Probit.cf {controlfunctionIV}

Causal inference in probit outcome models with possibly invalid IVs

Description

Perform causal inference in the probit outcome model with possibly invalid IVs.

Usage

Probit.cf(
  Y,
  D,
  Z,
  X = NULL,
  intercept = TRUE,
  invalid = TRUE,
  d1 = NULL,
  d2 = NULL,
  w0 = NULL,
  bs.Niter = 40
)

Arguments

Y

The outcome observation, a vector of length n.

D

The treatment observation, a vector of length n.

Z

The instrument observation of dimension n \times p_z.

X

The covariates observation of dimension n \times p_x.

intercept

Whether the intercept is included. (default = TRUE)

invalid

If TRUE, the method is robust to the presence of possibly invalid IVs; If FALSE, the method assumes all IVs to be valid. (default = TRUE)

d1

A treatment value for computing CATE(d1,d2|w0).

d2

A treatment value for computing CATE(d1,d2|w0).

w0

A vector of the instruments and baseline covariates for computing CATE(d1,d2|w0).

bs.Niter

The bootstrap resampling size for constructing the confidence interval.

Value

Probit.cf returns an object of class "SpotIV", which is a list containing the following components:

betaHat

The estimate of the model parameter in front of the treatment.

beta.sdHat

The estimated standard error of betaHat.

cateHat

The estimate of CATE(d1,d2|w0).

cate.sdHat

The estimated standard deviation of cateHat.

SHat

The estimated set of relevant IVs.

VHat

The estimated set of relevant and valid IVs.

Maj.pass

The indicator that the majority rule is satisfied.

References

Li, S., Guo, Z. (2020), Causal Inference for Nonlinear Outcome Models with Possibly Invalid Instrumental Variables, Preprint arXiv:2010.09922.

Examples

data("nonlineardata")
Y <- nonlineardata[,"CVD"]
D <- nonlineardata[,"bmi"]
Z <- as.matrix(nonlineardata[,c("Z.1","Z.2","Z.3","Z.4")])
X <- as.matrix(nonlineardata[,c("age","sex")])
d1 <- median(D)+1
d2 <- median(D)
w0 <- c(rep(0,4), 30, 1)
Probit.model <- Probit.cf(Y,D,Z,X,invalid = TRUE,d1 =d1, d2 = d2,w0 = w0)
summary(Probit.model)