A Quasi-Likelihood Approach to Assess Model Fit in Quadratic and Interaction SEM

For the assessment of model fit in linear structural equation modeling (SEM), several fit measures have been developed that use an unconstrained mean and covariance structure, but cannot be readily applied to SEM with quadratic and interaction effects. In this article, we propose the novel quasi-likelihood ratio test (Q-LRT) to evaluate global fit of nonlinear SEM models. The Q-LRT is based on a simplification of the quasi-maximum likelihood method for the estimation of model parameters. An empirical application of the Q-LRT is demonstrated for data in a study about aging in men. Results from a Monte Carlo study show that the Q-LRT performs reliably when sample size is sufficiently large. Also, simulations suggest robustness of Q-LRT for moderately skewed latent exogenous variables.