Conditional independence collapsibility for acyclic directed mixed graph models

Abstract

Collapsibility refers to the property that, when marginalizing over some variables that are not of interest from the full model, the resulting marginal model of the remaining variables is equivalent to the local model induced by the subgraph on these variables. This means that when the marginal model satisfies collapsibility, statistical inference results based on the marginal model and the local model are consistent. This has significant implications for small-sample data, modeling latent variable data, and reducing the computational complexity of statistical inference. This paper focuses on studying the conditional independence collapsibility of acyclic directed mixed graph (ADMG) models. By introducing the concept of inducing paths in ADMGs and exploring its properties, the conditional independence collapsibility of ADMGs is characterized equivalently from both graph theory and statistical perspectives.