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Statistical analysis of nonlinear structural equation models with continuous and polytomous data
Author(s) -
Lee SikYum,
Zhu HongTu
Publication year - 2000
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 - 10.1348/000711000159303
Subject(s) - polytomous rasch model , gibbs sampling , structural equation modeling , outlier , markov chain monte carlo , bayesian probability , latent variable , mathematics , markov chain , nonlinear system , goodness of fit , metropolis–hastings algorithm , monte carlo method , computer science , statistics , econometrics , item response theory , physics , quantum mechanics , psychometrics
A general nonlinear structural equation model with mixed continuous and polytomous variables is analysed. A Bayesian approach is proposed to estimate simultaneously the thresholds, the structural parameters and the latent variables. To solve the computational difficulties involved in the posterior analysis, a hybrid Markov chain Monte Carlo method that combines the Gibbs sampler and the Metropolis‐Hasting algorithm is implemented to produce the Bayesian solution. Statistical inferences, which involve estimation of parameters and their standard errors, residuals and outliers analyses, and goodness‐of‐fit statistics for testing the posited model, are discussed. The proposed procedure is illustrated by a simulation study and a real example.