Model Specification for Latent Interactive and Quadratic Effects in Matrix Form

Abstract

Estimating nonlinear effects between constructs is an important concern in the social sciences. In empirical studies, researchers often focus more on mediated moderation or moderated mediation as opposed to moderation by itself. This article generalizes the constrained approach with noncentered observed variables to a matrix form that encompasses the latent nonlinear effects of not only exogenous variables, but also endogenous variables or a combination of the two. Constraints are specified in matrix form and the matrices involved in model specification are partitioned to fit into the nonlinear model framework. The usage and validity of the procedure is demonstrated with a simulated data set example using the Mx program.