Statistical analysis of nonlinear structural equation models with continuous and polytomous data.
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.
Lee
S Y
SY
Department of Statistics, Chinese University of Hong Kong, Shatin, N.T., Hong Kong. sylee@sparc2.sta.cuhk.edu.hk
Zhu
H T
HT
D006801:Humans; D008960:Models, Psychological; D017711:Nonlinear Dynamics