Modeling Nonlinear Structural Equation Models: A Comparison of the Two-Stage Generalized Additive Model and the Finite Mixture Structural Equation Model

• In Event: Measurement and Modeling Issues in Structural Equation Modeling

Abstract

Researchers have developed methods for fitting nonlinear structural equation models (SEM). Most have focused on interactions between two exogenous latent variables, or quadratic relationships between exogenous and endogenous variables. These approaches require prespecification of the nonlinearity, and are limited to fairly simple nonlinear relationships. Other work has been done using mixture SEMs (SEMM) in an attempt to fit more complex nonlinear relationships. The current study expands upon this work by introducing the 2 stage generalized additive model (2SGAM) for fitting regression splines in the context of structural equation models, and comparing its performance with SEMM in a simulation study. Results demonstrate that 2SGAM is effective in fitting a variety of nonlinear latent variable relationships. Implications of these results are discussed.

Author

• William Holmes Finch, Ball State University