Determinantal Generalizations of Instrumental Variables

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Journal Title
Journal ISSN
Volume Title
A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
Date
2018-03
Major/Subject
Mcode
Degree programme
Language
en
Pages
Series
Journal of causal inference, Volume 6, issue 1
Abstract
Linear structural equation models relate the components of a random vector using linear interdependencies and Gaussian noise. Each such model can be naturally associated with a mixed graph whose vertices correspond to the components of the random vector. The graph contains directed edges that represent the linear relationships between components, and bidirected edges that encode unobserved confounding. We study the problem of generic identifiability, that is, whether a generic choice of linear and confounding effects can be uniquely recovered from the joint covariance matrix of the observed random vector. An existing combinatorial criterion for establishing generic identifiability is the half-trek criterion (HTC), which uses the existence of trek systems in the mixed graph to iteratively discover generically invertible linear equation systems in polynomial time. By focusing on edges one at a time, we establish new sufficient and necessary conditions for generic identifiability of edge effects extending those of the HTC. In particular, we show how edge coefficients can be recovered as quotients of subdeterminants of the covariance matrix, which constitutes a determinantal generalization of formulas obtained when using instrumental variables for identification.
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Keywords
trek separation, half-trek criterion, structural equation models, identifiability, generic identifiability
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Citation
Weihs , L , Robinson , B , Dufresne , E , Kenkel , J , Kubjas , K , McGee , R L II , Nguyen , N , Robeva , E & Drton , M 2018 , ' Determinantal Generalizations of Instrumental Variables ' , Journal of causal inference , vol. 6 , no. 1 , 20170009 . https://doi.org/10.1515/jci-2017-0009