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.
While in general the param-eters for these models are not identified, REF give necessary and sufficient conditions for global identifiability.
Global identifiability of linear structural equation models
Annals of Statistics 2011, Vol. 39, No. 2, 865-886
Mathematics