Bayesian Analysis of Nonlinear Structural Equation Models with Nonignorable Missing Data
Bayesian Analysis of Nonlinear Structural Equation Models with Nonignorable Missing Data
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DOI：
10.1007/s11336-006-1177-1
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发表时间：
2006-08
期刊：
影响因子：
3
通讯作者：
Sik-Yum Lee
中科院分区：
文献类型：
--
作者：
Sik-Yum Lee
提出了一种分析具有不可忽略缺失数据的非线性结构方程模型的贝叶斯方法。不可忽略的缺失机制由逻辑回归模型指定。采用Gibbs采样器和Metropolis-Hastings算法相结合的混合算法，对不可忽略缺失模型中的结构参数、潜在变量、参数及其标准误差估计进行联合贝叶斯估计。引入拟合优度统计量来评估假定的非线性结构方程模型的可信性，并通过路径抽样建立了计算模型比较的贝叶斯因子的程序。通过仿真研究比较了不同缺失数据模型和不同先验输入得到的结果。特别是，在存在不可忽略缺失数据的情况下，采用不可忽略缺失数据模型的方法得到的结果明显优于随机缺失假设下的结果。最后给出一个实例来说明贝叶斯方法的新发展。
A Bayesian approach is developed for analyzing nonlinear structural equation models with nonignorable missing data. The nonignorable missingness mechanism is specified by a logistic regression model. A hybrid algorithm that combines the Gibbs sampler and the Metropolis–Hastings algorithm is used to produce the joint Bayesian estimates of structural parameters, latent variables, parameters in the nonignorable missing model, as well as their standard errors estimates. A goodness-of-fit statistic for assessing the plausibility of the posited nonlinear structural equation model is introduced, and a procedure for computing the Bayes factor for model comparison is developed via path sampling. Results obtained with respect to different missing data models, and different prior inputs are compared via simulation studies. In particular, it is shown that in the presence of nonignorable missing data, results obtained by the proposed method with a nonignorable missing data model are significantly better than those that are obtained under the missing at random assumption. A real example is presented to illustrate the newly developed Bayesian methodologies.