The Annals of Statistics

Global identifiability of linear structural equation models

Mathias Drton, Rina Foygel, and Seth Sullivant

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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.

Article information

Ann. Statist., Volume 39, Number 2 (2011), 865-886.

First available in Project Euclid: 9 March 2011

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Zentralblatt MATH identifier

Primary: 62H05: Characterization and structure theory 62J05: Linear regression

Covariance matrix Gaussian distribution graphical model multivariate normal distribution parameter identification structural equation model


Drton, Mathias; Foygel, Rina; Sullivant, Seth. Global identifiability of linear structural equation models. Ann. Statist. 39 (2011), no. 2, 865--886. doi:10.1214/10-AOS859.

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