Causal Effect for Ordinal Outcomes from Observational Data: Bayesian Approach

Jirakom Sirisrisakulchai, Songsak Sriboonchitta

Abstract

Ordinal outcomes are often observed in the social and economic sciences. Itis frequently that the scale or magnitude of the outcomes is not available. The commonaverage treatment effect is not well-defined for causal inference. We define a usefulcausal estimands for ordinal outcomes in this research. To consistently estimate thecausal estimands, the data has to satisfy the ignorable treatment assignment assumption.This condition ensures that the outcome of interest is independent of the treatmentassignment mechanism. We discuss and propose the models for correcting self-selectionbias from this type of observed data using copula approach. Copula can capture thedependence between treatment assignment and outcomes of interest. Bayesian estimationprocedures play an important role in causal analysis [1]. Thus, Bayesian estimationprocedure is applied to help estimating the complex model structures. Finally, we discussthe framework for estimate causal effect of ordinal potential outcomes and apply thisframework to the healthcare survey data from [2] as a case study.