A0804
Title: A DAG-probit model for Bayesian causal inference and causal structure learning from ordinal data
Authors: Alessandro Mascaro - Universitat Pompeu Fabra (Spain) [presenting]
Federico Castelletti - Università Cattolica del Sacro Cuore (Milan) (Italy)
Augusto Fasano - Universita` Cattolica del Sacro Cuore and Collegio Carlo Alberto (Italy)
Abstract: Psychologists often aim to understand causal relationships between latent constructs observed only through ordinal data in the form of subjects' responses to items in tests and scales. In addition, they seek to quantify the strength of these relationships, as it may be of interest to identify optimal clinical interventions. Motivated by this, a fully Bayesian methodology is developed for causal structure learning and causal effect estimation from ordinal data. In particular, it is assumed that the causal structure underlying the latent constructs follows from a linear Gaussian structural equation model admitting a direct acyclic graph as a graphical representation. Ordinal data are then obtained via discretization of the latent variables, thus inducing a DAG-probit model. An MCMC scheme is devised to sample the joint posterior distribution of DAGs, DAG parameters, and unknown discretization thresholds, from which a Bayesian model averaging estimate of any causal effect of interest can be easily obtained. The methodology is evaluated in an extensive simulation study, and a real-data application is provided on survey data.
