) 1中山大学心理学系, 广州 510006
2浙江大学心理与行为科学系, 杭州 310028
收稿日期:2019-12-13出版日期:2020-10-15发布日期:2020-08-24通讯作者:潘俊豪E-mail:panjunh@mail.sysu.edu.cn基金资助:* 国家自然科学基金项目(31871128);教育部人文社会科学研究规划基金项目(18YJA190013)Lasso regression: From explanation to prediction
ZHANG Lijin1, WEI Xiayan2, LU Jiaqi2, PAN Junhao1() 1Department of Psychology, Sun Yat-sen University, Guangzhou 510006, China
2Department of Psychology and Behavioral Sciences, Zhejiang University, Hangzhou 310028, China
Received:2019-12-13Online:2020-10-15Published:2020-08-24Contact:PAN Junhao E-mail:panjunh@mail.sysu.edu.cn摘要/Abstract
摘要： 传统的最小二乘回归法关注于对当前数据集的准确估计, 容易导致模型的过拟合, 影响模型结论的可重复性。随着方法学领域的发展, 涌现出的新兴统计工具可以弥补传统方法的局限, 从过度关注回归系数值的解释转向提升研究结果的预测能力也愈加成为心理学领域重要的发展趋势。Lasso方法通过在模型估计中引入惩罚项的方式, 可以获得更高的预测准确度和模型概化能力, 同时也可以有效地处理过拟合和多重共线性问题, 有助于心理学理论的构建和完善。
图/表 6
图1偏差-方差权衡
图1偏差-方差权衡
图1变量间相关图 注：红色系代表负相关, 蓝色系代表正相关, 颜色越深代表相关值越大。
图1变量间相关图 注：红色系代表负相关, 蓝色系代表正相关, 颜色越深代表相关值越大。
图2十重交叉验证结果 注：图中两条竖线分别代表最小化MSE的λ值和λ + 1se值
图2十重交叉验证结果 注：图中两条竖线分别代表最小化MSE的λ值和λ + 1se值
图3惩罚项对系数的压缩结果
图3惩罚项对系数的压缩结果表1Lasso、OLS、Relaxed Lasso回归结果
| 系数估计值(p值) | |||
|---|---|---|---|
| 预测变量 | OLS | Lasso | Relaxed Lasso |
| age | -0.206(0.009)** | -(0.072) | - |
| famrel | 0.36(0.001)** | -(0.699) | - |
| freetime | 0.058(0.57) | -(0.913) | - |
| gout | -0.014(0.891) | -(0.981) | - |
| dalc | -0.108(0.448) | -(0.646) | - |
| walc | 0.17(0.105) | -(0.294) | - |
| health | 0.046(0.509) | -(0.899) | - |
| absences | 0.042(0.001)** | -(0.089) | - |
| G1 | 0.164(0.003)** | 0.057(0.005)** | 0.153(0.007)** |
| G2 | 0.977(<0.001)*** | 0.903(<0.001)*** | 0.987(<0.001)*** |
| R2 | 0.835 | - | 0.822 |
| adjusted R2 | 0.831 | - | 0.821 |
| Mean Square Error | 3.446 | - | 3.723 |
表1Lasso、OLS、Relaxed Lasso回归结果
| 系数估计值(p值) | |||
|---|---|---|---|
| 预测变量 | OLS | Lasso | Relaxed Lasso |
| age | -0.206(0.009)** | -(0.072) | - |
| famrel | 0.36(0.001)** | -(0.699) | - |
| freetime | 0.058(0.57) | -(0.913) | - |
| gout | -0.014(0.891) | -(0.981) | - |
| dalc | -0.108(0.448) | -(0.646) | - |
| walc | 0.17(0.105) | -(0.294) | - |
| health | 0.046(0.509) | -(0.899) | - |
| absences | 0.042(0.001)** | -(0.089) | - |
| G1 | 0.164(0.003)** | 0.057(0.005)** | 0.153(0.007)** |
| G2 | 0.977(<0.001)*** | 0.903(<0.001)*** | 0.987(<0.001)*** |
| R2 | 0.835 | - | 0.822 |
| adjusted R2 | 0.831 | - | 0.821 |
| Mean Square Error | 3.446 | - | 3.723 |
| student <- read.table("mat_2.txt",sep="\t",header=FALSE) IV<-(student[,1:10]) IV1=scale(IV,FALSE,FALSE) ## 不对自变量进行标准化处理 ## 十重交叉验证 install.packages(‘glmnet’) library(glmnet) set.seed(1222) ## 设定随机数种子, 保证每次运行十重交叉验证的结果一样 Lambda=cv.glmnet(IV1,student[,11]) ## lasso回归结果 coef(Lambda, s=Lambda\$lambda.1se) ## 绘图 plot(Lambda) ## 横坐标为lambda, 纵坐标为均方误差MSE savePlot(filename = "lambda", type ="png", device = dev.cur(), restoreConsole = TRUE) RegCoef=glmnet(IV1,student[,11],family = "gaussian",alpha = 1) plot(RegCoef, xvar="lambda",ylim=c(-1.5,1.5), lwd=1.8 ) ## 横坐标为lambda, 纵坐标为系数估计值 abline(v=log(Lambda\$lambda.1se)) abline(v=log(Lambda\$lambda.min)) savePlot(filename = "loglambda", type ="png", device = dev.cur(), restoreConsole = TRUE) ## 采用covTest包计算p值 library('devtools') install_github('cran/covTest') ## coveTest 软件包目前无法从CRAN上下载, 因此采用devtools软件包从github上下载 library(covTest) IV<-student[,1:10] df=nrow(IV)-1 IV2=scale(IV,TRUE,TRUE)/sqrt(df) ## 标准化自变量 LarsCoef=lars(IV2,student[,11]) covTest(LarsCoef,IV2,student[,11]) ## 计算p值 |
| student <- read.table("mat_2.txt",sep="\t",header=FALSE) IV<-(student[,1:10]) IV1=scale(IV,FALSE,FALSE) ## 不对自变量进行标准化处理 ## 十重交叉验证 install.packages(‘glmnet’) library(glmnet) set.seed(1222) ## 设定随机数种子, 保证每次运行十重交叉验证的结果一样 Lambda=cv.glmnet(IV1,student[,11]) ## lasso回归结果 coef(Lambda, s=Lambda\$lambda.1se) ## 绘图 plot(Lambda) ## 横坐标为lambda, 纵坐标为均方误差MSE savePlot(filename = "lambda", type ="png", device = dev.cur(), restoreConsole = TRUE) RegCoef=glmnet(IV1,student[,11],family = "gaussian",alpha = 1) plot(RegCoef, xvar="lambda",ylim=c(-1.5,1.5), lwd=1.8 ) ## 横坐标为lambda, 纵坐标为系数估计值 abline(v=log(Lambda\$lambda.1se)) abline(v=log(Lambda\$lambda.min)) savePlot(filename = "loglambda", type ="png", device = dev.cur(), restoreConsole = TRUE) ## 采用covTest包计算p值 library('devtools') install_github('cran/covTest') ## coveTest 软件包目前无法从CRAN上下载, 因此采用devtools软件包从github上下载 library(covTest) IV<-student[,1:10] df=nrow(IV)-1 IV2=scale(IV,TRUE,TRUE)/sqrt(df) ## 标准化自变量 LarsCoef=lars(IV2,student[,11]) covTest(LarsCoef,IV2,student[,11]) ## 计算p值 |
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