identificationDML {causalweight}

Testing identification with double machine learning

Description

Testing identification with double machine learning

Usage

identificationDML(
  y,
  d,
  x,
  z,
  score = "DR",
  bootstrap = FALSE,
  ztreat = 1,
  zcontrol = 0,
  seed = 123,
  MLmethod = "lasso",
  k = 3,
  DR_parameters = list(s = NULL, normalized = TRUE, trim = 0.01),
  squared_parameters = list(zeta_sigma = min(0.5, 500/dim(y)[1])),
  bootstrap_parameters = list(B = 2000, importance = 0.95, alpha = 0.1, share = 0.5)
)

Arguments

y

Dependent variable, must not contain missings.

d

Treatment variable, must be discrete, must not contain missings.

x

Covariates, must not contain missings.

z

Instrument, must not contain missings.

score

Orthogonal score used for testing identification, either "DR" for using the average of the doubly robust (DR) score function (see Section 6 of Huber and Kueck, 2022) for testing, or "squared" for using squared differences in the conditional means outcomes (see Section 7 of Huber and Kueck, 2022). Default is "DR". Note that this argument is ignored if bootstrap=TRUE.

bootstrap

If set to TRUE, testing identification is based on the DR score function within data-driven partitioning of the data (using a random forest with 200 trees) as described at the end of Sections 6 and 8 in Huber and Kueck (2022). Default is FALSE. Note that the argument score is ignored if bootstrap=TRUE.

ztreat

Value of the instrument in the "treatment" group. Default is 1.

zcontrol

Value of the instrument in the "control" group. Default is 0.

seed

Default is 123.

MLmethod

Machine learning method for estimating the nuisance parameters based on the SuperLearner package. Must be either "lasso" (default) for lasso estimation, "randomforest" for random forests, "xgboost" for xg boosting, "svm" for support vector machines, "ensemble" for using an ensemble algorithm based on all previously mentioned machine learners, or "parametric" for linear or logit regression.

k

Number of folds in k-fold cross-fitting. Default is 3.

DR_parameters

List of input parameters to test identification using the doubly robust score: s: Indicator function for defining a subpopulation for which the treatment effect is estimated as a function of the subpopulation's distribution of x. Default is NULL (estimation of the average treatment effect in the total population). normalized: If set to TRUE, then the inverse probability-based weights are normalized such that they add up to 1 within treatment groups. Default is TRUE trim: Trimming rule for discarding observations with treatment propensity scores that are smaller than trim or larger than 1-trim (to avoid too small denominators in weighting by the inverse of the propensity scores). Default is 0.01.

squared_parameters

List of input parameters to test identification using the squared deviation: zeta_sigma: standard deviation of the normal distributed errors to avoid degenerated limit distribution. Default is min(0.05,500/n).

bootstrap_parameters

List of input parameters to test identification using the DR score and sample splitting to detect heterogeneity (if bootstrap=TRUE): B: number of bootstrap samples to be used in the multiplier bootstrap. Default is 2000. importance: upper quantile of covariates in terms of their predictive importance for heterogeneity in the DR score function according to a random forest (with 200 trees). The data are split into subsets based on the median values of these predictive covariates (entering the upper quantile). Default is 0.95. alpha: level of the statistical test. Default is 0.1. share: share of observations used to detect heterogeneity in the DR score function by the random forest (while the remaining observations are used for hypothesis testing). Default is 0.5.

Details

Testing the identification of causal effects of a treatment d on an outcome y in observational data using a supposed instrument z and controlling for observed covariates x.

Value

An identificationDML object contains different parameters, at least the two following:

effect: estimate of the target parameter(s).

pval: p-value(s) of the identification test.

References

Huber, M., & Kueck, J. (2022): Testing the identification of causal effects in observational data. arXiv:2203.15890.

Examples

# Two examples with simulated data
## Not run: 
set.seed(777)
n <- 20000  # sample size
p <- 50    # number of covariates
s <- 5  # sparsity (relevant covariates)
alpha <- 0.1    # level

control violation of identification
delta <- 2    # effect of unobservable in outcome on index of treatment - either 0 or 2
gamma <- 0   # direct effect of the instrument on outcome  - either 0 or 0.1

DGP - general
xcorr <- 1   # if 1, then non-zero covariance between regressors
if (xcorr == 0) {
 sigmax <- diag(1,p)}       # covariate matrix at baseline
if (xcorr != 0){
 sigmax = matrix(NA,p,p)
for (i in 1:p){
   for (j in 1:p){
     sigmax[i,j] = 0.5^(abs(i-j))
   }
 }}
sparse = FALSE # if FALSE, an approximate sparse setting is considered
beta = rep(0,p)
if (sparse == TRUE){
 for (j in 1:s){ beta[j] <- 1} }
if (sparse != TRUE){
 for (j in 1:p) beta[j] <- (1/j)}
noise_U <- 0.1 # control signal-to-noise
noise_V <- 0.1
noise_W <- 0.25
x <- (rmvnorm(n,rep(0,p),sigmax))
w <- rnorm(n,0,sd=noise_W)
z <- 1*(rnorm(n)>0)
d <- (x%*%beta+z+w+rnorm(n,0,sd=noise_V)>0)*1         # treatment equation

DGP 1 - effect homogeneity

y <- x%*%beta+d+gamma*z+delta*w+rnorm(n,0,sd=noise_U)

output1 <- identificationDML(y = y, d=d, x=x, z=z, score = "DR", bootstrap = FALSE,
ztreat = 1, zcontrol = 0 , seed = 123, MLmethod ="lasso", k = 3,
DR_parameters = list(s = NULL , normalized = TRUE, trim = 0.01))
output1$pval
output2 <- identificationDML(y=y, d=d, x=x, z=z, score = "squared", bootstrap = FALSE,
ztreat = 1, zcontrol =0 , seed = 123, MLmethod ="lasso", k = 3)
output2$pval
output3 <- identificationDML(y=y, d=d, x=x, z=z, score = "squared", bootstrap = TRUE,
ztreat = 1, zcontrol =0 , seed = 123, MLmethod ="lasso", k = 3,
DR_parameters = list(s = NULL , normalized = TRUE, trim = 0.005),
bootstrap_parameters = list(B = 2000, importance = 0.95, alpha = 0.1, share = 0.5))
output3$pval

DGP 2 - effect heterogeneity

y = x%*%beta+d+gamma*z*x[,1]+gamma*z*x[,2]+delta*w*x[,1]+delta*w*x[,2]+rnorm(n/2,0,sd=noise_U)

output1 <- identificationDML(y = y, d=d, x=x, z=z, score = "DR", bootstrap = FALSE,
ztreat = 1, zcontrol = 0 , seed = 123, MLmethod ="lasso", k = 3,
DR_parameters = list(s = NULL , normalized = TRUE, trim = 0.01))
output1$pval
output2 <- identificationDML(y=y, d=d, x=x, z=z, score = "squared", bootstrap = FALSE,
ztreat = 1, zcontrol =0 , seed = 123, MLmethod ="lasso", k = 3)
output2$pval
output3 <- identificationDML(y=y, d=d, x=x, z=z, score = "DR", bootstrap = TRUE,
ztreat = 1, zcontrol =0 , seed = 123, MLmethod ="lasso", k = 3,
DR_parameters = list(s = NULL , normalized = TRUE, trim = 0.005),
bootstrap_parameters = list(B = 2000, importance = 0.95, alpha = 0.1, share = 0.5))
output3$pval

## End(Not run)