Global identifiability of linear structural equation models

TL;DR

This paper provides a necessary and sufficient condition for the global identifiability of linear structural equation models with Gaussian noise, crucial for ensuring the models' parameters can be uniquely recovered.

Contribution

It introduces a new criterion based on mixed graphs that characterizes when these models are globally identifiable, advancing the theoretical understanding of model identifiability.

Findings

Established a graph-based criterion for identifiability

Proved the criterion is both necessary and sufficient

Enhanced understanding of model parameter recovery

Abstract

Structural equation models are multivariate statistical models that are defined by specifying noisy functional relationships among random variables. We consider the classical case of linear relationships and additive Gaussian noise terms. We give a necessary and sufficient condition for global identifiability of the model in terms of a mixed graph encoding the linear structural equations and the correlation structure of the error terms. Global identifiability is understood to mean injectivity of the parametrization of the model and is fundamental in particular for applicability of standard statistical methodology.