Global identifiability of linear structural equation models

Details Global identifiability of linear structural equation models Global identifiability of linear structural equation models

2010-03-04

arxiv.org/abs/1003.1146v3

Annals of Statistics 2011, Vol. 39, No. 2, 865-886

Mathematics

Statistics Theory

Published in at http://dx.doi.org/10.1214/10-AOS859 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of

Scientific paper

10.1214/10-AOS859

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.

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