Package 'ddml'

Random subsample from the data of Angrist & Evans (1991).

Description

Random subsample from the data of Angrist & Evans (1991).

Usage

AE98

Format

A data frame with 5,000 rows and 13 variables.

worked

Indicator equal to 1 if the mother is employed.

weeksw

Number of weeks of employment.

hoursw

Hours worked per week.

morekids

Indicator equal to 1 if the mother has more than 2 kids.

samesex

Indicator equal to 1 if the first two children are of the same sex.

age

Age in years.

agefst

Age in years at birth of the first child.

black

Indicator equal to 1 if the mother is black.

hisp

Indicator equal to 1 if the mother is Hispanic.

othrace

Indicator equal to 1 if the mother is neither black nor Hispanic.

educ

Years of education.

boy1st

Indicator equal to 1 if the first child is male.

boy2nd

Indicator equal to 1 if the second child is male.

Source

https://dataverse.harvard.edu/dataset.xhtml?persistentId=hdl:1902.1/11288

References

Angrist J, Evans W (1998). "Children and Their Parents' Labor Supply: Evidence from Exogenous Variation in Family Size." American Economic Review, 88(3), 450-477.

---

Cross-Predictions using Stacking.

Description

Cross-predictions using stacking.

Usage

crosspred(
  y,
  X,
  Z = NULL,
  learners,
  sample_folds = 2,
  ensemble_type = "average",
  cv_folds = 5,
  custom_ensemble_weights = NULL,
  compute_insample_predictions = FALSE,
  compute_predictions_bylearner = FALSE,
  subsamples = NULL,
  cv_subsamples_list = NULL,
  silent = FALSE,
  progress = NULL,
  auxiliary_X = NULL
)

Arguments

y	The outcome variable.
X	A (sparse) matrix of predictive variables.
Z	Optional additional (sparse) matrix of predictive variables.
learners	May take one of two forms, depending on whether a single learner or stacking with multiple learners is used for estimation of the predictor. If a single learner is used, learners is a list with two named elements: what The base learner function. The function must be such that it predicts a named input y using a named input X. args Optional arguments to be passed to what. If stacking with multiple learners is used, learners is a list of lists, each containing four named elements: fun The base learner function. The function must be such that it predicts a named input y using a named input X. args Optional arguments to be passed to fun. assign_X An optional vector of column indices corresponding to predictive variables in X that are passed to the base learner. assign_Z An optional vector of column indices corresponding to predictive in Z that are passed to the base learner. Omission of the args element results in default arguments being used in fun. Omission of assign_X (and/or assign_Z) results in inclusion of all variables in X (and/or Z).
sample_folds	Number of cross-fitting folds.
ensemble_type	Ensemble method to combine base learners into final estimate of the conditional expectation functions. Possible values are: "nnls" Non-negative least squares. "nnls1" Non-negative least squares with the constraint that all weights sum to one. "singlebest" Select base learner with minimum MSPE. "ols" Ordinary least squares. "average" Simple average over base learners. Multiple ensemble types may be passed as a vector of strings.
cv_folds	Number of folds used for cross-validation in ensemble construction.
custom_ensemble_weights	A numerical matrix with user-specified ensemble weights. Each column corresponds to a custom ensemble specification, each row corresponds to a base learner in learners (in chronological order). Optional column names are used to name the estimation results corresponding the custom ensemble specification.
compute_insample_predictions	Indicator equal to 1 if in-sample predictions should also be computed.
compute_predictions_bylearner	Indicator equal to 1 if in-sample predictions should also be computed for each learner (rather than the entire ensemble).
subsamples	List of vectors with sample indices for cross-fitting.
cv_subsamples_list	List of lists, each corresponding to a subsample containing vectors with subsample indices for cross-validation.
silent	Boolean to silence estimation updates.
progress	String to print before learner and cv fold progress.
auxiliary_X	An optional list of matrices of length sample_folds, each containing additional observations to calculate predictions for.

