Quasi Maximum Likelihood Estimation of Structural Equation Models With Multiple Interaction and Quadratic Effects

The development of statistically efficient and computationally practicable estimation methods for the analysis of structural equation models with multiple nonlinear effects has been called for by substantive researchers in psychology, marketing research, and sociology. But the development of efficient methods is complicated by the fact that a nonlinear model structure implies specifically nonnormal multivariate distributions for the indicator variables. In this paper, nonlinear structural equation models with quadratic forms are introduced and a new QuasiMaximum Likelihood method for simultaneous estimation of model parameters is developed with the focus on statistical efficiency and computational practicability. The Quasi-ML method is based on an approximation of the nonnormal density function of the joint indicator vector by a product of a normal and a conditionally normal density. The results of Monte-Carlo studies for the new Quasi-ML method indicate that the parameter estimation is almost as efficient as ML estimation, whereas ML estimation is only computationally practical for elementary models. Also, the Quasi-ML method outperforms other currently available methods with respect to efficiency. It is demonstrated in a Monte-Carlo study that the Quasi-ML method permits computationally feasible and very efficient analysis of models with multiple latent nonlinear effects. Finally, the applicability of the Quasi-ML method is illustrated by an empirical example of an aging study in psychology.