Nonlinear structural equation modeling with distribution-free method

Abstract

Structural equation models (SEM) are widely used in many fields including economics and social science. Typical nonlinear SEMs consist of two parts: a linear measurement model relating observed measurements to underlying latent variables, and a nonlinear structural model describing relationships among the latent variables. For such models, we propose a pseudo likelihood approach based on a hypothetical normal mixture assumption on the latent variables. To obtain pseudo likelihood parameter estimates, a Monte Carlo EM algorithm is developed. Standard errors for the structural parameter estimates are obtained by combining an empirical observed information matrix and a bootstrap estimated covariance matrix. For nonlinear SEMs with latent variables with various distributions, we conduct simulations to show our approach produced unbiased parameter estimates and confidence intervals with nominal coverage.