Full Matching in an Observational Study of Coaching for the SAT

Abstract

Among matching techniques for observational studies, full matching is in principle the best, in the sense that its alignment of comparable treated and control subjects is as good as that of any alternate method, and potentially much better. This article evaluates the practical performance of full matching for the first time, modifying it in order to minimize variance as well as bias and then using it to compare coached and uncoached takers of the SAT. In this new version, with restrictions on the ratio of treated subjects to controls within matched sets, full matching makes use of many more observations than does pair matching, but achieves far closer matches than does matching with k ≥ 2 controls. Prior to matching, the coached and uncoached groups are separated on the propensity score by 1.1 SDs. Full matching reduces this separation to 1% or 2% of an SD. In older literature comparing matching and regression, Cochran expressed doubts that any method of adjustment could substantially reduce observed bias of this magnitude.To accommodate missing data, regression-based analyses by ETS researchers rejected a subset of the available sample that differed significantly from the subsample they analyzed. Full matching on the propensity score handles the same problem simply and without rejecting observations. In addition, it eases the detection and handling of nonconstancy of treatment effects, which the regression-based analyses had obscured, and it makes fuller use of covariate information. It estimates a somewhat larger effect of coaching on the math score than did ETS's methods.

CYP2D6 in the brain: genotype effects on resting brain perfusion

“…The 'optimal matching' algorithm was used. 41,44 This and other univariate models were estimated using the freely available statistical program R (version 2.9.2, available from www.rproject.org, The R Foundation for Statistical Computing, Vienna, Austria).…”

Estrategia para la inferencia causal y planificación de estudios observacionales en las ciencias sociales: el caso de Chaitén post erupción del 2008

“…Rosenbaum (1991) introdujo la técnica de Full Matching en el campo de estudios observacionales y Hansen (2004), posteriormente, explicó e ilustró el funcionamiento del método. 5 Sobre la base de un set de covariables definidas previamente, Full Maching construye bloques conformados por tratados y controles de modo tal que ambos grupos estén balanceados en las distribuciones de las covariables.…”

“…Si la razón de tratados y controles dentro de cada bloque está muy desbalanceada, dicho problema puede introducir sesgo en las estimaciones (Stuart y Green 2008). Tal como sugiere Hansen (2004), Full Matching permite solucionar este problema a través de la imposición de restricciones al número de tratados y controles que habrá dentro de cada bloque. Por ejemplo, definir de antemano el número mínimo y el número máximo de controles dentro de cada bloque.…”

The Neyman— Rubin Model of Causal Inference and Estimation Via Matching Methods

“…6 One can do matching with replacement or without. Alternatively one can do optimal full matching (Hansen 2004;Rosenbaum 1991) instead of the greedy matching. But this decision is a separate one from the choice of a distance metric.…”