Determinantal Generalizations of Instrumental Variables

Weihs Luca (), Robinson Bill (), Dufresne Emilie (), Kenkel Jennifer (), Kubjas Reginald McGee II Kaie (), Reginald McGee (), Nguyen Nhan (), Robeva Elina () and Drton Mathias ()
Additional contact information
Weihs Luca: Statistics, University of Washington, Box 354322, Seattle, USA
Robinson Bill: Mathematics, Denison University, Granville, Ohio, USA
Dufresne Emilie: University of Nottingham, Nottingham, UK
Kenkel Jennifer: Mathematics, University of Utah, Salt Lake City, USA
Kubjas Reginald McGee II Kaie: Mathematics and Systems Analysis, Aalto University, Espoo, Finland
Reginald McGee: Mathematical Biosciences Institute, Columbus, USA
Nguyen Nhan: Department of Mathematics, University of Montana, Missoula, USA
Robeva Elina: Department of Mathematics, Massachusetts Institute of Technology, Cambridge, USA
Drton Mathias: Statistics, University of Washington, Seattle, USA

Journal of Causal Inference, 2018, vol. 6, issue 1, 21

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 new 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. While our results do not completely close the gap between existing sufficient and necessary conditions we find, empirically, that our results allow us to prove the generic identifiability of many more mixed graphs than the prior state-of-the-art.

Keywords: trek separation; half-trek criterion; structural equation models; identifiability; generic identifiability (search for similar items in EconPapers)
Date: 2018
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
https://doi.org/10.1515/jci-2017-0009 (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:bpj:causin:v:6:y:2018:i:1:p:21:n:1

DOI: 10.1515/jci-2017-0009

Access Statistics for this article

Journal of Causal Inference is currently edited by Elias Bareinboim, Jin Tian and Iván Díaz

More articles in Journal of Causal Inference from De Gruyter
Bibliographic data for series maintained by Peter Golla ().