Empirical Likelihood for Linear Structural Equation Models with Dependent Errors

TL;DR

This paper develops empirical likelihood methods for linear structural equation models with correlated, non-Gaussian errors, enhancing inference accuracy and efficiency through proposed modifications and simulations.

Contribution

It introduces empirical likelihood procedures tailored for SEMs with dependent, non-Gaussian errors, including modifications for better performance.

Findings

EL methods improve inference with non-Gaussian errors

Proposed modifications enhance statistical efficiency

Simulations demonstrate better significance assessment

Abstract

We consider linear structural equation models that are associated with mixed graphs. The structural equations in these models only involve observed variables, but their idiosyncratic error terms are allowed to be correlated and non-Gaussian. We propose empirical likelihood (EL) procedures for inference, and suggest several modifications, including a profile likelihood, in order to improve tractability and performance of the resulting methods. Through simulations, we show that when the error distributions are non-Gaussian, the use of EL and the proposed modifications may increase statistical efficiency and improve assessment of significance.