Application of Bayesian Networks to Infer Causality for Structural Equation Modeling

[[abstract]]In statistics, general statistical analysis stresses on the relevance between the variables. But it is unable to express the causality between the variables. Take the height and body weight as example. Height higher, his body weight is also heavier. It is connected between the variables. As a matter of fact, however, does the height affect the body weight or the body weight affects the height? If the change of the body weight would not affect the height, it is not the cause that the weight can be affected by the height. There are lots of the variables in real life or in the researches of social science. The causality is not as obvious as the example that we have mentioned. On variable, which one is a cause? Which one is a result? Therefore, it is always an issue that the researchers like to find out in the statistic. By means of the constructions of specialists and the mode of learning, the Bayesian networks play the important roles in the causality and the diagnoses, and they are used generally in the researches of medicine and the data survey, too. However, the educts of the causality come from the theories, the observations of a long time and the data of the laboratory. In the meantime, the Bayesian networks cannot control the latent variables so far. It must be constructed by specialists’ knowledge. These results in the research are too late to the social sciences. Therefore, it is very important to find out the latent variables and the causality that could be existed possibly. In order to build a measurement model that matches the structural equation model, these variables will be analyzed individual and observed then to be divide into the same latent variables under the d-separation and partial correlation condition. By combining PC2 algorithm and conditional probability and after the Bayesian Networks, the structural equation model will be built base on Bayesian Network