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Bayesian analysis of two‐level nonlinear structural equation models with continuous and polytomous data
Author(s) -
Song XinYuan,
Lee SikYum
Publication year - 2004
Publication title -
british journal of mathematical and statistical psychology
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.157
H-Index - 51
eISSN - 2044-8317
pISSN - 0007-1102
DOI - 10.1348/000711004849259
Subject(s) - polytomous rasch model , gibbs sampling , structural equation modeling , markov chain monte carlo , bayesian probability , metropolis–hastings algorithm , bayes factor , mathematics , nonlinear system , bayes' theorem , statistics , computer science , item response theory , physics , quantum mechanics , psychometrics
Two‐level structural equation models with mixed continuous and polytomous data and nonlinear structural equations at both the between‐groups and within‐groups levels are important but difficult to deal with. A Bayesian approach is developed for analysing this kind of model. A Markov chain Monte Carlo procedure based on the Gibbs sampler and the Metropolis‐Hasting algorithm is proposed for producing joint Bayesian estimates of the thresholds, structural parameters and latent variables at both levels. Standard errors and highest posterior density intervals are also computed. A procedure for computing Bayes factor, based on the key idea of path sampling, is established for model comparison.