Bayesian Analysis of Covariance Structure Model to Identify Causal Relationships

导出了协方差结构模型中各相关参数的联合后验分布。然后，基于这些条件分布，我们使用Gibbs Sampler数值推导出感兴趣参数的边际分布。该方法成功地应用于模拟数据和真实的数据，并提出了新的贝叶斯准则来选择最佳的协方差结构模型。该标准是每个模型为真的后验概率的近似值。使用模拟数据，我们比较了这个新的标准与已建立的信息准则和拟合优度指标的性能。结果表明，新的标准成功地识别出真正的模型比任何其他标准。

The joint posterior distributions for all relevant parameters in covariance structure model are derived. Further, full conditional distributions for each parameter set with the rest of parameter given are derived Then, based on these conditional distributions, we used Gibbs Sampler to derive numerically the marginal distributions for interested parameters.. This procedure was applied successfully to both simulated data and real data.We also proposed the new Bayesian criterion to choose the best covariance structure model. This criterion is the approximation of the posterior probability that each model is true. Using simulated data, we compared the performance of this new criterion with the established information criteria and goodness of fit indexes. The results showed that the new criterion succeeded in identifying the true model better than any other criteria.