Value

crosspred returns a list containing the following components:

oos_fitted

A matrix of out-of-sample predictions, each column corresponding to an ensemble type (in chronological order).

weights

An array, providing the weight assigned to each base learner (in chronological order) by the ensemble procedures.

is_fitted

When compute_insample_predictions = T. a list of matrices with in-sample predictions by sample fold.

auxiliary_fitted

When auxiliary_X is not NULL, a list of matrices with additional predictions.

oos_fitted_bylearner

When compute_predictions_bylearner = T, a matrix of out-of-sample predictions, each column corresponding to a base learner (in chronological order).

is_fitted_bylearner

When compute_insample_predictions = T and compute_predictions_bylearner = T, a list of matrices with in-sample predictions by sample fold.

auxiliary_fitted_bylearner

When auxiliary_X is not NULL and compute_predictions_bylearner = T, a list of matrices with additional predictions for each learner.

References

Ahrens A, Hansen C B, Schaffer M E, Wiemann T (2023). "ddml: Double/debiased machine learning in Stata." https://arxiv.org/abs/2301.09397

Wolpert D H (1992). "Stacked generalization." Neural Networks, 5(2), 241-259.

See Also

Other utilities: crossval(), shortstacking()

Examples

# Construct variables from the included Angrist & Evans (1998) data
y = AE98[, "worked"]
X = AE98[, c("morekids", "age","agefst","black","hisp","othrace","educ")]

# Compute cross-predictions using stacking with base learners ols and lasso.
#     Two stacking approaches are simultaneously computed: Equally
#     weighted (ensemble_type = "average") and MSPE-minimizing with weights
#     in the unit simplex (ensemble_type = "nnls1"). Predictions for each
#     learner are also calculated.
crosspred_res <- crosspred(y, X,
                           learners = list(list(fun = ols),
                                           list(fun = mdl_glmnet)),
                           ensemble_type = c("average",
                                             "nnls1",
                                             "singlebest"),
                           compute_predictions_bylearner = TRUE,
                           sample_folds = 2,
                           cv_folds = 2,
                           silent = TRUE)
dim(crosspred_res$oos_fitted) # = length(y) by length(ensemble_type)
dim(crosspred_res$oos_fitted_bylearner) # = length(y) by length(learners)

---

Estimator of the Mean Squared Prediction Error using Cross-Validation.

Description

Estimator of the mean squared prediction error of different learners using cross-validation.

Usage

crossval(
  y,
  X,
  Z = NULL,
  learners,
  cv_folds = 5,
  cv_subsamples = NULL,
  silent = FALSE,
  progress = NULL
)

Arguments

y	The outcome variable.
X	A (sparse) matrix of predictive variables.
Z	Optional additional (sparse) matrix of predictive variables.
learners	learners is a list of lists, each containing four named elements: fun The base learner function. The function must be such that it predicts a named input y using a named input X. args Optional arguments to be passed to fun. assign_X An optional vector of column indices corresponding to variables in X that are passed to the base learner. assign_Z An optional vector of column indices corresponding to variables in Z that are passed to the base learner. Omission of the args element results in default arguments being used in fun. Omission of assign_X (and/or assign_Z) results in inclusion of all predictive variables in X (and/or Z).
cv_folds	Number of folds used for cross-validation.
cv_subsamples	List of vectors with sample indices for cross-validation.
silent	Boolean to silence estimation updates.
progress	String to print before learner and cv fold progress.

Value

crossval returns a list containing the following components:

mspe

A vector of MSPE estimates, each corresponding to a base learners (in chronological order).

oos_resid

A matrix of out-of-sample prediction errors, each column corresponding to a base learners (in chronological order).

cv_subsamples

Pass-through of cv_subsamples. See above.

See Also

Other utilities: crosspred(), shortstacking()

Examples

# Construct variables from the included Angrist & Evans (1998) data
y = AE98[, "worked"]
X = AE98[, c("morekids", "age","agefst","black","hisp","othrace","educ")]

# Compare ols, lasso, and ridge using 4-fold cross-validation
cv_res <- crossval(y, X,
                   learners = list(list(fun = ols),
                                   list(fun = mdl_glmnet),
                                   list(fun = mdl_glmnet,
                                        args = list(alpha = 0))),
                   cv_folds = 4,
                   silent = TRUE)
cv_res$mspe

---

ddml: Double/Debiased Machine Learning in R

Description

Estimate common causal parameters using double/debiased machine learning as proposed by Chernozhukov et al. (2018). 'ddml' simplifies estimation based on (short-)stacking, which leverages multiple base learners to increase robustness to the underlying data generating process.

