Tools for Causal Inference with Possibly Invalid Instrumental Variables

Two stage curvature identification with machine learning for causal inference in settings when instrumental variable regression is not suitable because of potentially invalid instrumental variables. Based on Guo and Buehlmann (2022) "Two Stage Curvature Identification with Machine Learning: Causal Inference with Possibly Invalid Instrumental Variables" . The vignette is available in Carl, Emmenegger, Bühlmann and Guo (2025) "TSCI: Two Stage Curvature Identification for Causal Inference with Invalid Instruments in R" .

TSCI

R Package of TSCI

Data generation

library(MASS)
library(TSCI)

# set seeds for reproducibility
RNGkind("L'Ecuyer-CMRG")
set.seed(1)
# dimension
p <- 10
# sample size
n <- 1000
# interaction value
inter_val <- 1
# the IV strength
a <- 1
# violation strength
tau <- 1
f <- function(x) {a * (1 * sin(2 * pi * x) + 1.5 * cos(2 * pi * x))}
rho <- 0.5
Cov <- stats::toeplitz(rho^c(0 : p))
mu <- rep(0, p + 1)
# true effect
beta <- 1
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 <- MASS::mvrnorm(n, mu_error, Cov_error)
W_original <- MASS::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
Y <- D * beta + tau * Z + X %*% gamma + Error[, 2]

Create violation space candidates

vio_space <- create_monomials(Z, 4, "monomials_main")

TSCI with random forest

output_RF <- tsci_forest(Y = Y, D = D, Z = Z, X = X, vio_space = vio_space)
summary(output_RF)

TSCI with boosting

output_BO <- tsci_boosting(Y = Y, D = D, Z = Z, X = X, vio_space = vio_space)
summary(output_BO)

TSCI with polynomials

output_PY <- tsci_poly(Y = Y, D = D, Z = Z, X = X)
summary(output_PY)

TSCI with user defined hat matrix

A <- cbind(1, Z, Z^2, Z^3, Z^4, X)
weight <- A %*% chol2inv(chol(t(A) %*% A)) %*% t(A)
output_UD <- tsci_secondstage(Y = Y, D = D, Z = Z, W = X, vio_space = vio_space, weight = weight)
summary(output_UD)