doubleml.DoubleMLIIVM

class doubleml.DoubleMLIIVM(obj_dml_data, ml_g, ml_m, ml_r, n_folds=5, n_rep=1, score='LATE', subgroups=None, dml_procedure='dml2', trimming_rule='truncate', trimming_threshold=1e-12, draw_sample_splitting=True, apply_cross_fitting=True)

Double machine learning for interactive IV regression models

Parameters

• obj_dml_data (DoubleMLData object) – The DoubleMLData object providing the data and specifying the variables for the causal model.

• ml_g (estimator implementing fit() and predict()) – A machine learner implementing fit() and predict() methods (e.g. sklearn.ensemble.RandomForestRegressor) for the nuisance function \(g_0(Z,X) = E[Y|X,Z]\). For a binary outcome variable \(Y\) (with values 0 and 1), a classifier implementing fit() and predict_proba() can also be specified. If sklearn.base.is_classifier() returns True, predict_proba() is used otherwise predict().

• ml_m (classifier implementing fit() and predict_proba()) – A machine learner implementing fit() and predict_proba() methods (e.g. sklearn.ensemble.RandomForestClassifier) for the nuisance function \(m_0(X) = E[Z|X]\).

• ml_r (classifier implementing fit() and predict_proba()) – A machine learner implementing fit() and predict_proba() methods (e.g. sklearn.ensemble.RandomForestClassifier) for the nuisance function \(r_0(Z,X) = E[D|X,Z]\).

• n_folds (int) – Number of folds. Default is 5.

• n_rep (int) – Number of repetitons for the sample splitting. Default is 1.

• score (str or callable) – A str ('LATE' is the only choice) specifying the score function or a callable object / function with signature psi_a, psi_b = score(y, z, d, g_hat0, g_hat1, m_hat, r_hat0, r_hat1, smpls). Default is 'LATE'.

• subgroups (dict or None) – Dictionary with options to adapt to cases with and without the subgroups of always-takers and never-takes. The logical item always_takers speficies whether there are always takers in the sample. The logical item never_takers speficies whether there are never takers in the sample. Default is {'always_takers': True, 'never_takers': True}.

• dml_procedure (str) – A str ('dml1' or 'dml2') specifying the double machine learning algorithm. Default is 'dml2'.

• trimming_rule (str) – A str ('truncate' is the only choice) specifying the trimming approach. Default is 'truncate'.

• trimming_threshold (float) – The threshold used for trimming. Default is 1e-12.

• draw_sample_splitting (bool) – Indicates whether the sample splitting should be drawn during initialization of the object. Default is True.

• apply_cross_fitting (bool) – Indicates whether cross-fitting should be applied. Default is True.

Examples

>>> import numpy as np
>>> import doubleml as dml
>>> from doubleml.datasets import make_iivm_data
>>> from sklearn.ensemble import RandomForestRegressor, RandomForestClassifier
>>> np.random.seed(3141)
>>> ml_g = RandomForestRegressor(n_estimators=100, max_features=20, max_depth=5, min_samples_leaf=2)
>>> ml_m = RandomForestClassifier(n_estimators=100, max_features=20, max_depth=5, min_samples_leaf=2)
>>> ml_r = RandomForestClassifier(n_estimators=100, max_features=20, max_depth=5, min_samples_leaf=2)
>>> data = make_iivm_data(theta=0.5, n_obs=1000, dim_x=20, alpha_x=1.0, return_type='DataFrame')
>>> obj_dml_data = dml.DoubleMLData(data, 'y', 'd', z_cols='z')
>>> dml_iivm_obj = dml.DoubleMLIIVM(obj_dml_data, ml_g, ml_m, ml_r)
>>> dml_iivm_obj.fit().summary
       coef   std err         t     P>|t|     2.5 %    97.5 %
d  0.378351  0.190648  1.984551  0.047194  0.004688  0.752015

Notes

Interactive IV regression (IIVM) models take the form

\[ \begin{align}\begin{aligned}Y = \ell_0(D, X) + \zeta, & &\mathbb{E}(\zeta | Z, X) = 0,\\Z = m_0(X) + V, & &\mathbb{E}(V | X) = 0,\end{aligned}\end{align} \]

where the treatment variable is binary, \(D \in \lbrace 0,1 \rbrace\) and the instrument is binary, \(Z \in \lbrace 0,1 \rbrace\). Consider the functions \(g_0\), \(r_0\) and \(m_0\), where \(g_0\) maps the support of \((Z,X)\) to \(\mathbb{R}\) and \(r_0\) and \(m_0\) respectively map the support of \((Z,X)\) and \(X\) to \((\varepsilon, 1-\varepsilon)\) for some \(\varepsilon \in (0, 1/2)\), such that

\[ \begin{align}\begin{aligned}Y = g_0(Z, X) + \nu, & &\mathbb{E}(\nu| Z, X) = 0,\\D = r_0(Z, X) + U, & &\mathbb{E}(U | Z, X) = 0,\\Z = m_0(X) + V, & &\mathbb{E}(V | X) = 0.\end{aligned}\end{align} \]

