Estimating and Visualizing Nonlinear Relations Among Latent Variables: A Semiparametric Approach

The graphical presentation of any scientific finding enhances its description, interpretation, and evaluation. Research involving latent variables is no exception, especially when potential nonlinear effects are suspect. This article has multiple aims. First, it provides a nontechnical overview of a semiparametric approach to modeling nonlinear relationships among latent variables using mixtures of linear structural equations. Second, it provides several examples showing how the method works and how it is implemented and interpreted in practical applications. In particular, this article examines the potentially nonlinear relationships between positive and negative affect and cognitive processing. Third, a recommended display format for illustrating latent bivariate relationships is demonstrated. Finally, the article describes an R package and an online utility that generate these displays automatically.