Global identifiability of linear structural equation models

By Mathias Drton, Rina Foygel, Seth Sullivant. 2010

98 citations recorded by the source corpus.

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.

Subfields: Artificial Intelligence, Management Science and Operations Research, Molecular Biology

View Paper: https://www.semanticscholar.org/paper/1e2565c5c3f5dcdffe1f24cd804c0f73b597eac2

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In Artificial Intelligence

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Citations in the corpus

Learning Directed Acyclic Graphs with Penalized Neighbourhood Regression (2015, methodology): “Our approach is based on the well-known structural equation model (SEM) interpretation of Gaussian DAGs (Wright, 1934; Drton et al., 2011).”
Counterfactual analyses with graphical models based on local independence (2011, background): “It was shown in [12, 27] and [10] that this strategy gives a complete theory in the simpler setting of finite state or Gaussian–Bayesian networks.”
Algebraic problems in structural equation modeling (2016, background): “If m ≥ 3, then it is possible to show that φG is generically 2-to-1, that is, the fiber FG(Λ,Ω) is generically of size two [16].”