Robustly estimating heterogeneity in factorial data using Rashomon Partitions

TL;DR

This paper introduces Rashomon Partition Sets (RPSs), a Bayesian framework that enumerates all high-evidence models to better capture outcome heterogeneity in data, avoiding oversimplification or spurious patterns.

Contribution

The paper presents a novel enumeration-based Bayesian approach using RPSs and an l0 prior to robustly estimate heterogeneity without strong assumptions, ensuring comprehensive model exploration.

Findings

RPS effectively captures complex heterogeneity in various datasets.

Enumeration approach guarantees exploration of all high-evidence models.

Empirical examples demonstrate improved understanding of outcome variability.

Abstract

In both observational data and randomized control trials, researchers select statistical models to articulate how the outcome of interest varies with combinations of observable covariates. Choosing a model that is too simple can obfuscate important heterogeneity in outcomes between covariate groups, while too much complexity risks identifying spurious patterns. In this paper, we propose a novel Bayesian framework for model uncertainty called Rashomon Partition Sets (RPSs). The RPS consists of all models that have posterior density close to the maximum a posteriori (MAP) model. We construct the RPS by enumeration, rather than sampling, which ensures that we explore all models models with high evidence in the data, even if they offer dramatically different substantive explanations. We use a l0 prior, which allows the allows us to capture complex heterogeneity without imposing strong assumptions about the associations between effects, showing this prior is minimax optimal from an information-theoretic perspective. We characterize the approximation error of (functions of) parameters computed conditional on being in the RPS relative to the entire posterior. We propose an algorithm to enumerate the RPS from the class of models that are interpretable and unique, then provide bounds on the size of the RPS. We give simulation evidence along with three empirical examples: price effects on charitable giving, heterogeneity in chromosomal structure, and the introduction of microfinance.