| 胡良平.变量变换回归分析（Ⅰ）———拟合含间断点资料的方法[J].四川精神卫生杂志,2019,32(3):193-196.,Regression analysis based on the variable transformation(Ⅰ)——the approach of fitting the data with discontinuous points[J].SICHUAN MENTAL HEALTH,2019,32(3):193-196 |
| 变量变换回归分析（Ⅰ）———拟合含间断点资料的方法 |
| Regression analysis based on the variable transformation(Ⅰ)——the approach of fitting the data with discontinuous points |
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| DOI：10.11886/j.issn.1007-3256.2019.03.001 |
| 中文关键词: 节点 样条 变量变换 曲线拟合 回归分析 |
| 英文关键词:Knot Spline Variable transformation Curve fitting Regression analysis |
| 基金项目:国家高技术研究发展计划课题资助(2015AA020102) |
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| 中文摘要: |
| 【摘要】 本文目的是介绍一种能很好地拟合具有间断点资料的方法。当资料中具有明确的间断点或整个资料包含多段不同变化趋势的曲线类型时，为了提高曲线回归模型对资料的拟合优度，需要充分发挥“节点”的作用。可基于两种不同视角来利用“节点”：其一，人为设定不同数目的节点，利用样条变换方法拟合分段多项式曲线；其二，在客观存在的节点上，求曲线的一阶乃至四阶导数，并据此构建曲线回归模型。得到的结论是：后者的拟合效果优于前者。 |
| 英文摘要: |
| The paper introduced one good approach of fitting the data with discontinuous points. In order to improve the goodness of curve fitting, it was necessary that the knots should play a role when the following situations appeared, such as the data with definite discontinuous points and /or the data with several types of curvilinear trend in the whole interval of the independent variable.From two perspectives, the knots could be deal with the two approaches as follows. First, artificial setting various number of the knots and then fitting the piece - wise polynomial curve by using the spline transformation. Second, the first derivative, the second derivative,until the fourth derivative was computed on the objectively existent knots, based on the previous results, the curve regression model was structured. The conclusion proved that the fitted effect of the latter approach provided better fitting effect than the former. |
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