Unit Selection with Nonbinary Treatment and Effect

TL;DR

This paper extends the unit selection problem to nonbinary treatments and effects, providing algorithms to test identifiability and compute bounds of the benefit function using combined data sources.

Contribution

It introduces a generalized benefit function framework for nonbinary treatments and effects, along with algorithms for testing identifiability and computing bounds.

Findings

Algorithms for testing identifiability of nonbinary benefit functions.

Methods to compute bounds of the benefit function from data.

Extension of prior binary treatment models to nonbinary cases.

Abstract

The unit selection problem aims to identify a set of individuals who are most likely to exhibit a desired mode of behavior, for example, selecting individuals who would respond one way if encouraged and a different way if not encouraged. Using a combination of experimental and observational data, Li and Pearl derived tight bounds on the "benefit function", which is the payoff/cost associated with selecting an individual with given characteristics. This paper extends the benefit function to the general form such that the treatment and effect are not restricted to binary. We propose an algorithm to test the identifiability of the nonbinary benefit function and an algorithm to compute the bounds of the nonbinary benefit function using experimental and observational data.