Department of Statistics, Sun Yat-Sen University, Guangzhou, People's Republic of China.
Br J Math Stat Psychol. 2010 Nov;63(Pt 3):491-508. doi: 10.1348/000711009X475187. Epub 2009 Dec 23.
Structural equation models (SEMs) have become widely used to determine the interrelationships between latent and observed variables in social, psychological, and behavioural sciences. As heterogeneous data are very common in practical research in these fields, the analysis of mixture models has received a lot of attention in the literature. An important issue in the analysis of mixture SEMs is the presence of missing data, in particular of data missing with a non-ignorable mechanism. However, only a limited amount of work has been done in analysing mixture SEMs with non-ignorable missing data. The main objective of this paper is to develop a Bayesian approach for analysing mixture SEMs with an unknown number of components and non-ignorable missing data. A simulation study shows that Bayesian estimates obtained by the proposed Markov chain Monte Carlo methods are accurate and the Bayes factor computed via a path sampling procedure is useful for identifying the correct number of components, selecting an appropriate missingness mechanism, and investigating various effects of latent variables in the mixture SEMs. A real data set on a study of job satisfaction is used to demonstrate the methodology.
结构方程模型（SEMs）已广泛应用于社会、心理和行为科学中，用于确定潜在变量和观测变量之间的相互关系。由于在这些领域的实际研究中，异质数据非常常见，因此混合模型的分析在文献中受到了很多关注。在混合 SEM 分析中，一个重要的问题是存在缺失数据，特别是存在不可忽略机制的数据缺失。然而，对于不可忽略缺失数据的混合 SEM 分析，所做的工作非常有限。本文的主要目的是开发一种贝叶斯方法，用于分析具有未知组件数量和不可忽略缺失数据的混合 SEM。模拟研究表明，通过所提出的马尔可夫链蒙特卡罗方法获得的贝叶斯估计是准确的，通过路径抽样程序计算的贝叶斯因子对于识别正确的组件数量、选择适当的缺失机制以及研究混合 SEM 中潜在变量的各种效应非常有用。使用一个关于工作满意度的实际数据集来说明该方法。
