| 胡良平.提高回归模型拟合优度的策略（Ⅲ）———校正均值变换与其他变量变换[J].四川精神卫生杂志,2019,32(1):16-20.,Strategy of improving the goodness of fit of the regression model(Ⅲ) ——the transformation of the corrected arithmetic mean and the other variable transformations[J].SICHUAN MENTAL HEALTH,2019,32(1):16-20 |
| 提高回归模型拟合优度的策略（Ⅲ）———校正均值变换与其他变量变换 |
| Strategy of improving the goodness of fit of the regression model(Ⅲ) ——the transformation of the corrected arithmetic mean and the other variable transformations |
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| DOI：10.11886/j.issn.1007-3256.2019.01.003 |
| 中文关键词: 变量变换 校正均值变换 Logistic变换 派生变量 拟合优度 |
| 英文关键词:Variable transformation Transformation of the corrected mean Logistic transformation Derived variable Goodness of fit |
| 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】 本文目的是介绍第三种提高回归模型拟合优度的策略，即校正均值变换与其他变量变换。 具体方法包括以下几个方面：①对多值名义自变量采取“校正均值变换”；②对定量自变量引入派生变量，包括“对数变换”“平方根变换”“指数变换”“平方变换”“立方变换”和“交叉乘积变换”的结果；③对定量因变量分别采取“对数变换”“平方根变换”“指数变换”“倒数变换”和“ Logistic 变换”；④构建回归模型时，在假定“ 包含截距项”与“不含截距项”的条件下，分别采取“前进法”“后退法”和“逐步法”筛选自变量。得到了如下结论：①对定量因变量和自变量不做变量变换时，回归模型的拟合优度非常低；②根据资料所具备的条件，对定量因变量采取不同的变量变换方法，其回归模型的拟合优度是不同的；③对多值名义自变量进行“校正均值变换”是合理的，且有助于提高回归模型拟合优度；④对定量自变量引入派生变量是非常有价值的；⑤假定回归模型中不含截距项有助于提高回归模型的拟合优度。 |
| 英文摘要: |
| The purpose of this paper was to introduce the third strategy of improving the goodness of fit of the regression model, the transformation of the corrected mean and the other variable transformations. The concrete approaches were as follows: ①“ The transformation of the corrected mean” was adopted to the multi - value nominal independent variable. ②The derived variables were introduced to the quantitative independent variables, such as the results of “ logarithmic transformation ” “ square root transformation” “ exponential transformation” “ square transformation” “ cubic transformation” and “ cross product terms transformation” . ③“ Logarithmic transformation” “ square root transformation” “ exponential transformation” “ reciprocal transformation” and “ Logistic transformation” were adopted to the quantitative dependent variable, respectively. ④ During building the regression models, the “ forward selection” “ backward selection” and “ stepwise selection ” were used for screening the independent variables under the conditions both with the intercept term and without it. The several conclusions were achieved as below: ①The goodness of fit of the regression models was very poor when no transformations were applied to the quantitative dependent variable and independent variables. ②The distinct results of the goodness of fit of the regression models could be gotten by using the distinct transformations to the
quantitative dependent variable in accordance with the data conditions. ③ It was rational to transform the multi - value nominal independent variable by using the corrected mean transformation, which was conducive to improving the goodness of fit of the regression models. ④It was wonderful to introduce the derived variables to the quantitative independent variables in fitting the regression models. ⑤It was helpful to improve the goodness of fit of the regression models by getting rid of the intercept term. |
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