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

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

Inherited methods

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, character(1))
An object of the class mlr3 regression learner to pass a learner, possibly with specified parameters, for example lrn("regr.cv_glmnet", s = "lambda.min"). Alternatively, a character(1) specifying the name of a mlr3 regression learner that is available in mlr3 or its extension packages mlr3learners or mlr3extralearners, for example "regr.cv_glmnet".
ml_g refers to the nuisance function \(g_0(Z,X) = E[Y|X,Z]\).

ml_m

(LearnerClassif, character(1))
An object of the class mlr3 classification learner to pass a learner, possibly with specified parameters, for example lrn("classif.cv_glmnet", s = "lambda.min"). Alternatively, a character(1) specifying the name of a mlr3 classification learner that is available in mlr3 or its extension packages mlr3learners or mlr3extralearners, for example "classif.cv_glmnet".
ml_m refers to the nuisance function \(m_0(X) = E[Z|X]\).

ml_r

(LearnerClassif, character(1))
An object of the class mlr3 classification learner to pass a learner, possibly with specified parameters, for example lrn("classif.cv_glmnet", s = "lambda.min"). Alternatively, a character(1) specifying the name of a mlr3 classification learner that is available in mlr3 or its extension packages mlr3learners or mlr3extralearners, for example "classif.cv_glmnet".
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() }