A Marginal Maximum Likelihood Approach for Extended Quadratic Structural Equation Modeling with Ordinal Data

The literature on non-linear structural equation modeling is plentiful. Despite this fact, few studies consider interactions between exogenous and endogenous latent variables. Further, it is well known that treating ordinal data as continuous produces bias, a problem which is enhanced when non-linear relationships between latent variables are incorporated. A marginal maximum likelihood-based approach is proposed in order to fit a non-linear structural equation model including interactions between exogenous and endogenous latent variables in the presence of ordinal data. In this approach, the exact gradient of the approximated observed log-likelihood is calculated in order to attain the approximated maximum likelihood estimator. A simulation study shows that the proposed method provides estimates with low bias and accurate coverage probabilities.