Graphical Representations for Algebraic Constraints of Linear Structural Equations Models

TL;DR

This paper introduces a graphical notation to represent polynomial constraints in linear structural equation models, aiming to simplify their complexity and improve understanding of observational characteristics.

Contribution

The paper proposes a new graphical notation for polynomial constraints in linear SEMs, with theoretical and empirical analysis of its expressive power.

Findings

Graphical notation effectively captures polynomial constraints

The notation simplifies the analysis of SEM observational characteristics

Empirical results support the notation's expressive capabilities

Abstract

The observational characteristics of a linear structural equation model can be effectively described by polynomial constraints on the observed covariance matrix. However, these polynomials can be exponentially large, making them impractical for many purposes. In this paper, we present a graphical notation for many of these polynomial constraints. The expressive power of this notation is investigated both theoretically and empirically.