A dataset simulated as in Tan (2020), Section 4.
data(simu.data)A data matrix with 800 rows and 202 columns.
The dataset is generated as follows, where y, tr, and x represent an outcome, a treatment, and covariates respectively.
library(MASS)### mt0 <- 1-pnorm(-1) mt1 <- dnorm(-1) mt2 <- -(2*pnorm(-1)-1)/2 - dnorm(-1) +1/2 mt3 <- 3*dnorm(-1) mt4 <- -3/2*(2*pnorm(-1)-1) - 4*dnorm(-1) +3/2
m.z1 <- mt0 + 2*mt1 + mt2 v.z1 <- mt0 + 4*mt1 + 6*mt2 + 4*mt3 + mt4 v.z1 <- v.z1 + 1 + 2*(mt1 + 2*mt2 + mt3)
sd.z1 <- sqrt(v.z1 -m.z1^2) ###
set.seed(123)
n <- 800 p <- 200
noise <- rnorm(n)
covm <- matrix(1,p,p) for (i1 in 1:p) for (i2 in 1:p) { covm[i1,i2] <- 2^(-abs(i1-i2)) } x <- mvrnorm(n, mu=rep(0,p), Sigma=covm)
# transformation z <- x for (i in 1:4) { z[,i] <- ifelse(x[,i]>-1,x[,i]+(x[,i]+1)^2,x[,i]) z[,i] <- (z[,i]-m.z1) /sd.z1 # standardized }
# treatment eta <- 1+ c( z[,1:4] %*% c(1, .5, .25, .125) ) tr <- rbinom(n, size=1, prob=expit(eta))
# outcome eta.y <- c( z[,1:4] %*% c(1, .5, .25, .125) ) y <- eta.y + noise
# save; if using main effects of x, then both the propensity score # and outcome regression models are misspecified
simu.data <- cbind(y, tr, x) save(simu.data, file="simu.data.rda")
Tan, Z. (2020) Model-assisted inference for treatment effects using regularized calibrated estimation with high-dimensional data, Annals of Statistics, 48, 811<U+2013>837.