A Hybrid Symbolic/Numeric Solution To Polynomial SEM

TL;DR

This paper introduces a hybrid symbolic/numeric method for nonlinear SEM using Isserlis' theorem, enabling direct extension of linear SEM to nonlinear cases with improved accuracy in estimating complex models.

Contribution

It presents a novel approach combining symbolic and numeric calculations for nonlinear SEM, which was not previously explored extensively.

Findings

The method accurately estimates tricky nonlinear models.

Simulation results demonstrate high effectiveness of the approach.

Higher moments improve model estimation accuracy.

Abstract

There are many approaches to nonlinear SEM (structural equation modeling) but it seems that a rather straightforward approach using Isserlis' theorem has not yet been investigated although it allows the direct extension of the standard linear approach to nonlinear linear SEM. The reason may be that this method requires some symbolic calculations done at runtime. This paper describes the class of appropriate models and outlines the algorithm that calculates the covariance matrix and higher moments. Simulation studies show that the method works very well and especially that tricky models can be estimated accurately by taking higher movements into account, too.