Department of Statistics, Sun Yat-sen University, Guangzhou, China.
Stat Med. 2010 Aug 15;29(18):1861-74. doi: 10.1002/sim.3915.
In behavioral, biomedical, and social-psychological sciences, it is common to encounter latent variables and heterogeneous data. Mixture structural equation models (SEMs) are very useful methods to analyze these kinds of data. Moreover, the presence of missing data, including both missing responses and missing covariates, is an important issue in practical research. However, limited work has been done on the analysis of mixture SEMs with non-ignorable missing responses and covariates. The main objective of this paper is to develop a Bayesian approach for analyzing mixture SEMs with an unknown number of components, in which a multinomial logit model is introduced to assess the influence of some covariates on the component probability. Results of our simulation study show that the Bayesian estimates obtained by the proposed method are accurate, and the model selection procedure via a modified DIC is useful in identifying the correct number of components and in selecting an appropriate missing mechanism in the proposed mixture SEMs. A real data set related to a longitudinal study of polydrug use is employed to illustrate the methodology.
在行为、生物医学和社会心理学科学中，遇到潜在变量和异质数据是很常见的。混合结构方程模型（SEM）是分析这类数据的非常有用的方法。此外，包括缺失响应和缺失协变量在内的缺失数据的存在是实际研究中的一个重要问题。然而，对于具有不可忽略缺失响应和协变量的混合 SEM 的分析，所做的工作有限。本文的主要目的是开发一种用于分析具有未知成分数量的混合 SEM 的贝叶斯方法，其中引入了多项逻辑回归模型来评估一些协变量对成分概率的影响。我们的模拟研究结果表明，所提出方法获得的贝叶斯估计是准确的，并且通过修改后的 DIC 进行的模型选择过程有助于识别正确的成分数量，并在提出的混合 SEM 中选择适当的缺失机制。一个与多药使用纵向研究相关的真实数据集被用来说明该方法。
