Affinely invariant matching methods with discriminant mixtures of proportional ellipsoidally symmetric distributions

By Donald B. Rubin, Elizabeth A. Stuart. 2006

79 citations recorded by the source corpus.

In observational studies designed to estimate the effects of interventions or exposures, such as cigarette smoking, it is desirable to try to control background differences between the treated group (e.g., current smokers) and the control group (e.g., never smokers) on covariates X (e.g., age, education). Matched sampling attempts to effect this control by selecting subsets of the treated and control groups with similar distributions of such covariates. This paper examines the consequences of matching using affinely invariant methods when the covariate distributions are "discriminant mixtures of proportional ellipsoidally symmetric" (DMPES) distributions, a class herein defined, which generalizes the ellipsoidal symmetry class of Rubin and Thomas [Ann. Statist. 20 (1992) 1079-1093]. The resulting generalized results help indicate why earlier results hold quite well even when the simple assumption of ellipsoidal symmetry is not met [e.g., Biometrics 52 (1996) 249-264]. Extensions to conditionally affinely invariant matching with conditionally DMPES distributions are also discussed.

Subfields: Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/20707a1e6a398763ebad1df7ed6ae7a5a01122bc

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Citations in the corpus

Matching With Multiple Control Groups With Adjustment for Group Differences (2008, background): “There are theoretical reasons supporting such pooling for this estimation (Rubin & Stuart, 2006).”
Matching methods for causal inference: A review and a look forward (2010, background): “However, in fact, under fairly general conditions (Rubin and Thomas, 1996; Rubin and Stuart, 2006), using estimated rather than true propensity scores leads to an overestimate of variance, implying that not accounting for the uncertainty in using estimated rather than true values will be conservativ”
Multivariate Matching Methods That Are Monotonic Imbalance Bounding (2011, methodology): “In this section, we summarize the existing EPBR class of matching methods, introduce our new MIB class, discuss example methods within each class along with various compar-3 isons, and show how MIB is able to explicitly bound model dependence, a longstanding goal of matching methods.”
The prognostic analogue of the propensity score (2008, result): “…the hypothesis has been corroborated in a variety of studies (see e.g. Drake 1993; Dehejia and Wahba 1999; Rubin and Thomas 2000; Kurth et al. 2006; Rubin and Stuart 2006); however, propensity balance can be checked for a whole sample, whereas prognostic balance can ordinarily be checked only in…”
The Neyman— Rubin Model of Causal Inference and Estimation Via Matching Methods (2008, background): “The EPBR results of Rubin and Thomas (1992) have been extended by Rubin and Stuart (2005) to the case of discriminant mixtures of proportional ellipsoidally symmetric (DMPES) distributions.”
Multivariate and Propensity Score Matching Software with Automated Balance Optimization: The Matching Package for R (2008, unknown): “…invariance means that the matching output is invariant to matching on X or an affine transformation of X. 2The EPBR results of Rubin and Thomas (1992) have been extended by Rubin and Stuart (2006) to the case of discriminant mixtures of proportional ellipsoidally symmetric (DMPES) distributions.”
Matching as Nonparametric Preprocessing for Reducing Model Dependence in Parametric Causal Inference (2007, background): “…normal or t within classes deﬁned by categorical covariates; Rubin and Thomas 1996), as well as ‘‘discriminant mixtures of proportional ellipsoidally symmetric distributions’’ (Rubin and Stuart 2006). a fraction of observations, and so variance usually does drop following properly applied matching.”
You Can't Stay Here (2017, methodology): “In our work, we use Mahalanobis Distance Matching [40], to construct a set of control users who have similar characteristics as the treatment users.”
Misunderstandings between experimentalists and observationalists about causal inference (2008, background): “This also shows that no measure of balance which is a function of X alone can be guaranteed to be a monotone function of bias without special assumptions (Rubin and Stuart, 2006), and so proper measures of imbalance should always be minimized without limit, subject to efficiency constraints.”
A Cautionary Note on the Use of Matching to Estimate Causal Effects: An Empirical Example Comparing Matching Estimates to an Experimental Benchmark (2010, background): “Only 1 of these review pieces mentions the need to conduct sensitivity tests (Rubin and Stuart 2006), but the authors of the piece do not go into much detail about the sorts of sensitivity tests researchers should use.”