The target parameter of interest in this model is the local average treatment effect (LATE),

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

Methods

bootstrap([method, n_rep_boot])	Multiplier bootstrap for DoubleML models.
confint([joint, level])	Confidence intervals for DoubleML models.
draw_sample_splitting()	Draw sample splitting for DoubleML models.
fit([n_jobs_cv, keep_scores, ...])	Estimate DoubleML models.
get_params(learner)	Get hyperparameters for the nuisance model of DoubleML models.
p_adjust([method])	Multiple testing adjustment for DoubleML models.
set_ml_nuisance_params(learner, treat_var, ...)	Set hyperparameters for the nuisance models of DoubleML models.
set_sample_splitting(all_smpls)	Set the sample splitting for DoubleML models.
tune(param_grids[, tune_on_folds, ...])	Hyperparameter-tuning for DoubleML models.

Attributes

all_coef	Estimates of the causal parameter(s) for the n_rep different sample splits after calling fit().
all_dml1_coef	Estimates of the causal parameter(s) for the n_rep x n_folds different folds after calling fit() with dml_procedure='dml1'.
all_se	Standard errors of the causal parameter(s) for the n_rep different sample splits after calling fit().
apply_cross_fitting	Indicates whether cross-fitting should be applied.
boot_coef	Bootstrapped coefficients for the causal parameter(s) after calling fit() and bootstrap().
boot_t_stat	Bootstrapped t-statistics for the causal parameter(s) after calling fit() and bootstrap().
coef	Estimates for the causal parameter(s) after calling fit().
dml_procedure	The double machine learning algorithm.
learner	The machine learners for the nuisance functions.
learner_names	The names of the learners.
models	The fitted nuisance models.
n_folds	Number of folds.
n_rep	Number of repetitions for the sample splitting.
n_rep_boot	The number of bootstrap replications.
params	The hyperparameters of the learners.
params_names	The names of the nuisance models with hyperparameters.
predictions	The predictions of the nuisance models.
psi	Values of the score function \(\psi(W; \theta, \eta) = \psi_a(W; \eta) \theta + \psi_b(W; \eta)\) after calling fit().
psi_a	Values of the score function component \(\psi_a(W; \eta)\) after calling fit().
psi_b	Values of the score function component \(\psi_b(W; \eta)\) after calling fit().
pval	p-values for the causal parameter(s) after calling fit().
score	The score function.
se	Standard errors for the causal parameter(s) after calling fit().
smpls	The partition used for cross-fitting.
smpls_cluster	The partition of clusters used for cross-fitting.
summary	A summary for the estimated causal effect after calling fit().
t_stat	t-statistics for the causal parameter(s) after calling fit().

DoubleMLIIVM.bootstrap(method='normal', n_rep_boot=500)

Multiplier bootstrap for DoubleML models.

Parameters

• method (str) – A str ('Bayes', 'normal' or 'wild') specifying the multiplier bootstrap method. Default is 'normal'

• n_rep_boot (int) – The number of bootstrap replications.

Returns

self

Return type

object

DoubleMLIIVM.confint(joint=False, level=0.95)

Confidence intervals for DoubleML models.

Parameters

• joint (bool) – Indicates whether joint confidence intervals are computed. Default is False

• level (float) – The confidence level. Default is 0.95.

Returns

df_ci – A data frame with the confidence interval(s).

Return type

pd.DataFrame

DoubleMLIIVM.draw_sample_splitting()

Draw sample splitting for DoubleML models.

The samples are drawn according to the attributes n_folds, n_rep and apply_cross_fitting.

Returns

self

Return type

object

DoubleMLIIVM.fit(n_jobs_cv=None, keep_scores=True, store_predictions=False, store_models=False)

Estimate DoubleML models.

Parameters

• n_jobs_cv (None or int) – The number of CPUs to use to fit the learners. None means 1. Default is None.

• keep_scores (bool) – Indicates whether the score function evaluations should be stored in psi, psi_a and psi_b. Default is True.

• store_predictions (bool) – Indicates whether the predictions for the nuisance functions should be stored in predictions. Default is False.

• store_models (bool) – Indicates whether the fitted models for the nuisance functions should be stored in models. This allows to analyze the fitted models or extract information like variable importance. Default is False.

Returns

self

Return type

object

DoubleMLIIVM.get_params(learner)

Get hyperparameters for the nuisance model of DoubleML models.

Parameters

learner (str) – The nuisance model / learner (see attribute params_names).

Returns

params – Parameters for the nuisance model / learner.

Return type

dict

DoubleMLIIVM.p_adjust(method='romano-wolf')

Multiple testing adjustment for DoubleML models.

Parameters

method (str) – A str ('romano-wolf'', 'bonferroni', 'holm', etc) specifying the adjustment method. In addition to 'romano-wolf'', all methods implemented in statsmodels.stats.multitest.multipletests() can be applied. Default is 'romano-wolf'.

Returns

p_val – A data frame with adjusted p-values.

Return type

pd.DataFrame

DoubleMLIIVM.set_ml_nuisance_params(learner, treat_var, params)

Set hyperparameters for the nuisance models of DoubleML models.

