Multivariate Causal Effect: a Bayesian Regression Factor Model

In observational studies, a single cause or exposure can influence multiple, often highly correlated outcomes. For example, in environmental health, air pollution can simultaneously affect several diseases or causes of mortality, while in genomics, a treatment or cancer type can alter genomic or mutational signature profiles. Similarly, wildfire smoke represents a specific exposure that can modify the chemical composition of pollutants in the air. We address this setting within the potential outcomes framework and propose a Bayesian causal regression factor model to estimate multivariate causal effects in the presence of correlated outcomes. Our approach introduces two key innovations:(i) a causal inference framework for multivariate potential outcomes, and (ii) a novel Bayesian factor model that employs a dependent probit stick-breaking process as a distribution for treatment-specific factor scores. By modeling factor scores directly, the proposed method overcomes the missing data challenges inherent in causal inference and flexibly captures latent structures underlying outcome correlations. We apply our method to U.S. air quality data, estimating the causal effect of wildfire smoke on 27 chemical species in fine particulate matter pm2.5, providing a deeper understanding of their interdependencies.