Confidence Intervals for a Semiparametric Approach to Modeling Nonlinear Relations among Latent Variables

Abstract

Compared to parametric models, nonparametric and semiparametric approaches to modeling nonlinearity between latent variables have the advantage of recovering global relationships of unknown functional form. Bauer (2005) proposed an indirect application of finite mixtures of structural equation models where latent components are estimated in the service of more flexibly recovering characteristics of the latent aggregate regression function. This article develops and evaluates delta method and parametric bootstrap approaches for obtaining approximate confidence intervals for Bauer's semiparametric approach to modeling latent nonlinear functions. Coverage rates of these approximate point-wise confidence intervals or nonsimultaneous confidence bands are evaluated by Monte Carlo and recommendations for their use are suggested.

Keywords:

• confidence interval
• delta method
• parametric bootstrap
• structural equation mixture model
• nonlinear

Notes

¹In the context of no model error, bootstrapped nonsimultaneous confidence bands were found to have approximate coverage rates of 95% that improved with increasing sample size.