References

Chernozhukov V, Chetverikov D, Demirer M, Duflo E, Hansen C B, Newey W, Robins J (2018). "Double/debiased machine learning for treatment and structural parameters." The Econometrics Journal, 21(1), C1-C68.

---

Estimators of Average Treatment Effects.

Description

Estimators of the average treatment effect and the average treatment effect on the treated.

Usage

ddml_ate(
  y,
  D,
  X,
  learners,
  learners_DX = learners,
  sample_folds = 10,
  ensemble_type = "nnls",
  shortstack = FALSE,
  cv_folds = 10,
  custom_ensemble_weights = NULL,
  custom_ensemble_weights_DX = custom_ensemble_weights,
  cluster_variable = seq_along(y),
  subsamples_byD = NULL,
  cv_subsamples_byD = NULL,
  trim = 0.01,
  silent = FALSE
)

ddml_att(
  y,
  D,
  X,
  learners,
  learners_DX = learners,
  sample_folds = 10,
  ensemble_type = "nnls",
  shortstack = FALSE,
  cv_folds = 10,
  custom_ensemble_weights = NULL,
  custom_ensemble_weights_DX = custom_ensemble_weights,
  cluster_variable = seq_along(y),
  subsamples_byD = NULL,
  cv_subsamples_byD = NULL,
  trim = 0.01,
  silent = FALSE
)

Arguments

y	The outcome variable.
D	The binary endogenous variable of interest.
X	A (sparse) matrix of control variables.
learners	May take one of two forms, depending on whether a single learner or stacking with multiple learners is used for estimation of the conditional expectation functions. If a single learner is used, learners is a list with two named elements: what The base learner function. The function must be such that it predicts a named input y using a named input X. args Optional arguments to be passed to what. If stacking with multiple learners is used, learners is a list of lists, each containing four named elements: fun The base learner function. The function must be such that it predicts a named input y using a named input X. args Optional arguments to be passed to fun. assign_X An optional vector of column indices corresponding to control variables in X that are passed to the base learner. Omission of the args element results in default arguments being used in fun. Omission of assign_X results in inclusion of all variables in X.
learners_DX	Optional argument to allow for different estimators of $E[D|X]$. Setup is identical to learners.
sample_folds	Number of cross-fitting folds.
ensemble_type	Ensemble method to combine base learners into final estimate of the conditional expectation functions. Possible values are: "nnls" Non-negative least squares. "nnls1" Non-negative least squares with the constraint that all weights sum to one. "singlebest" Select base learner with minimum MSPE. "ols" Ordinary least squares. "average" Simple average over base learners. Multiple ensemble types may be passed as a vector of strings.
shortstack	Boolean to use short-stacking.
cv_folds	Number of folds used for cross-validation in ensemble construction.
custom_ensemble_weights	A numerical matrix with user-specified ensemble weights. Each column corresponds to a custom ensemble specification, each row corresponds to a base learner in learners (in chronological order). Optional column names are used to name the estimation results corresponding the custom ensemble specification.
custom_ensemble_weights_DX	Optional argument to allow for different custom ensemble weights for learners_DX. Setup is identical to custom_ensemble_weights. Note: custom_ensemble_weights and custom_ensemble_weights_DX must have the same number of columns.
cluster_variable	A vector of cluster indices.
subsamples_byD	List of two lists corresponding to the two treatment levels. Each list contains vectors with sample indices for cross-fitting.
cv_subsamples_byD	List of two lists, each corresponding to one of the two treatment levels. Each of the two lists contains lists, each corresponding to a subsample and contains vectors with subsample indices for cross-validation.
trim	Number in (0, 1) for trimming the estimated propensity scores at trim and 1-trim.
silent	Boolean to silence estimation updates.

Details

ddml_ate and ddml_att provide double/debiased machine learning estimators for the average treatment effect and the average treatment effect on the treated, respectively, in the interactive model given by

$Y = g_0(D, X) + U,$

where $(Y, D, X, U)$ is a random vector such that $\operatorname{supp} D = \{0,1\}$, $E[U\vert D, X] = 0$, and $\Pr(D=1\vert X) \in (0, 1)$ with probability 1, and $g_0$ is an unknown nuisance function.

