Causal Inference of Ordinal Outcomes: A Bayesian Solution

2026-07-25

AI Summary

This study addresses the challenge of interpreting causal effects in randomized experiments with ordinal outcomes, where conventional estimands are often uninterpretable due to unknown spacing between categories. The authors propose a Bayesian latent-variable ordered probit model that jointly models the potential outcomes, enabling both super-population and finite-population inference for two interpretable causal quantities: “treatment beneficial” and “strictly beneficial.” This approach overcomes existing identification limitations, yielding sharper estimates than nonparametric bounds and incorporating a sensitivity analysis to assess the impact of unknown dependence between potential outcomes. Simulations and an application to a randomized trial on scalp health demonstrate that the method provides precise and substantively meaningful evaluations of treatment effects.

Abstract

Randomized experiments with ordinal outcomes are common in many scientific applications, but conventional causal estimands such as the average treatment effect are difficult to interpret because ordinal categories lack meaningful numerical spacing. We develop a Bayesian latent variable framework for drawing coherent super population and finite population inference on two interpretable causal estimands that quantify the probabilities that treatment is beneficial and strictly beneficial. By modeling the joint distribution of potential outcomes through an ordered probit model, the proposed approach overcomes the identifiability limitations of existing methods and yields substantially sharper inference than nonparametric bounds. We also investigate the impact of the unknown association between potential outcomes and propose a sensitivity analysis to assess its influence. Simulation studies and an application to a randomized experiment on human scalp health demonstrate that the method provides precise and practically relevant assessments of treatment effectiveness.

Problem

• ordinal outcomes
• causal inference
• treatment effect
• interpretability
• randomized experiments

Innovation

• Bayesian latent variable
• ordinal outcomes
• causal inference
• ordered probit model
• sensitivity analysis