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March 2014 Matching for balance, pairing for heterogeneity in an observational study of the effectiveness of for-profit and not-for-profit high schools in Chile
José R. Zubizarreta, Ricardo D. Paredes, Paul R. Rosenbaum
Ann. Appl. Stat. 8(1): 204-231 (March 2014). DOI: 10.1214/13-AOAS713

Abstract

Conventionally, the construction of a pair-matched sample selects treated and control units and pairs them in a single step with a view to balancing observed covariates $\mathbf{x}$ and reducing the heterogeneity or dispersion of treated-minus-control response differences, $Y$. In contrast, the method of cardinality matching developed here first selects the maximum number of units subject to covariate balance constraints and, with a balanced sample for $\mathbf{x}$ in hand, then separately pairs the units to minimize heterogeneity in $Y$. Reduced heterogeneity of pair differences in responses $Y$ is known to reduce sensitivity to unmeasured biases, so one might hope that cardinality matching would succeed at both tasks, balancing $\mathbf{x}$, stabilizing $Y$. We use cardinality matching in an observational study of the effectiveness of for-profit and not-for-profit private high schools in Chile—a controversial subject in Chile—focusing on students who were in government run primary schools in 2004 but then switched to private high schools. By pairing to minimize heterogeneity in a cardinality match that has balanced covariates, a meaningful reduction in sensitivity to unmeasured biases is obtained.

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José R. Zubizarreta. Ricardo D. Paredes. Paul R. Rosenbaum. "Matching for balance, pairing for heterogeneity in an observational study of the effectiveness of for-profit and not-for-profit high schools in Chile." Ann. Appl. Stat. 8 (1) 204 - 231, March 2014. https://doi.org/10.1214/13-AOAS713

Information

Published: March 2014
First available in Project Euclid: 8 April 2014

zbMATH: 06302233
MathSciNet: MR3191988
Digital Object Identifier: 10.1214/13-AOAS713

Keywords: design sensitivity , integer programming , testing twice

Rights: Copyright © 2014 Institute of Mathematical Statistics

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Vol.8 • No. 1 • March 2014
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