Double machine learning for interactive IV regression models

Double machine learning for interactive IV regression models.

Format

R6::R6Class object inheriting from DoubleML.

Details

Interactive IV regression (IIVM) models take the form

\(Y = \ell_0(D,X) + \zeta\),

\(Z = m_0(X) + V\),

with \(E[\zeta|X,Z]=0\) and \(E[V|X] = 0\). \(Y\) is the outcome variable, \(D \in \{0,1\}\) is the binary treatment variable and \(Z \in \{0,1\}\) is a binary instrumental variable. Consider the functions \(g_0\), \(r_0\) and \(m_0\), where \(g_0\) maps the support of \((Z,X)\) to \(R\) and \(r_0\) and \(m_0\), respectively, map the support of \((Z,X)\) and \(X\) to \((\epsilon, 1-\epsilon)\) for some \(\epsilon \in (1, 1/2)\), such that

\(Y = g_0(Z,X) + \nu,\)

\(D = r_0(Z,X) + U,\)

\(Z = m_0(X) + V,\)

with \(E[\nu|Z,X]=0\), \(E[U|Z,X]=0\) and \(E[V|X]=0\). The target parameter of interest in this model is the local average treatment effect (LATE),

\(\theta_0 = \frac{E[g_0(1,X)] - E[g_0(0,X)]}{E[r_0(1,X)] - E[r_0(0,X)]}.\)

See also

Other DoubleML: DoubleMLIRM, DoubleMLPLIV, DoubleMLPLR, DoubleML

Super class

DoubleML::DoubleML -> DoubleMLIIVM

Active bindings

subgroups

(named list(2))
Named list(2) with options to adapt to cases with and without the subgroups of always-takers and never-takes. The entry always_takers(logical(1)) speficies whether there are always takers in the sample. The entry never_takers (logical(1)) speficies whether there are never takers in the sample.

trimming_rule

(character(1))
A character(1) specifying the trimming approach.

trimming_threshold

(numeric(1))
The threshold used for timming.

Methods

Public methods

• DoubleMLIIVM$new()

• DoubleMLIIVM$clone()

Inherited methods

• DoubleML::DoubleML$bootstrap()
• DoubleML::DoubleML$confint()
• DoubleML::DoubleML$fit()
• DoubleML::DoubleML$get_params()
• DoubleML::DoubleML$learner_names()
• DoubleML::DoubleML$p_adjust()
• DoubleML::DoubleML$params_names()
• DoubleML::DoubleML$print()
• DoubleML::DoubleML$set_ml_nuisance_params()
• DoubleML::DoubleML$set_sample_splitting()
• DoubleML::DoubleML$split_samples()
• DoubleML::DoubleML$summary()
• DoubleML::DoubleML$tune()

---

Method new()

Creates a new instance of this R6 class.

Usage

DoubleMLIIVM$new(
  data,
  ml_g,
  ml_m,
  ml_r,
  n_folds = 5,
  n_rep = 1,
  score = "LATE",
  subgroups = list(always_takers = TRUE, never_takers = TRUE),
  dml_procedure = "dml2",
  trimming_rule = "truncate",
  trimming_threshold = 1e-12,
  draw_sample_splitting = TRUE,
  apply_cross_fitting = TRUE
)

Arguments

data

(DoubleMLData)
The DoubleMLData object providing the data and specifying the variables of the causal model.

ml_g

(LearnerRegr, LearnerClassif, Learner, character(1))
A learner of the class LearnerRegr, which is available from mlr3 or its extension packages mlr3learners or mlr3extralearners. For binary treatment outcomes, an object of the class LearnerClassif can be passed, for example lrn("classif.cv_glmnet", s = "lambda.min"). Alternatively, a Learner object with public field task_type = "regr" or task_type = "classif" can be passed, respectively, for example of class GraphLearner.
ml_g refers to the nuisance function \(g_0(Z,X) = E[Y|X,Z]\).

ml_m

(LearnerClassif, Learner, character(1))
A learner of the class LearnerClassif, which is available from mlr3 or its extension packages mlr3learners or mlr3extralearners. Alternatively, a Learner object with public field task_type = "classif" can be passed, for example of class GraphLearner. The learner can possibly be passed with specified parameters, for example lrn("classif.cv_glmnet", s = "lambda.min").
ml_m refers to the nuisance function \(m_0(X) = E[Z|X]\).

