12. Structural Equation Models with Nonparametric Structural Equations

  1. Xin-Yuan Song and
  2. Sik-Yum Lee

Published Online: 18 JUL 2012

DOI: 10.1002/9781118358887.ch12

Basic and Advanced Bayesian Structural Equation Modeling: With Applications in the Medical and Behavioral Sciences

Basic and Advanced Bayesian Structural Equation Modeling: With Applications in the Medical and Behavioral Sciences

How to Cite

Song, X.-Y. and Lee, S.-Y. (2012) Structural Equation Models with Nonparametric Structural Equations, in Basic and Advanced Bayesian Structural Equation Modeling: With Applications in the Medical and Behavioral Sciences, John Wiley & Sons, Ltd, Chichester, UK. doi: 10.1002/9781118358887.ch12

Author Information

  1. Department of Statistics, The Chinese University of Hong Kong

Publication History

  1. Published Online: 18 JUL 2012
  2. Published Print: 24 AUG 2012

Book Series:

  1. Wiley Series in Probability and Statistics

Book Series Editors:

  1. Walter A. Shewhart and
  2. Samuel S. Wilks

ISBN Information

Print ISBN: 9780470669525

Online ISBN: 9781118358887

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Keywords:

  • Bayesian P-splines approach;
  • covariates;
  • latent variables;
  • nonparametric structural equation

Summary

This chapter presents SEM in which a nonparametric structural equation is used to model the functional relationships among latent variables and covariates. The Bayesian approach, together with a Bayesian analogue of P-splines estimates the nonparametric functions and unknown parameters in the model. To extend the applicability of SEMs, the chapter introduces a nonparametric SEM, in which the important structural equation is formulated via unspecified smooth functions of latent variables, along with covariates if applicable. The Bayesian P-splines approach, together with a MCMC algorithm is introduced to estimate smooth functions, unknown parameters, and latent variables in the model. The chapter focuses on the strategies to statistically assess whether the nonparametric approach is necessary and whether it offers meaningful benefits over its simpler parametric counterparts, and to compare the performance. It presents nonparametric SEMs with continuous and/or various types of discrete data to assess the functional relationships between latent and observed variables.

Controlled Vocabulary Terms

Bayesian statistics; covariate; latent class model; multivariate adaptive regression splines; non-parametric methods