Causal Inference of Ordinal Outcomes: A Bayesian Solution

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.