Bayesian empirical likelihood estimation of quantile structural equation models

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• 作者：Yanqing Zhang ; Niansheng Tang
• 关键词：Bayesian empirical likelihood ; estimating equations ; latent variable models ; MCMC algorithm ; quantile regression ; structural equation models
• 刊名：Journal of Systems Science and Complexity
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：30
• 期：1
• 页码：122-138
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Systems Theory, Control; Operation Research/Decision Theory; Mathematics of Computing; Complex Systems; Statistics, general;
• 出版者：Academy of Mathematics and Systems Science, Chinese Academy of Sciences
• ISSN：1559-7067
• 卷排序：30

文摘

Structural equation model (SEM) is a multivariate analysis tool that has been widely applied to many fields such as biomedical and social sciences. In the traditional SEM, it is often assumed that random errors and explanatory latent variables follow the normal distribution, and the effect of explanatory latent variables on outcomes can be formulated by a mean regression-type structural equation. But this SEM may be inappropriate in some cases where random errors or latent variables are highly nonnormal. The authors develop a new SEM, called as quantile SEM (QSEM), by allowing for a quantile regression-type structural equation and without distribution assumption of random errors and latent variables. A Bayesian empirical likelihood (BEL) method is developed to simultaneously estimate parameters and latent variables based on the estimating equation method. A hybrid algorithm combining the Gibbs sampler and Metropolis-Hastings algorithm is presented to sample observations required for statistical inference. Latent variables are imputed by the estimated density function and the linear interpolation method. A simulation study and an example are presented to investigate the performance of the proposed methodologies.