Sequences of regressions and their dependences

TL;DR

This paper introduces traceable regressions, a concept involving sequences of regressions represented by graphs that capture both independence and dependence pathways, enhancing understanding of complex dependence structures.

Contribution

It defines traceable regressions and provides graphical criteria for dependence pathways, expanding the tools for analyzing dependence structures in statistical models.

Findings

Traceable regressions are characterized by specific graphical properties.

Regression graphs can be transformed to reveal dependence pathways.

Conditions for faithfulness to a graph are compared to those for traceable regressions.

Abstract

In this paper, we define and study the concept of traceable regressions. These are sequences of regressions in joint or single responses for which a corresponding regression graph captures not only an independence structure but represents, in addition, conditional dependences that permit the tracing of pathways of dependence. We give the properties needed for transforming these graphs and graphical criteria to decide whether a path in the graph induces a dependence. The much stronger constraints on distributions that are faithful to a graph are compared to those needed for traceable regressions.