testmedident {causalweight}

Test for identification in causal mediation and dynamic treatment models

Description

This function tests for identification in causal mediation and dynamic treatment models based on covariates and instrumental variables using machine learning methods.

Usage

testmedident(
  y,
  d,
  m = NULL,
  x,
  w = NULL,
  z1,
  z2 = NULL,
  testmediator = TRUE,
  seed = 123,
  MLmethod = "lasso",
  k = 3,
  zeta_sigma = min(0.5, 500/length(y))
)

Arguments

y

Outcome variable.

d

Treatment variable.

m

Mediator variable (optional).

x

Baseline covariates (prior to treatment assignment).

w

Post-treatment covariates (prior to mediator assignment, optional).

z1

Instrument for the treatment.

z2

Instrument for the mediator (optional).

testmediator

Logical indicating if the mediator should be used as dependent variable (in addition to outcome y) when testing if the effect of treatment d is identified. Default is TRUE.

seed

Random seed for sample splitting in cross-fitting. Default is 123.

MLmethod

Machine learning method for estimating conditional outcome/mediator means required for testing. Default is "lasso".

k

Number of cross-fitting folds. Default is 3.

zeta_sigma

Tuning parameter defining the standard deviation of a random, mean zero, and normal variable that is added to the test statistic to avoid a degenerate distribution of test statistic under the null hypothesis. zeta_sigma gauges the trade-off between power and size of the test. Default is the minimum of 0.5 and 500/(# of observations).

Details

This function implements a hypothesis test for identifying causal effects in mediation and dynamic treatment models involving sequential assignment of treatment and mediator variables. The test jointly verifies the exogeneity/ignorability of treatment and mediator variables conditional on covariates and the validity of (distinct) instruments for the treatment and mediator (ignorability of instrument assignment and exclusion restriction). If the null hypothesis holds, dynamic and pathwise causal effects may be identified based on the sequential exogeneity/ignorability of the treatment and the mediator given the covariates. The function employs machine learning techniques to control for covariates in a data-driven manner.

Value

A list with the following components:

teststat

Test statistic.

se

Standard error of the test statistic.

pval

Two-sided p-value of the test.

References

Huber, M., Kloiber, K., and Lafférs, L. (2024): "Testing identification in mediation and dynamic treatment models", arXiv preprint 2406.13826.

Examples

## Not run: 
# Example with simulated data in which null hypothesis holds
n=2000
x=rnorm(n)
z1=rnorm(n)
z2=rnorm(n)
d=1*(0.5*x+0.5*z1+rnorm(n)>0)      # Treatment equation
m=0.5*x+0.5*d+0.5*z2+rnorm(n)      # Mediator equation
y=0.5*x+d+0.5*m+rnorm(n)           # Outcome equation
# Run test and report p-value
testmedident(y=y, d=d, m=m, x=x, z1=z1, z2=z2)$pval

## End(Not run)