Effect Analysis Using Nonlinear Structural Equation Mixture Modeling

Abstract

In this article, we present an approach for comprehensive analysis of the effectiveness of interventions based on nonlinear structural equation mixture models (NSEMM). We provide definitions of average and conditional effects and show how they can be computed. We extend the traditional moderated regression approach to include latent continous and discrete (mixture) variables as well as their higher order interactions, quadratic or more general nonlinear relationships. This new approach can be considered a combination of the recently proposed EffectLiteR approach and the NSEMM approach. A key advantage of this synthesis is that it gives applied researchers the opportunity to gain greater insight into the effectiveness of the intervention. For example, it makes it possible to consider structural equation models for situations where the treatment is noneffective for extreme values of a latent covariate but is effective for medium values, as we illustrate using an example from the educational sciences.