Seemingly Unrelated Regression Model And Its Applications In Medicine

Seemingly unrelated regression model are multiple regression equation systems which can be abbreviate as SUR. It differs from the multivariate regressions model in that it allows difference explanatory variables between difference equations. This feature let great flexibility to statistics modeling. At the same time, while takes the jointness information of the equations into account, the parameter estimators of this model are more efficient, at some general situation, than the traditional counterparts that are estimate equation by equation. In the field of medical research, due to the complexity of health and disease phenomenon, different health or illness situations account for different factors, and moreover, the same health or illness situations in different populations which have distinct character also due to different factors. In addition, being affected by some common known or unknown factors, different health or illness measurement values have somewhat correlations, large or small. As a results, seemingly unrelated regression model have important practical value in the field of medical research. In this paper we have attempted to discuss systematically the modeling and estimation method of seemingly unrelated regression, accompany with the analysis of several medical research examples. All the contents we involve here are as follow: first we introduce the seemingly unrelated linear regression model, and then the seemingly unrelated nonlinear regression model, and following the generalized seemingly unrelated regressing, at last, we extend the context to the nonparametric and semiparametric seemingly unrelated regression. For the examples, we focus our attentions to the problem of semiparametric seemingly unrelated regression modeling for the adverse effects of air pollution on human health based on multiple time series data.In the first chapter we begin our discussion of the basic model structure of SUR and tell the relationship between SUR and multiple linear regression model, and between SUR and multivariate linear regression model. We discuss various estimate methods of this model such as two-step feasible generalized least squares estimator,iterative generalized least squares estimator and maximum likelihood estimator and their large sample properties. We figure out that when the variance-covariance matrix of model disturbances vectors is diagonal, the SUR estimator isn't superior to the OLS estimator. Thus we should make an inference at first when we involve SUR modeling. We introduce some goodness of fit statistics and illustrate how they are constructed. The linear restrict inference of parameters in multiple equations model has additional contents compare with its counterpart in single equation model, for the former we can test the equality of the coefficient vectors of multiple equation, while the latter only focus on the significance testing of some coefficient element in the same equation. We discuss the statistics using to implement the inference of coefficients in SUR context. When the...