Searching-Sampling

Description

Construct Searching and Sampling confidence intervals for the causal effect, which provides the robust inference of the treatment effect in the presence of invalid instrumental variables in both low-dimensional and high-dimensional settings. It is robust to the mistakes in separating valid and invalid instruments.

Usage

SearchingSampling(
  Y,
  D,
  Z,
  X = NULL,
  intercept = TRUE,
  method = c("OLS", "DeLasso", "Fast.DeLasso"),
  robust = TRUE,
  Sampling = TRUE,
  alpha = 0.05,
  CI.init = NULL,
  a = 0.6,
  rho = NULL,
  M = 1000,
  prop = 0.1,
  filtering = TRUE,
  tuning.1st = NULL,
  tuning.2nd = NULL
)

Arguments

Details

When robust = TRUE, the method will be input as ’OLS’. For rho, M, prop, and filtering, they are required only for Sampling = TRUE. As for tuning parameter in the 1st stage and 2nd stage, if do not specify, for method "OLS" we adopt \sqrt{\log n} for both tuning parameters, and for other methods we adopt \max{(\sqrt{2.01 \log p_z}, \sqrt{\log n})} for both tuning parameters.

Value

SearchingSampling returns an object of class "SS", which is a list containing the following components:

References

Guo, Z. (2021), Causal Inference with Invalid Instruments: Post-selection Problems and A Solution Using Searching and Sampling, Preprint arXiv:2104.06911.

Examples

data("lineardata")
Y <- lineardata[,"Y"]
D <- lineardata[,"D"]
Z <- as.matrix(lineardata[,c("Z.1","Z.2","Z.3","Z.4","Z.5","Z.6","Z.7","Z.8")])
X <- as.matrix(lineardata[,c("age","sex")])
Searching.model <- SearchingSampling(Y,D,Z,X, Sampling = FALSE)
summary(Searching.model)
Sampling.model <- SearchingSampling(Y,D,Z,X)
summary(Sampling.model)

Two-Stage Hard Thresholding

Description

Perform Two-Stage Hard Thresholding method, which provides the robust inference of the treatment effect in the presence of invalid instrumental variables.

Usage

TSHT(
  Y,
  D,
  Z,
  X,
  intercept = TRUE,
  method = c("OLS", "DeLasso", "Fast.DeLasso"),
  voting = c("MaxClique", "MP", "Conservative"),
  robust = TRUE,
  alpha = 0.05,
  tuning.1st = NULL,
  tuning.2nd = NULL
)

Arguments

Details

When robust = TRUE, the method will be input as ’OLS’. When voting = MaxClique and there are multiple maximum cliques, betaHat,beta.sdHat,ci, and VHat will be list objects where each element of list corresponds to each maximum clique. As for tuning parameter in the 1st stage and 2nd stage, if do not specify, for method "OLS" we adopt \sqrt{\log n} for both tuning parameters, and for other methods we adopt \max{(\sqrt{2.01 \log p_z}, \sqrt{\log n})} for both tuning parameters.

Value

TSHT returns an object of class "TSHT", which is a list containing the following components:

References

Guo, Z., Kang, H., Tony Cai, T. and Small, D.S. (2018), Confidence intervals for causal effects with invalid instruments by using two-stage hard thresholding with voting, J. R. Stat. Soc. B, 80: 793-815.

Examples

data("lineardata")
Y <- lineardata[,"Y"]
D <- lineardata[,"D"]
Z <- as.matrix(lineardata[,c("Z.1","Z.2","Z.3","Z.4","Z.5","Z.6","Z.7","Z.8")])
X <- as.matrix(lineardata[,c("age","sex")])
TSHT.model <- TSHT(Y=Y,D=D,Z=Z,X=X)
summary(TSHT.model)

Endogeneity test in high dimensions

Description

Conduct the endogeneity test with high dimensional and possibly invalid instrumental variables.

Usage

endo.test(
  Y,
  D,
  Z,
  X,
  intercept = TRUE,
  invalid = FALSE,
  method = c("Fast.DeLasso", "DeLasso", "OLS"),
  voting = c("MP", "MaxClique"),
  alpha = 0.05,
  tuning.1st = NULL,
  tuning.2nd = NULL
)

Arguments

Details

When voting = MaxClique and there are multiple maximum cliques, the null hypothesis is rejected if one of maximum clique rejects the null. As for tuning parameter in the 1st stage and 2nd stage, if do not specify, for method "OLS" we adopt \sqrt{\log n} for both tuning parameters, and for other methods we adopt \max{(\sqrt{2.01 \log p_z}, \sqrt{\log n})} for both tuning parameters.

Value

endo.test returns an object of class "endotest", which is a list containing the following components:

References

Guo, Z., Kang, H., Tony Cai, T. and Small, D.S. (2018), Testing endogeneity with high dimensional covariates, Journal of Econometrics, Elsevier, vol. 207(1), pages 175-187.

Examples

n = 500; L = 11; s = 3; k = 10; px = 10;
beta = 1; gamma = c(rep(1,k),rep(0,L-k))
phi<-(1/px)*seq(1,px)+0.5; psi<-(1/px)*seq(1,px)+1
epsilonSigma = matrix(c(1,0.8,0.8,1),2,2)
Z = matrix(rnorm(n*L),n,L)
X = matrix(rnorm(n*px),n,px)
epsilon = MASS::mvrnorm(n,rep(0,2),epsilonSigma)
D =  0.5 + Z %*% gamma + X %*% psi + epsilon[,1]
Y = -0.5 + Z %*% c(rep(1,s),rep(0,L-s)) + D * beta + X %*% phi + epsilon[,2]
endo.test.model <- endo.test(Y,D,Z,X,invalid = TRUE)
summary(endo.test.model)

lineardata

Description

Psuedo data provided by Youjin Lee, which is generated mimicing the structure of Framingham Heart Study data.

Usage

data(lineardata)

Format

A data.frame with 1445 observations on 12 variables:

• Y: The globulin level.

• D: The LDL-C level.

• Z.1: SNP genotypes.

• Z.2: SNP genotypes.

• Z.3: SNP genotypes.

• Z.4: SNP genotypes.

• Z.5: SNP genotypes.

• Z.6: SNP genotypes.

• Z.7: SNP genotypes.

• Z.8: SNP genotypes.

• age: the age of the subject.

• sex: the sex of the subject.

Source

The Framingham Heart Study data supported by the National Heart, Lung, and Blood Institute (NHLBI) in collaboration with Boston University.

Examples

data(lineardata)

Summary of SS

Description

Summary function for SearchingSampling

Usage

## S3 method for class 'SS'
summary(object, ...)

Value

No return value, called for summary.

Summary of TSHT

Description

Summary function for TSHT

Usage

## S3 method for class 'TSHT'
summary(object, ...)

Value

No return value, called for summary.

Summary of endotest

Description

Summary function for endo.test

Usage

## S3 method for class 'endotest'
summary(object, ...)

Value

No return value, called for summary.