Parameters

• learner (str) – The nuisance model / learner (see attribute params_names).

• treat_var (str) – The treatment variable (hyperparameters can be set treatment-variable specific).

• params (dict or list) – A dict with estimator parameters (used for all folds) or a nested list with fold specific parameters. The outer list needs to be of length n_rep and the inner list of length n_folds.

Returns

self

Return type

object

DoubleMLIIVM.set_sample_splitting(all_smpls)

Set the sample splitting for DoubleML models.

The attributes n_folds and n_rep are derived from the provided partition.

Parameters

all_smpls (list or tuple) –

If nested list of lists of tuples:

The outer list needs to provide an entry per repeated sample splitting (length of list is set as n_rep). The inner list needs to provide a tuple (train_ind, test_ind) per fold (length of list is set as n_folds). If tuples for more than one fold are provided, it must form a partition and apply_cross_fitting is set to True. Otherwise apply_cross_fitting is set to False and n_folds=2.

If list of tuples:

The list needs to provide a tuple (train_ind, test_ind) per fold (length of list is set as n_folds). If tuples for more than one fold are provided, it must form a partition and apply_cross_fitting is set to True. Otherwise apply_cross_fitting is set to False and n_folds=2. n_rep=1 is always set.

If tuple:

Must be a tuple with two elements train_ind and test_ind. No sample splitting is achieved if train_ind and test_ind are range(n_rep). Otherwise n_folds=2. apply_cross_fitting=False and n_rep=1 is always set.

Returns

self

Return type

object

Examples

>>> import numpy as np
>>> import doubleml as dml
>>> from doubleml.datasets import make_plr_CCDDHNR2018
>>> from sklearn.ensemble import RandomForestRegressor
>>> from sklearn.base import clone
>>> np.random.seed(3141)
>>> learner = RandomForestRegressor(max_depth=2, n_estimators=10)
>>> ml_g = learner
>>> ml_m = learner
>>> obj_dml_data = make_plr_CCDDHNR2018(n_obs=10, alpha=0.5)
>>> dml_plr_obj = dml.DoubleMLPLR(obj_dml_data, ml_g, ml_m)
>>> # simple sample splitting with two folds and without cross-fitting
>>> smpls = ([0, 1, 2, 3, 4], [5, 6, 7, 8, 9])
>>> dml_plr_obj.set_sample_splitting(smpls)
>>> # sample splitting with two folds and cross-fitting
>>> smpls = [([0, 1, 2, 3, 4], [5, 6, 7, 8, 9]),
>>>          ([5, 6, 7, 8, 9], [0, 1, 2, 3, 4])]
>>> dml_plr_obj.set_sample_splitting(smpls)
>>> # sample splitting with two folds and repeated cross-fitting with n_rep = 2
>>> smpls = [[([0, 1, 2, 3, 4], [5, 6, 7, 8, 9]),
>>>           ([5, 6, 7, 8, 9], [0, 1, 2, 3, 4])],
>>>          [([0, 2, 4, 6, 8], [1, 3, 5, 7, 9]),
>>>           ([1, 3, 5, 7, 9], [0, 2, 4, 6, 8])]]
>>> dml_plr_obj.set_sample_splitting(smpls)

DoubleMLIIVM.tune(param_grids, tune_on_folds=False, scoring_methods=None, n_folds_tune=5, search_mode='grid_search', n_iter_randomized_search=100, n_jobs_cv=None, set_as_params=True, return_tune_res=False)

Hyperparameter-tuning for DoubleML models.

The hyperparameter-tuning is performed using either an exhaustive search over specified parameter values implemented in sklearn.model_selection.GridSearchCV or via a randomized search implemented in sklearn.model_selection.RandomizedSearchCV.

Parameters

• param_grids (dict) – A dict with a parameter grid for each nuisance model / learner (see attribute learner_names).

• tune_on_folds (bool) – Indicates whether the tuning should be done fold-specific or globally. Default is False.

• scoring_methods (None or dict) – The scoring method used to evaluate the predictions. The scoring method must be set per nuisance model via a dict (see attribute learner_names for the keys). If None, the estimator’s score method is used. Default is None.

• n_folds_tune (int) – Number of folds used for tuning. Default is 5.

• search_mode (str) – A str ('grid_search' or 'randomized_search') specifying whether hyperparameters are optimized via sklearn.model_selection.GridSearchCV or sklearn.model_selection.RandomizedSearchCV. Default is 'grid_search'.

• n_iter_randomized_search (int) – If search_mode == 'randomized_search'. The number of parameter settings that are sampled. Default is 100.

• n_jobs_cv (None or int) – The number of CPUs to use to tune the learners. None means 1. Default is None.

• set_as_params (bool) – Indicates whether the hyperparameters should be set in order to be used when fit() is called. Default is True.

• return_tune_res (bool) – Indicates whether detailed tuning results should be returned. Default is False.

Returns

• self (object) – Returned if return_tune_res is False.

• tune_res (list) – A list containing detailed tuning results and the proposed hyperparameters. Returned if return_tune_res is True.