Towards Conditional Path Analysis

TL;DR

This paper extends path analysis by providing conditions to compute partial covariance from covariance, maintaining the factorization property over paths, which enhances understanding of variable relationships.

Contribution

It introduces a method to calculate partial covariance using covariance and partial variance ratios, preserving path factorization in analysis.

Findings

Partial covariance can be computed from covariance with variance ratio correction.

The method preserves the factorization over paths in the analysis.

Provides sufficient conditions for the computation.

Abstract

We extend path analysis by giving sufficient conditions for computing the partial covariance of two random variables from their covariance. This is specifically done by correcting the covariance with the product of some partial variance ratios. As a result, the partial covariance retains the covariance's salient feature of factorizing over the edges in the paths between the two variables of interest.