Balabanov O.S.
Upper bound on correlation sum for three indicators under absence of common factor

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

Keywords: correlation, cycle with three colliders, hidden common cause, inequality constraint, linear structural equation model, Constraint theory, Correlation methods, Common factors, Generative model, hidden common cause, Incomplete observability, Indicator variables, Inequality constraint, Linear modeling, Structural equation modeling, Observability

Cite:
Balabanov O.S. (2019). Upper bound on correlation sum for three indicators under absence of common factor. Cybernetics and Systems Analysis, 55 (2), 10-21. doi: https://doi.org/10.1007/s10559-019-00122-x http://jnas.nbuv.gov.ua/article/UJRN-0000968692 [In Russian].