Global identifiability of linear structural equation models. (English) Zbl 1215.62052

Summary: 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.


62H05 Characterization and structure theory for multivariate probability distributions; copulas
05C90 Applications of graph theory
62J05 Linear regression; mixed models


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