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 exp...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.展开更多
基金国家自然科学基金(the National Natural Science Foundation of China under Grant No.60573096) 山东理工大学科研基金(the ScienceFoundation of Shandong University of Technology under Grant No.2006KJM15) 。
基金supported by the National Natural Science Foundation of China under Grant No.11165016
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.
