是否有一个简单的命令可以使用 lm() 函数进行留一法交叉验证？

Question

在 R 中是否有一个简单的命令来使用 lm() 函数进行留一法交叉验证？

具体有没有针对下面代码的简单命令？

x <- rnorm(1000,3,2)
y <- 2*x + rnorm(1000)

pred_error_sq <- c(0)
for(i in 1:1000) {
  x_i <- x[-i]
  y_i <- y[-i]
  mdl <- lm(y_i ~ x_i) # leave i'th observation out
  y_pred <- predict(mdl, data.frame(x_i = x[i])) # predict i'th observation
  pred_error_sq <- pred_error_sq + (y[i] - y_pred)^2 # cumulate squared prediction errors
}

y_squared <- sum((y-mean(y))^2)/100 # Variation of the data

R_squared <- 1 - (pred_error_sq/y_squared) # Measure for goodness of fit

Answer 1

您可以从 DAAG 包中尝试 cv.lm：

cv.lm(data = DAAG::houseprices, form.lm = formula(sale.price ~ area),
              m = 3, dots = FALSE, seed = 29, plotit = c("Observed","Residual"),
              main="Small symbols show cross-validation predicted values",
              legend.pos="topleft", printit = TRUE)

Arguments

data        a data frame
form.lm,    a formula or lm call or lm object
m           the number of folds
dots        uses pch=16 for the plotting character
seed        random number generator seed
plotit      This can be one of the text strings "Observed", "Residual", or a logical value. The logical TRUE is equivalent to "Observed", while FALSE is equivalent to "" (no plot)
main        main title for graph
legend.pos      position of legend: one of "bottomright", "bottom", "bottomleft", "left", "topleft", "top", "topright", "right", "center".
printit     if TRUE, output is printed to the screen

Answer 2

另一个解决方案是使用 caret

library(caret)

data <- data.frame(x = rnorm(1000, 3, 2), y = 2*x + rnorm(1000))

train(y ~ x, method = "lm", data = data, trControl = trainControl(method = "LOOCV"))

Linear Regression

1000 samples 1 predictor

No pre-processing Resampling: Leave-One-Out Cross-Validation Summary of sample sizes: 999, 999, 999, 999, 999, 999, ... Resampling results:

RMSE Rsquared MAE
1.050268 0.940619 0.836808

Tuning parameter 'intercept' was held constant at a value of TRUE

Answer 3

您可以只使用自定义函数，使用统计技巧避免实际计算所有 N 个模型：

loocv=function(fit){
  h=lm.influence(fit)$h
  mean((residuals(fit)/(1-h))^2)
}

这里有解释：https://gerardnico.com/wiki/lang/r/cross_validation 它仅适用于线性模型我想您可能想在公式中的均值之后添加一个平方根。

Answer 4

https://www.rdocumentation.org/packages/boot/versions/1.3-20/topics/cv.glm 中的

cv.glm 默认执行 LOOCV，只需要数据和 lm 或 glm 函数。

Answer 5

只需编写您自己的代码，使用索引变量来标记样本外的一个观察值。使用插入符号针对最高票测试此方法。尽管 caret 简单易用，但我的残酷方法花费的时间更少。（而不是 lm，我使用 LDA，但没有太大区别）

for (index in 1:dim(df)[1]){
   # here write your lm function
}

是否有一个简单的命令可以使用 lm() 函数进行留一法交叉验证？

Is there a simple command to do leave-one-out cross validation with the lm() function?

r

cross-validation

lm