# Double machine learning for interactive IV regression models

Source:`R/double_ml_iivm.R`

`DoubleMLIIVM.Rd`

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:
`DoubleML`

,
`DoubleMLIRM`

,
`DoubleMLPLIV`

,
`DoubleMLPLR`

## 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

## 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`

.

## 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()
}
```