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Optimal Multilevel Matching in Clustered Observational Studies: A Case Study of the Effectiveness of Private Schools Under a Large-Scale Voucher System

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  • José R. Zubizarreta
  • Luke Keele

Abstract

A distinctive feature of a clustered observational study is its multilevel or nested data structure arising from the assignment of treatment, in a nonrandom manner, to groups or clusters of units or individuals. Examples are ubiquitous in the health and social sciences including patients in hospitals, employees in firms, and students in schools. What is the optimal matching strategy in a clustered observational study? At first thought, one might start by matching clusters of individuals and then, within matched clusters, continue by matching individuals. But as we discuss in this article, the optimal strategy is the opposite: in typical applications, where the intracluster correlation is not one, it is best to first match individuals and, once all possible combinations of matched individuals are known, then match clusters. In this article, we use dynamic and integer programming to implement this strategy and extend optimal matching methods to hierarchical and multilevel settings. Among other matched designs, our strategy can approximate a paired clustered randomized study by finding the largest sample of matched pairs of treated and control individuals within matched pairs of treated and control clusters that is balanced according to specifications given by the investigator. This strategy directly balances covariates both at the cluster and individual levels and does not require estimating the propensity score, although the propensity score can be balanced as an additional covariate. We illustrate our results with a case study of the comparative effectiveness of public versus private voucher schools in Chile, a question of intense policy debate in the country at the present.

Suggested Citation

  • José R. Zubizarreta & Luke Keele, 2017. "Optimal Multilevel Matching in Clustered Observational Studies: A Case Study of the Effectiveness of Private Schools Under a Large-Scale Voucher System," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(518), pages 547-560, April.
  • Handle: RePEc:taf:jnlasa:v:112:y:2017:i:518:p:547-560
    DOI: 10.1080/01621459.2016.1240683
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    Cited by:

    1. Youjin Lee & Trang Q. Nguyen & Elizabeth A. Stuart, 2021. "Partially pooled propensity score models for average treatment effect estimation with multilevel data," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 184(4), pages 1578-1598, October.
    2. Fatih Unlu & Douglas Lee Lauen & Sarah Crittenden Fuller & Tiffany Berglund & Elc Estrera, 2021. "Can Quasi‐Experimental Evaluations That Rely On State Longitudinal Data Systems Replicate Experimental Results?," Journal of Policy Analysis and Management, John Wiley & Sons, Ltd., vol. 40(2), pages 572-613, March.
    3. Md Saiful Islam & Md Sarowar Morshed & Gary J Young & Md Noor-E-Alam, 2019. "Robust policy evaluation from large-scale observational studies," PLOS ONE, Public Library of Science, vol. 14(10), pages 1-19, October.
    4. Bikram Karmakar, 2022. "An approximation algorithm for blocking of an experimental design," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 84(5), pages 1726-1750, November.
    5. Aleksey Oshchepkov & Anna Shirokanova, 2020. "Multilevel Modeling For Economists: Why, When And How," HSE Working papers WP BRP 233/EC/2020, National Research University Higher School of Economics.

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