Causal effect for ordinal outcomes from observational data: Bayesian approach

Abstract

© 2016 by the Mathematical Association of Thailand. All rights reserved. Ordinal outcomes are often observed in the social and economic sciences. It is frequently that the scale or magnitude of the outcomes is not available. The common average treatment effect is not well-defined for causal inference. We define a useful causal estimands for ordinal outcomes in this research. To consistently estimate the causal estimands, the data has to satisfy the ignorable treatment assignment assumption. This condition ensures that the outcome of interest is independent of the treatment assignment mechanism. We discuss and propose the models for correcting self-selection bias from this type of observed data using copula approach. Copula can capture the dependence between treatment assignment and outcomes of interest. Bayesian estimation procedures play an important role in causal analysis [1]. Thus, Bayesian estimation procedure is applied to help estimating the complex model structures. Finally, we discuss the framework for estimate causal effect of ordinal potential outcomes and apply this framework to the healthcare survey data from [2] as a case study.