Upper Bound on the Sum of Correlations of Three Indicators Under the Absence of a Common Factor
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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).
Keywordscorrelation inequality constraint cycle with three colliders hidden common cause linear structural equation model
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