| ,Adaptive regression analysis(Ⅰ)——the construction and solution of the regression model[J].SICHUAN MENTAL HEALTH,2019,32(2):97-100 |
| Adaptive regression analysis(Ⅰ)——the construction and solution of the regression model |
DOI：10.11886/j.issn.1007-3256.2019.02.001 |
| English keywords:Adaptability Spline Regression analysis Basis function Node Generalized cross validation Lack of fit |
| Fund projects:国家高技术研究发展计划课题资助(2015AA020102) |
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| This paper was to introduce the construction and solution method of the adaptive regression models. As we all know, when the number of independent variables was large, the dimensional disaster would occur. At this time, statisticians tended to use a non - parametric regression model instead of a parametric regression model. However, when the number of independent variables was large to a certain extent, the usual non - parametric regression model was also overwhelmed, so the adaptive regression spline algorithm came into being. This method consisted of the following statistical techniques: ①the special variable transformations were used; ②the overfitted regression model was constructed based on the approach of forward selection, and then the regression model was" pruned" based on the approach of backward selection; ③based on the basic idea of " reducing the number of combinations of B, V and t in each step of the forward selection" , a fast algorithm was implemented; ④using " GCV" and " LOF" as the boundary value of" goodness of fit" , the fitted effect of the established regression model was evaluated. The method mentioned before provided a new way for the regression modeling of the complex data structures. |
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