Bounds on the omitted variable bias for causal machine learning

Computes confidence bounds on the target parameter of interest accounting for omitted variable biases.

dml_bounds(model, cf.y, cf.d, rho2 = 1)

confidence_bounds(...)

# S3 method for class 'numeric'
confidence_bounds(
  theta.s,
  S2,
  se.theta.s,
  se.S2,
  cov.theta.S2,
  cf.y,
  cf.d,
  rho2 = 1,
  combine.method = "median",
  level = 0.95,
  ...
)

# S3 method for class 'dml'
confidence_bounds(
  model,
  cf.y,
  cf.d,
  rho2 = 1,
  level = 0.95,
  combine.method = "median",
  ...
)

# S3 method for class 'dml.bounds'
confidence_bounds(
  model,
  cf.y = NULL,
  cf.d = NULL,
  rho2 = NULL,
  level = 0.95,
  combine.method = "median",
  return = c("lwr", "upr"),
  ...
)

Arguments

model: an object of class dml or dml_bounds.
cf.y: (nonparametric) partial R2 of the omitted variables with the outcome. Must be a number between (0, 1).
cf.d: how much variation latent variables create in the Riesz Representer of the target parameters. Must be a number between (0, 1). When the target of interest is the ATE in a partially linear model, this corresponds to the partial R2 of omitted variables with the treatment. When the target of interest is the ATE in a non-parametric model with a binary treatment, this corresponds to the gains in precision (i.e, 1/variance) when predicting who is assigned to treatment.
rho2: degree of adversity. Default is rho=1, which assumes the maximum degree of adversity of confounding.
...: arguments passed to other methods.
theta.s: short estimate of the target parameter (used as the first argument for the numeric method).
S2: estimated variance product (sigma2 * nu2).
se.theta.s: standard error of the short estimate.
se.S2: standard error of S2.
cov.theta.S2: covariance of theta.s and S2.
combine.method: method to combine the results of each repetition. Options are mean and median. Default is median.
level: confidence level. Default is 0.95.
return: character vector specifying which bounds to return. Options are "lwr" and "upr".

Value

For dml_bounds: an object of class dml.bounds. For confidence_bounds: a matrix or numeric vector of confidence bounds.