Global identifiability of linear structural equation models

Drton Mathias, Foygel Rina, Sullivant Seth

Research output: Contribution to journalArticlepeer-review

50 Scopus citations

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.

Original languageEnglish
Pages (from-to)865-886
Number of pages22
JournalAnnals of Statistics
Volume39
Issue number2
DOIs
StatePublished - Apr 2011
Externally publishedYes

Keywords

  • Covariance matrix
  • Gaussian distribution
  • Graphical model
  • Multivariate normal distribution
  • Parameter identification
  • Structural equation model

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