Bayesian Elastic-Net and Fused Lasso for Semiparametric Structural Equation Models

SUMMARY: Structural equation models are well-developed statistical tools for multivariate data with latent variables. Recently, much attention has been given to developing structural equation models that account for nonlinear relationships between the endogenous latent variables, the covariates, and the exogenous latent variables. [Guo et al. (2012)], developed a semiparametric structural equation model where the nonlinear functional relationships are approximated using basis expansions and used Bayesian Lasso for simulations analysis and model selection. In this paper we consider semiparametric structural equation models when cubic splines are used for the basis expansion. Cubic splines are known to induce correlations. Bayesian fused Lasso and Bayesian elastic-net are used to account for correlations in both the covariates and basis expansions. We illustrate the usefulness of our proposed methods through a simulation study. The semiparametric structural equation models based on Bayesian fused Lasso and Bayesian elastic-net outperform the Bayesian Lasso model.