ml_r

(LearnerClassif, Learner, character(1))
A learner of the class LearnerClassif, which is available from mlr3 or its extension packages mlr3learners or mlr3extralearners. Alternatively, a Learner object with public field task_type = "classif" can be passed, for example of class GraphLearner. The learner can possibly be passed with specified parameters, for example lrn("classif.cv_glmnet", s = "lambda.min").
ml_r refers to the nuisance function \(r_0(Z,X) = E[D|X,Z]\).

n_folds

(integer(1))
Number of folds. Default is 5.

n_rep

(integer(1))
Number of repetitions for the sample splitting. Default is 1.

score

(character(1), function())
A character(1) ("LATE" is the only choice) specifying the score function. If a function() is provided, it must be of the form function(y, z, d, g0_hat, g1_hat, m_hat, r0_hat, r1_hat, smpls) and the returned output must be a named list() with elements psi_a and psi_b. Default is "LATE".

subgroups

(named list(2))
Named list(2) with options to adapt to cases with and without the subgroups of always-takers and never-takes. The entry always_takers(logical(1)) speficies whether there are always takers in the sample. The entry never_takers (logical(1)) speficies whether there are never takers in the sample. Default is list(always_takers = TRUE, never_takers = TRUE).

dml_procedure

(character(1))
A character(1) ("dml1" or "dml2") specifying the double machine learning algorithm. Default is "dml2".

trimming_rule

(character(1))
A character(1) ("truncate" is the only choice) specifying the trimming approach. Default is "truncate".

trimming_threshold

(numeric(1))
The threshold used for timming. Default is 1e-12.

draw_sample_splitting

(logical(1))
Indicates whether the sample splitting should be drawn during initialization of the object. Default is TRUE.

apply_cross_fitting

(logical(1))
Indicates whether cross-fitting should be applied. Default is TRUE.

---

Method clone()

The objects of this class are cloneable with this method.

Usage

DoubleMLIIVM$clone(deep = FALSE)

Arguments

deep

Whether to make a deep clone.

Examples

# \donttest{
library(DoubleML)
library(mlr3)
library(mlr3learners)
library(data.table)
set.seed(2)
ml_g = lrn("regr.ranger",
  num.trees = 100, mtry = 20,
  min.node.size = 2, max.depth = 5)
ml_m = lrn("classif.ranger",
  num.trees = 100, mtry = 20,
  min.node.size = 2, max.depth = 5)
ml_r = ml_m$clone()
obj_dml_data = make_iivm_data(
  theta = 0.5, n_obs = 1000,
  alpha_x = 1, dim_x = 20)
dml_iivm_obj = DoubleMLIIVM$new(obj_dml_data, ml_g, ml_m, ml_r)
dml_iivm_obj$fit()
dml_iivm_obj$summary()
#> Estimates and significance testing of the effect of target variables
#>   Estimate. Std. Error t value Pr(>|t|)  
#> d    0.5418     0.2149   2.522   0.0117 *
#> ---
#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#> 
#> 
# }

if (FALSE) {
library(DoubleML)
library(mlr3)
library(mlr3learners)
library(mlr3tuning)
library(data.table)
set.seed(2)
ml_g = lrn("regr.rpart")
ml_m = lrn("classif.rpart")
ml_r = ml_m$clone()
obj_dml_data = make_iivm_data(
  theta = 0.5, n_obs = 1000,
  alpha_x = 1, dim_x = 20)
dml_iivm_obj = DoubleMLIIVM$new(obj_dml_data, ml_g, ml_m, ml_r)
param_grid = list(
  "ml_g" = paradox::ParamSet$new(list(
    paradox::ParamDbl$new("cp", lower = 0.01, upper = 0.02),
    paradox::ParamInt$new("minsplit", lower = 1, upper = 2))),
  "ml_m" = paradox::ParamSet$new(list(
    paradox::ParamDbl$new("cp", lower = 0.01, upper = 0.02),
    paradox::ParamInt$new("minsplit", lower = 1, upper = 2))),
  "ml_r" = paradox::ParamSet$new(list(
    paradox::ParamDbl$new("cp", lower = 0.01, upper = 0.02),
    paradox::ParamInt$new("minsplit", lower = 1, upper = 2))))
# minimum requirements for tune_settings
tune_settings = list(
  terminator = mlr3tuning::trm("evals", n_evals = 5),
  algorithm = mlr3tuning::tnr("grid_search", resolution = 5))
dml_iivm_obj$tune(param_set = param_grid, tune_settings = tune_settings)
dml_iivm_obj$fit()
dml_iivm_obj$summary()
}