Dirichlet Process Mixture Models for Regression Discontinuity Designs

TL;DR

This paper introduces a novel clustering-based method using Dirichlet process mixture models to improve bandwidth selection in Regression Discontinuity Designs by focusing on exchangeability and covariate similarity.

Contribution

It proposes a new approach that clusters units based on covariate similarity to select balanced groups for RDD analysis, moving beyond traditional distance-based bandwidth methods.

Findings

Method effectively identifies homogeneous clusters for RDD analysis.

Simulation and real data demonstrate improved causal effect estimation.

Clustering approach enhances robustness to bandwidth sensitivity.

Abstract

The Regression Discontinuity Design (RDD) is a quasi-experimental design that estimates the causal effect of a treatment when its assignment is defined by a threshold value for a continuous assignment variable. The RDD 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 just below. Bandwidth selection represents a compelling decision for the RDD analysis as the results may be highly sensitive to its choice. A number of methods to select the optimal bandwidth, mainly originating 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, consider units' exchangeability, i.e., 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 carry out clustering on 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 MCMC sample. Thus we include in the RDD 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 to lower cholesterol level, using UK primary care data.