Joint modelling of multiple treatment variables for a single outcome: A Bayesian approach

Abstract

Current frameworks for causal inference in observational studies do not readily allow for the joint modelling of different types of treatment variables, such as a mix of continuous and discrete data. In this work, we propose an extended rank likelihood method [Hoff (2007)] for the inference of two latent parameterisations of the propensity score; the latent nature of the score is due to the copula framework. This allows for the simultaneous inclusion of different types of treatment variables (discrete, ordinal, and continuous). One parameterisation, the LPF, is an adaptation of the non-latent propensity function by Imai and Van Dyk (2004), who showcase their method on a canonical data set in the causal inference literature. Our other parameterisation, LPGS, is an adaptation of the generalised propensity score by Hirano and Imbens (2004). We compare the performance of the three approaches when applied to the canonical data set, as well as the data from our work on the latent causal socio-economic health (LACSH) index [Kuh (2022)]. Show more