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Journal of Causal Inference

Ed. by Imai, Kosuke / Pearl, Judea / Petersen, Maya Liv / Sekhon, Jasjeet / van der Laan, Mark J.

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A Kernel-Based Metric for Balance Assessment

Yeying Zhu
  • Corresponding author
  • University of Waterloo, Department of Statistics and Actuarial Science, 200 University Ave W, Waterloo, Ontario, N2L 3G1, Canada
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/ Jennifer S. Savage
  • 8082 Pennsylvania State University, Center for Childhood Obesity Research, University Park, Pennsylvania, United States
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/ Debashis Ghosh
  • University of Colorado School of Public Health, Biostatistics and Informatics, 13001 E. 17th Place, Aurora, 80045, Colorado, United States
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Published Online: 2018-05-18 | DOI: https://doi.org/10.1515/jci-2016-0029


An important goal in causal inference is to achieve balance in the covariates among the treatment groups. In this article, we introduce the concept of distributional balance preserving which requires the distribution of the covariates to be the same in different treatment groups. We also introduce a new balance measure called kernel distance, which is the empirical estimate of the probability metric defined in the reproducing kernel Hilbert spaces. Compared to the traditional balance metrics, the kernel distance measures the difference in the two multivariate distributions instead of the difference in the finite moments of the distributions. Simulation results show that the kernel distance is the best indicator of bias in the estimated casual effect compared to several commonly used balance measures. We then incorporate kernel distance into genetic matching, the state-of-the-art matching procedure and apply the proposed approach to analyze the Early Dieting in Girls study. The study indicates that mothers’ overall weight concern increases the likelihood of daughters’ early dieting behavior, but the causal effect is not significant.

Keywords: Causal effect; Distributional covariate balance; Probability metric; Reproducing kernel Hilbert space


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About the article

Received: 2016-12-18

Revised: 2018-04-02

Accepted: 2018-05-02

Published Online: 2018-05-18

Published in Print: 2018-09-25

Funding Source: Social Sciences and Humanities Research Council of Canada

Award identifier / Grant number: 430-2016-00163

Funding Source: Natural Sciences and Engineering Research Council of Canada

Award identifier / Grant number: RGPIN-2017-04064

The project described was supported by Award Number 430-2016-00163 from the Social Sciences and Humanities Research Council and by Grant Number RGPIN-2017-04064 from the Natural Sciences and Engineering Research Council of Canada.

Citation Information: Journal of Causal Inference, Volume 6, Issue 2, 20160029, ISSN (Online) 2193-3685, DOI: https://doi.org/10.1515/jci-2016-0029.

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