–Ann Arbor

Robert Rosenthal

Harvard University Press

Paul R. Rosenbaum

Uppsala University

Fabrizia Mealli

University of Florence

Elizabeth R. Zell

Centers for Disease Control and Prevention

Constantine Frangakis

Johns Hopkins University

Nathaniel Schenker

National Center for Health Statistics

Marie‐Abèle Bind

Harvard University

Ralph L. Rosnow

Temple University

Cooperative Institutions

Harvard University

John Wiley & Sons (United States)

University of Michigan–Ann Arbor

The Ohio State University

National Council on Family Relations

Harvard University Press

University of Maryland, College Park

Pennsylvania State University

University of North Carolina at Chapel Hill

University of Pennsylvania

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The Acceptability of Regression Solutions: Another Look at Computational Accuracy

Journal of the American Statistical Association (1976)

Albert E. Beaton Donald B. Rubin John L. Barone

Abstract Longley [10] proposed a set of data for use in testing regression programs. This paper shows that the numerically accurate solution in this example was probably an unreasonable estimate of the regression coefficients. This is true because the accuracy of the data and appropriateness of the model may affect the solution more than the computational method. An easily computed index is derived that can be used to indicate such computational instability. The basic conclusion is that a concern about highly accurate computational methods must be tempered with a concern for whether the data are accurate enough to make the results meaningful.

Data set

10.1080/01621459.1976.10481507

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Citations (110)

The ECME algorithm: A simple extension of EM and ECM with faster monotone convergence

Biometrika (1994)

Chuanhai Liu Donald B. Rubin

A generalisation of the ecm algorithm (Meng & Rubin, 1993), which is itself an extension of the em algorithm (Dempster, Laird & Rubin, 1977), can be obtained by replacing some CM-steps of ECM, which maximise the constrained expected complete-data loglikelihood function, with steps that maximise the correspondingly constrained actual likelihood function. This algorithm, which we call ecme algorithm, for Expectation/Conditional Maximisation Either, shares with both em and ecm their stable monotone convergence and basic simplicity of implementation relative to competing faster converging methods. Moreover, ecme can have a substantially faster convergence rate than either EM or ECM, measured using either the number of iterations or actual computer time. There are two reasons for this improvement. First, in some of ECME'S maximisation steps, the actual likelihood is being conditionally maximised, rather than a current approximation to it, as with EM and ECM. Secondly, ecme allows faster converging numerical methods to be used on only those constrained maximisations where they are most efficacious. Illustrative ecme algorithms are presented with both closed-form and iterative CM-steps, which demonstrate the faster rate of convergence and the associated easier assessment of convergence. Also, theoretical expressions are presented and illustrated regarding the rate of convergence of ecme. Finally, relationships with Markov chain Monte Carlo methods are discussed.

10.1093/biomet/81.4.633

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Citations (559)

Best Practices in Quasi–Experimental Designs: Matching Methods for Causal Inference

SAGE Publications, Inc. eBooks (2008)

Elizabeth A. Stuart Donald B. Rubin

10.4135/9781412995627.d14

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Citations (299)

The Use of Matched Sampling and Regression Adjustment to Remove Bias in Observational Studies

Biometrics (1973)

Donald B. Rubin

10.2307/2529685

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Citations (430)

Propensity Score Methods for Creating Covariate Balance in Observational Studies

Revista Española de Cardiología (English Edition) (2011)

Cassandra Wolos Pattanayak Donald B. Rubin Elizabeth R. Zell

10.1016/j.rec.2011.06.008

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Citations (92)

Maximum Likelihood Estimation via the ECM Algorithm: A General Framework

Biometrika (1993)

Xiao-Li Meng Donald B. Rubin

10.2307/2337198

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Citations (168)

A Single Series from the Gibbs Sampler Provides a False Sense of Security

Oxford University Press eBooks (1992)

Andrew Gelman Donald B. Rubin

Abstract The Gibbs sampler can be very useful for simulating multivariate distributions, but naive use of it can give misleading—falsely precise—answers. An example with the using lattice model demonstrates that it is generally impossibile to assess convergence of a Gibbs sampler from a single sample series. This conclusion also applies to other iterative simulation methods such as the Metropolis algorithm.

Gibbs sampling

Sample (material)

10.1093/oso/9780198522669.003.0038

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Citations (169)

Composite Points in Weighted Least Squares Regressions

Technometrics (1980)

Donald B. Rubin

In a p-variate weighted least squares multiple regression based on n points, each of the p regression coefficients can be calculated from a univariate weighted regression through the origin using N = ( n p ) composite points. This result can be applied to (1) display the p-dimensional multiple regression as p univariate regressions each based on N composite points, (2) isolate collections of points with large leverage, and (3) characterize the region of regression coefficients that can be obtained from fixed data with varying weights. Consequently, composite points are diagnostically useful in the context of robust regression.

Univariate

Leverage (statistics)

Robust regression

Regression diagnostic

Local regression

10.1080/00401706.1980.10486165

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Citations (9)

Discussion

Calcutta Statistical Association Bulletin (2008)

Donald B. Rubin

10.1177/0008068320080305

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Citations (2)

Towards more scientific meta-analyses

arXiv (Cornell University) (2023)

Lily H. Zhang Menelaos Konstantinidis Marie‐Abèle Bind Donald B. Rubin

Meta-analysis can be a critical part of the research process, often serving as the primary analysis on which the practitioners, policymakers, and individuals base their decisions. However, current literature synthesis approaches to meta-analysis typically estimate a different quantity than what is implicitly intended; concretely, standard approaches estimate the average effect of a treatment for a population of imperfect studies, rather than the true scientific effect that would be measured in a population of hypothetical perfect studies. We advocate for an alternative method, called response-surface meta-analysis, which models the relationship between the quality of the study design as predictor variables and its reported estimated effect size as the outcome variable in order to estimate the effect size obtained by the hypothetical ideal study. The idea was first introduced by Rubin several decades ago, and here we provide a practical implementation. First, we reintroduce the idea of response-surface meta-analysis, highlighting its focus on a scientifically-motivated estimand while proposing a straightforward implementation. Then we compare the approach to traditional meta-analysis techniques used in practice. We then implement response-surface meta-analysis and contrast its results with existing literature-synthesis approaches on both simulated data and a real-world example published by the Cochrane Collaboration. We conclude by detailing the primary challenges in the implementation of response-surface meta-analysis and offer some suggestions to tackle these challenges.

10.48550/arxiv.2308.13514

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