Empirical Likelihood for Linear Structural Equation Models with Dependent Errors

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.