13. Transformation Structural Equation Models

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

Published Online: 18 JUL 2012

DOI: 10.1002/9781118358887.ch13

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) Transformation Structural Equation Models, 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.ch13

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:

  • Markov chain Monte Carlo (MCMC) techniques;
  • nonparametric transformations;
  • transformation structural equation model (SEM)

Summary

This chapter presents a transformation structural equation model (SEM) for handling various kinds of highly nonnormal data and stabilizing error variances simultaneously. The model has the following features: (i) nonparametric transformations are applied to response variables so that the resulting model can justify the model assumptions in SEMs; and (ii) fixed covariates are incorporated into both the measurement and structural equations to help establish a better model. The chapter presents a simulation study to examine the empirical performance of the transformation SEM. The chapter applies a nonparametric transformation model to analyze a data set involving highly nonnormal variables. To solve the difficulties encountered in the analysis, a modified constrained Bayesian P-splines approach incorporating powerful Markov chain Monte Carlo (MCMC) techniques is employed.

Controlled Vocabulary Terms

Markov chain Monte Carlo estimation; non-parametric Bayesian methods