Design and Analysis of Bipartite Experiments under a Linear Exposure-Response Model

TL;DR

This paper introduces the ERL estimator for bipartite experiments under a linear model, proving its statistical properties and proposing a design to improve estimation precision.

Contribution

It presents the ERL estimator, analyzes its properties, and introduces a new cluster-based design to enhance estimation accuracy in bipartite experiments.

Findings

ERL estimator is unbiased, consistent, and asymptotically normal.

Variance estimator for ERL is unbiased and consistent.

Exposure-Design improves the precision of treatment effect estimates.

Abstract

A bipartite experiment consists of one set of units being assigned treatments and another set of units for which we measure outcomes. The two sets of units are connected by a bipartite graph, governing how the treated units can affect the outcome units. In this paper, we consider estimation of the average total treatment effect in the bipartite experimental framework under a linear exposure-response model. We introduce the Exposure Reweighted Linear (ERL) estimator, and show that the estimator is unbiased, consistent and asymptotically normal, provided that the bipartite graph is sufficiently sparse. To facilitate inference, we introduce an unbiased and consistent estimator of the variance of the ERL point estimator. In addition, we introduce a cluster-based design, Exposure-Design, that uses heuristics to increase the precision of the ERL estimator by realizing a desirable exposure distribution.