UDC 004.855:519.216
1 Institute of Software Systems of the National Acedemy of Sciences of Ukraine, Kyiv, Ukraine
 bas@isofts.kiev.ua
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UPPER BOUND ON CORRELATION SUM FOR THREE INDICATORS
UNDER ABSENCE OF COMMON FACTOR
Abstract. We demonstrate that in linear model with three indicator variables, where each pair of indicators is associated by separate hidden pairwise factor, the sum of correlations is upper bounded. The inequality constraint violation manifests that the underlying causal structure differs from the supposed one. In the case of the inequality violation, one may suggest that there is a common cause of the three indicators, or one indicator variable causally influences the other one. The inequality constraint remains efficient under partial observability (for instance, when two indicators only are observed).
Keywords: correlation, inequality constraint, cycle with three colliders, hidden common cause, linear SEM.
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