Cybernetics and Systems Analysis

, Volume 55, Issue 2, pp 174–185 | Cite as

Upper Bound on the Sum of Correlations of Three Indicators Under the Absence of a Common Factor

  • O. S. BalabanovEmail author


It is shown that, in a linear model with three indicator variables where each pair of indicators has a separate hidden “paired” factor, and the sum of three correlations is upper bounded. A violation of an established inequality constraint testifies that the causal structure of a generative model differs from the supposed one. When such a constraint is violated, it is arguable that there is a common cause of these three indicators or that one of them causally influences another. An inequality constraint can be efficiently used even under incomplete observability (in particular, when only two indicator variables are observed).


correlation inequality constraint cycle with three colliders hidden common cause linear structural equation model 


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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Institute of Software SystemsNational Academy of Sciences of UkraineKyivUkraine

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