How to compute high dimensional regression statistics

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I have a model below

A = matrix(1, nrow = 400, ncol = 400)
A = 0.5**abs(row(A) - col(A))
X=mvtnorm::rmvnorm(300,mean=rep(0,400),sigma=A)))  
Y=X[,6]+X[,12]+X[,15]+X[,20]+0.7*pnorm(X[,1])*rnorm(300) 
df <- data.frame(Y, X)

and i want to fit least squares lasso to it. I need to summarise the following:

  1. The percentage of times including X6, X12, X15 and X20 in simulation runs
  2. The proportion of simulation runs including X1

How can i calculate 1. and 2.? The results should be 100% and 6%.

av_model_size <- c(NULL)
a1 <- c(NULL)
a2 <- c(NULL)
for (i in 1:100) {
  lassocv <- glmnet::cv.glmnet(X, Y, alpha = 1)
  modelcv <- glmnet::glmnet(X, Y, alpha = 1, lambda = lassocv$lambda.min, standardize = TRUE)
  lasso.coef <- modelcv$beta
  av_model_size[[i]] <- sum(lasso.coef!=0)
  a1[[i]] <- sum(lasso.coef[6] != 0 && lasso.coef[12] != 0 && lasso.coef[15] != 0 && lasso.coef[20] != 0)
  a2[[i]] <- sum(lasso.coef[1] != 0)
}

mean(ams)

regression r
1 Answers

You will need to include the data generation in your simulation process. As you have outlined your example, you are executing the functions on the same set of data. Consider the following: 

set.seed(42)

get_simulated_data <- function(){
  A = matrix(1, nrow = 400, ncol = 400)
  A = 0.5**abs(row(A) - col(A))
  X = mvtnorm::rmvnorm(300,mean=rep(0,400),sigma=A)
  Y = X[,6]+X[,12]+X[,15]+X[,20]+0.7*pnorm(X[,1])*rnorm(300)
  dat <- list(Y=Y, X=X)
  return(dat)
}

get_coefficients <- function(){
  dat <- get_simulated_data()
  lassocv <- glmnet::cv.glmnet(dat$X, dat$Y, alpha = 1)
  modelcv <- glmnet::glmnet(dat$X, dat$Y, alpha = 1, lambda = lassocv$lambda.min, standardize = TRUE)
  return(modelcv$beta)
}


out <- do.call(cbind, lapply(1:100, function(i) get_coefficients()))

rowMeans(out[c("V1", "V6", "V12", "V15", "V20"),] == 0)
  V1   V6  V12  V15  V20 
0.93 0.00 0.00 0.00 0.00
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