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Dirichlet process mixture models for regression discontinuity designs

Ricciardi, Federico; Liverani, Silvia; Baio, Gianluca; (2022) Dirichlet process mixture models for regression discontinuity designs. Statistical Methods in Medical Research 10.1177/09622802221129044. (In press). Green open access

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Abstract

The regression discontinuity design is a quasi-experimental design that estimates the causal effect of a treatment when its assignment is defined by a threshold for a continuous variable. The regression discontinuity design assumes that subjects with measurements within a bandwidth around the threshold belong to a common population, so that the threshold can be seen as a randomising device assigning treatment to those falling just above the threshold and withholding it from those who fall below. Bandwidth selection represents a compelling decision for the regression discontinuity design analysis as results may be highly sensitive to its choice. A few methods to select the optimal bandwidth, mainly from the econometric literature, have been proposed. However, their use in practice is limited. We propose a methodology that, tackling the problem from an applied point of view, considers units' exchangeability, that is, their similarity with respect to measured covariates, as the main criteria to select subjects for the analysis, irrespectively of their distance from the threshold. We cluster the sample using a Dirichlet process mixture model to identify balanced and homogeneous clusters. Our proposal exploits the posterior similarity matrix, which contains the pairwise probabilities that two observations are allocated to the same cluster in the Markov chain Monte Carlo sample. Thus we include in the regression discontinuity design analysis only those clusters for which we have stronger evidence of exchangeability. We illustrate the validity of our methodology with both a simulated experiment and a motivating example on the effect of statins on cholesterol levels.

Type: Article
Title: Dirichlet process mixture models for regression discontinuity designs
Location: England
Open access status: An open access version is available from UCL Discovery
DOI: 10.1177/09622802221129044
Publisher version: https://doi.org/10.1177/09622802221129044
Language: English
Additional information: This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions.
Keywords: Bayesian inference, causal inference, dirichlet process mixture models, Regression discontinuity design
UCL classification: UCL
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Statistical Science
URI: https://discovery.ucl.ac.uk/id/eprint/10161878
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