r - R 中的 Monte Carlo 模拟、Bootstrap 和回归

Question

我已经使用 SAS 很长时间了，现在我想用 R 翻译我的代码。我需要帮助来执行以下操作:

生成多个引导样本

对每个样本运行线性回归模型

通过复制样本将参数存储在新数据集中

为了更清晰，我编辑了这段代码。
我用了很多 for 循环，我知道并不总是推荐。这个过程很慢

是否有代码/包(例如应用系列函数，“插入符号”包)可以使这个非常干净高效/快速，尤其是当 samplesize*bootsample > 10 百万

任何帮助将非常感激。

samplesize <- 200
bootsize<- 500
myseed <- 123

#generating a fake dataset
       id=1:n
       set.seed(myseed)
       x <-  rnorm(samplesize, 5, 5)
       y <-  rnorm(samplesize, 2 + 0.4*x, 0.5)
      data <- data.frame(id, x, y)

head(data)
  id         x        y
1  1  2.197622 3.978454
2  2  3.849113 4.195852
3  3 12.793542 6.984844
4  4  5.352542 4.412614
5  5  5.646439 4.051405
6  6 13.575325 7.192007

# generate bootstrap samples

bootstrap <- function(nbootsamples, data, seed) {
   bootdata <-  data.frame() #to initialize it
   set.seed(seed) 
   for (i in 1:nbootsamples) {
     replicate <- i
     bootstrapIndex <- sample(1:nrow(data), replace = TRUE)
     datatemp <- data[bootstrapIndex, ]
     tempall <- cbind(replicate, datatemp)
     bootdata <- rbind(bootdata, tempall)
   }
   return(bootdata)
 }
 bootdata <- bootstrap(nbootsamples=bootsize, data=data, seed=myseed)
 bootdata <- dplyr::arrange(bootdata, replicate, id)
 head(bootdata)
 #The data should look like this
  replicate id         x        y
1         1  1  2.197622 3.978454
2         1  3 12.793542 6.984844
3         1  5  5.646439 4.051405
4         1  9  1.565736 3.451748
5         1 10  2.771690 3.081662
6         1 10  2.771690 3.081662

#Model-fitting and saving coefficient and means

modelFitting <- function(y, x, data) {
   modeltemp <-  glm(y ~ x,
     data = data,
     family = gaussian('identity'))
   Inty <-  coef(modeltemp)["(Intercept)"]
   betaX <-  coef(modeltemp)["x"]
   sdy <-  sd(residuals.glm(modeltemp))
   data.frame(Inty, betaX, sdy, row.names = NULL)
 }

saveParameters <- function(nbootsamples, data, seed) {
   parameters <-  data.frame() #to initialize it
   for (i in 1:length(unique(data$replicate))) {
     replicate <- i
     datai <- data[ which(data$replicate==i),]
     datatemp <- modelFitting(y, x,data=datai)
     meandata <- data.frame(Pr_X=mean(datai$x))
     tempall <- cbind(replicate, datatemp, meandata)
     parameters <- rbind(parameters, tempall)
   }
   return(parameters)
 }
parameters <- saveParameters(nbootsamples=bootsize, data=bootdata, seed=myseed)
 head(parameters)

#Ultimately all I want is my final dataset to look like the following

  replicate     Inty     betaX       sdy     Pr_X
1         1 2.135529 0.3851757 0.5162728 4.995836
2         2 1.957152 0.4094682 0.5071635 4.835884
3         3 2.044257 0.3989742 0.4734178 5.111185
4         4 2.093452 0.3861861 0.4921470 4.741299
5         5 2.017825 0.4037699 0.5240363 4.931793
6         6 2.026952 0.3979731 0.4898346 5.502320

Answer 1

使用 caret 可以轻松实现重采样回归包裹。给定您的示例数据，通过广义线性模型运行 200 个引导样本的代码如下所示。

library(caret)
x = round(rnorm(200, 5, 5))
y= rnorm(200, 2 + 0.4*x, 0.5)
theData <- data.frame(id=1:200,x, y)
# configure caret training parameters to 200 bootstrap samples
fitControl <- trainControl(method = "boot",
                           number = 200)
fit <- train(y ~ x, method="glm",data=theData,
             trControl = fitControl)
# print output object
fit
# print first 10 resamples 
fit$resample[1:10,]

插入符号的输出如下所示:

> fit
Generalized Linear Model 

200 samples
  1 predictor

No pre-processing
Resampling: Bootstrapped (200 reps) 
Summary of sample sizes: 200, 200, 200, 200, 200, 200, ... 
Resampling results:

  RMSE       Rsquared   MAE      
  0.4739306  0.9438834  0.3772199

> fit$resample[1:10,]
        RMSE  Rsquared       MAE    Resample
1  0.5069606 0.9520896 0.3872257 Resample001
2  0.4636029 0.9460214 0.3711900 Resample002
3  0.4446103 0.9549866 0.3435148 Resample003
4  0.4464119 0.9443726 0.3636947 Resample004
5  0.5193685 0.9191259 0.4010104 Resample005
6  0.4995917 0.9451417 0.4044659 Resample006
7  0.4347831 0.9494606 0.3383224 Resample007
8  0.4725041 0.9483434 0.3716319 Resample008
9  0.5295650 0.9458453 0.4241543 Resample009
10 0.4796985 0.9514595 0.3927207 Resample010
> 

有关如何使用插入符号的详细信息，包括生成的模型对象的内容(例如，访问各个模型，以便您可以使用 predict() 函数为模拟生成预测)，请访问 caret GitHub site。 .

Caret 还支持并行处理。有关如何使用插入符号进行并行处理的示例，请阅读 Improving Performance of Random Forest with caret::train() .

此外，R 中通过 Monte Carlo 支持蒙特卡罗模拟。 R中的包。