A New RegreSsion Method:Screening Stepwise RegreSsion

Regression analysis method is a statistical method which quantifies the relationship between variables. Linear regression analysis has a longer applied history than most other statistical methods. For most applying assumptions could be satisfied, its statistical inference is valid on the whole. The results from regression analyses are reliable on most cases. Besides, the procedure of linear regression analysis is relative simple and can run on most statistical software. Most users can easily handle the method, so it has been widely used in many fields. However, the relationship between variable are rarely linear, most accurate functions between causal traits and effect ones are nonlinear such as power response and interaction effect in many areas of Science. Otherwise, multicollinearity between variables is common in multivariate linear regression. In this case, it can not get the parameters with least squared method accurately. It may results that the number of the observation is larger than the times of test in that the limits of funds, test condition and so on in Scientific research, specially the medicine experiment and the commercial test. This case could be noted as oversaturated model problem. It has proposed several methods for different kinds of multivariate linear regression problems.The thesis introduced some common methods for dealing with multicollinearity and oversaturated model and analyzed the characteristics of them. The concept of multicollinearity has proposed for a long time and it has produced many methods for this problem. The common methods have been showed as ridge regression, principal components regression, stepwise regression, partial least square regression and so on. In general, there are two ways to handle such oversaturated regreSsion models:variable selection and shrinkage estimation. Variable selection involving optimal subset method and stepwise regression method is an important technique for dimension reduction. The selection criterion is one of the key issues in variable selection. In the shrinkage analysis we include all variables but shrink the estimates toward zero. The Screen stepwise regression, a new regreSsion analysis method by Shiliang Gu, et al. in2006, belongs to the variable selection. This method has the power of traditional stepwise regression and also could be applied to handle multiconllinearity and oversaturated regression model. It has a accurate estimation of parameter and could be understood easily. However, we should have to optimization to the model for raising the operation efficiency because operation time is slightly long.This study focused on the Screen stepwise regression method in order to solve different kinds of problems existing in the multivariate linear regression analysis, obtain optimized parameter estimation, promoted extensive application of multivariate linear regression analysis. The new method adopts deleting and selecting one by one variable under basic regression, and Screening for those deleted variables in several rounds, getting the optimal regression equation containing the main effects. The new Matlab program was compiled based on the improved algorithm, and various kinds of models and examples were used to demonstrate its function.The simulated study analyzed the different complex degree of QTL effects, with improved Screen stepwise regression method. The comparison between this method and other four common algorithms (E-bayes, PENAL, SSVS, and Stepwise) indicated that the new algorithm has the strong examination ability and the confidence level, especially when there are more variables, effects are more complex and error is higher.