Affiliations: [a] Department of Clinical Sciences and Simmons Cancer Center, UT Southwestern Medical Center, Dallas, TX, USA | [b] Department of Clinical Sciences, UT Southwestern Medical Center, Dallas, TX, USA
Correspondence:
[*]
Corresponding author: Yan D. Zhao, 5323 Harry Hines Blvd, Room ND3.101E, Dallas, Texas 75390-8590, USA. E-mail: Daniel.Zhao@utsouthwestern.edu.
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.
Keywords: Bootstrap, deconvolution, latent variable modeling, MCEM algorithm, normal mixture, standard error estimation
