Lee Sik-Yum, Tang Nian-Sheng
Department of Statistics, The Chinese University of Hong Kong, Shatin.
Br J Math Stat Psychol. 2006 May;59(Pt 1):151-72. doi: 10.1348/000711005X81403.
Structural equation models are very popular for studying relationships among observed and latent variables. However, the existing theory and computer packages are developed mainly under the assumption of normality, and hence cannot be satisfactorily applied to non-normal and ordered categorical data that are common in behavioural, social and psychological research. In this paper, we develop a Bayesian approach to the analysis of structural equation models in which the manifest variables are ordered categorical and/or from an exponential family. In this framework, models with a mixture of binomial, ordered categorical and normal variables can be analysed. Bayesian estimates of the unknown parameters are obtained by a computational procedure that combines the Gibbs sampler and the Metropolis-Hastings algorithm. Some goodness-of-fit statistics are proposed to evaluate the fit of the posited model. The methodology is illustrated by results obtained from a simulation study and analysis of a real data set about non-adherence of hypertension patients in a medical treatment scheme.
结构方程模型在研究观测变量和潜在变量之间的关系方面非常受欢迎。然而，现有的理论和计算机软件包主要是在正态性假设下开发的，因此不能令人满意地应用于行为、社会和心理研究中常见的非正态和有序分类数据。在本文中，我们开发了一种贝叶斯方法来分析结构方程模型，其中显变量是有序分类变量和/或来自指数族。在此框架下，可以分析包含二项式、有序分类变量和正态变量混合的模型。通过结合吉布斯采样器和梅特罗波利斯-黑斯廷斯算法的计算程序获得未知参数的贝叶斯估计。提出了一些拟合优度统计量来评估所假定模型的拟合度。通过模拟研究的结果以及对一个关于高血压患者在医疗治疗方案中不依从性的真实数据集的分析来说明该方法。
