Factorization of the Partial Covariance in Singly-Connected Path Diagrams

Jose Peña
Proceedings of the Second Conference on Causal Learning and Reasoning, PMLR 213:814-849, 2023.

Abstract

We extend path analysis by showing that, for a singly-connected path diagram, the partial covariance of two random variables factorizes over the nodes and edges in the path between the variables. This result allows us to determine the contribution of each node and edge to the partial covariance. It also allows us to show that Simpson’s paradox cannot occur in singly-connected path diagrams.

Cite this Paper

BibTeX
@InProceedings{pmlr-v213-pena23a, title = {Factorization of the Partial Covariance in Singly-Connected Path Diagrams}, author = {Pe\~na, Jose}, booktitle = {Proceedings of the Second Conference on Causal Learning and Reasoning}, pages = {814--849}, year = {2023}, editor = {van der Schaar, Mihaela and Zhang, Cheng and Janzing, Dominik}, volume = {213}, series = {Proceedings of Machine Learning Research}, month = {11--14 Apr}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v213/pena23a/pena23a.pdf}, url = {https://proceedings.mlr.press/v213/pena23a.html}, abstract = {We extend path analysis by showing that, for a singly-connected path diagram, the partial covariance of two random variables factorizes over the nodes and edges in the path between the variables. This result allows us to determine the contribution of each node and edge to the partial covariance. It also allows us to show that Simpson’s paradox cannot occur in singly-connected path diagrams.} }
Endnote
%0 Conference Paper %T Factorization of the Partial Covariance in Singly-Connected Path Diagrams %A Jose Peña %B Proceedings of the Second Conference on Causal Learning and Reasoning %C Proceedings of Machine Learning Research %D 2023 %E Mihaela van der Schaar %E Cheng Zhang %E Dominik Janzing %F pmlr-v213-pena23a %I PMLR %P 814--849 %U https://proceedings.mlr.press/v213/pena23a.html %V 213 %X We extend path analysis by showing that, for a singly-connected path diagram, the partial covariance of two random variables factorizes over the nodes and edges in the path between the variables. This result allows us to determine the contribution of each node and edge to the partial covariance. It also allows us to show that Simpson’s paradox cannot occur in singly-connected path diagrams.
APA
Peña, J.. (2023). Factorization of the Partial Covariance in Singly-Connected Path Diagrams. Proceedings of the Second Conference on Causal Learning and Reasoning, in Proceedings of Machine Learning Research 213:814-849 Available from https://proceedings.mlr.press/v213/pena23a.html.

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