Bayesian Analysis of Covariance Structure Model to Identify Causal Relationships

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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.