TSCI

This package implements the Two Stage Curvature Idetification (TSCI) method proposed in the paper https://arxiv.org/abs/2203.12808 using Ramdom Forests and Basis Approach. It constructs a robust point estimator of the treatment effect even the instrumental variabls are possibly invalid. Confidence intervals are futher constructed.

Installation

The package can be installed from Github using the following code.

# install.packages("devtools")
library(devtools)
devtools::install_github("https://github.com/zijguo/TSCI")

Data generation

#We generate the data where the instrumental variable has a linear violation form.

library(TSCI)
library(MASS)

# dimension
p = 20
# sample size
n = 1000
# interaction value of Z and X
inter.val = 0.5
# the IV strength
a = 1
# the conditional mean function for the treatment model
f = function(x){a*(1*sin(2*pi*x) + 1.5*cos(2*pi*x))}
# function to generate covariance matrix
A1gen=function(rho,p){
  A1=matrix(0,p,p)
  for(i in 1:p){
    for(j in 1:p){
      A1[i,j]=rho^(abs(i-j))
    }
  }
  A1
}
rho1=0.5
Cov=(A1gen(rho1,p+1))
mu=rep(0,p+1)
# true effect
beta=1
# violation strength
tau = 1
# other model parameters
alpha=as.matrix(rep(-0.3,p))
gamma=as.matrix(rep(0.2,p))
inter=as.matrix(c(rep(inter.val,5),rep(0,p-5)))


# generate the data
mu.error=rep(0,2)
Cov.error=matrix(c(1,0.5,0.5,1),2,2)
Error=mvrnorm(n, mu.error, Cov.error)
W.original=mvrnorm(n, mu, Cov)
W=pnorm(W.original)
# instrument variable
Z=W[,1]
# baseline covariates
X=W[,-1]
# generate the treatment variable D
D=f(Z)+X%*%alpha+Z*X%*%inter+Error[,1]
# generate the outcome variable Y, linear violation of Z
Y=D*beta+tau*Z+X%*%gamma+Error[,2]

TSCI with Random Forests

# implement TSCI with Random Forests 
output.RF = TSRF(Y,D,Z,X)
# point estimates
output.RF$Coef.robust
# standard errors
output.RF$sd.robust
# confidence intervals
output.RF$CI.robust
# estimated violation space
output.RF$q.hat

TSCI with Basis Approaches

# implement TSCI with Basis Approach
output.BA = TSBA(Y,D,Z,X)
# point estimates
output.BA$Coef.robust
# standard errors
output.BA$sd.robust
# confidence intervals
output.BA$CI.robust
# estimated violation space
output.BA$q.hat

Analysis of Card Education Data by TSCI

library(TSCI)
# card data
library(ivmodel)
data(card.data)

Xname2=c("exper", "expersq", "black", "south", "smsa", "reg661","reg662", "reg663", "reg664", "reg665", "reg666", "reg667","reg668", "smsa66")

Y=card.data[,"lwage"]
D=card.data[,"educ"]
Z=card.data[,"nearc4"]
X2=card.data[,Xname2]

# results for TSLS
TSLS = ivmodel(Y=Y,D=D,Z=Z,X=X2)
summary(TSLS)

# results for TSCI with Random Forest
card.RF = TSRF(Y,D,Z,X2)
# point estimates
card.RF$Coef.robust
# standard errors
card.RF$sd.robust
# confidence intervals
card.RF$CI.robust