In this model, the average treatment effect is defined as

$\theta_0^{\textrm{ATE}} \equiv E[g_0(1, X) - g_0(0, X)]$.

and the average treatment effect on the treated is defined as

$\theta_0^{\textrm{ATT}} \equiv E[g_0(1, X) - g_0(0, X)\vert D = 1]$.

Value

ddml_ate and ddml_att return an object of S3 class ddml_ate and ddml_att, respectively. An object of class ddml_ate or ddml_att is a list containing the following components:

ate / att

A vector with the average treatment effect / average treatment effect on the treated estimates.

weights

A list of matrices, providing the weight assigned to each base learner (in chronological order) by the ensemble procedure.

mspe

A list of matrices, providing the MSPE of each base learner (in chronological order) computed by the cross-validation step in the ensemble construction.

psi_a, psi_b

Matrices needed for the computation of scores. Used in summary.ddml_ate() or summary.ddml_att().

oos_pred

List of matrices, providing the reduced form predicted values.

learners,learners_DX,cluster_variable, subsamples_D0,subsamples_D1, cv_subsamples_list_D0,cv_subsamples_list_D1, ensemble_type

Pass-through of selected user-provided arguments. See above.

References

Ahrens A, Hansen C B, Schaffer M E, Wiemann T (2023). "ddml: Double/debiased machine learning in Stata." https://arxiv.org/abs/2301.09397

Chernozhukov V, Chetverikov D, Demirer M, Duflo E, Hansen C B, Newey W, Robins J (2018). "Double/debiased machine learning for treatment and structural parameters." The Econometrics Journal, 21(1), C1-C68.

Wolpert D H (1992). "Stacked generalization." Neural Networks, 5(2), 241-259.

See Also

summary.ddml_ate(), summary.ddml_att()

Other ddml: ddml_fpliv(), ddml_late(), ddml_pliv(), ddml_plm()

Examples

# Construct variables from the included Angrist & Evans (1998) data
y = AE98[, "worked"]
D = AE98[, "morekids"]
X = AE98[, c("age","agefst","black","hisp","othrace","educ")]

# Estimate the average treatment effect using a single base learner, ridge.
ate_fit <- ddml_ate(y, D, X,
                    learners = list(what = mdl_glmnet,
                                    args = list(alpha = 0)),
                    sample_folds = 2,
                    silent = TRUE)
summary(ate_fit)

# Estimate the average treatment effect using short-stacking with base
#     learners ols, lasso, and ridge. We can also use custom_ensemble_weights
#     to estimate the ATE using every individual base learner.
weights_everylearner <- diag(1, 3)
colnames(weights_everylearner) <- c("mdl:ols", "mdl:lasso", "mdl:ridge")
ate_fit <- ddml_ate(y, D, X,
                    learners = list(list(fun = ols),
                                    list(fun = mdl_glmnet),
                                    list(fun = mdl_glmnet,
                                         args = list(alpha = 0))),
                    ensemble_type = 'nnls',
                    custom_ensemble_weights = weights_everylearner,
                    shortstack = TRUE,
                    sample_folds = 2,
                    silent = TRUE)
summary(ate_fit)

---

Estimator for the Flexible Partially Linear IV Model.

Description

Estimator for the flexible partially linear IV model.

Usage

ddml_fpliv(
  y,
  D,
  Z,
  X,
  learners,
  learners_DXZ = learners,
  learners_DX = learners,
  sample_folds = 10,
  ensemble_type = "nnls",
  shortstack = FALSE,
  cv_folds = 10,
  enforce_LIE = TRUE,
  custom_ensemble_weights = NULL,
  custom_ensemble_weights_DXZ = custom_ensemble_weights,
  custom_ensemble_weights_DX = custom_ensemble_weights,
  cluster_variable = seq_along(y),
  subsamples = NULL,
  cv_subsamples_list = NULL,
  silent = FALSE
)

Arguments

y	The outcome variable.
D	A matrix of endogenous variables.
Z	A (sparse) matrix of instruments.
X	A (sparse) matrix of control variables.
learners	May take one of two forms, depending on whether a single learner or stacking with multiple learners is used for estimation of the conditional expectation functions. If a single learner is used, learners is a list with two named elements: what The base learner function. The function must be such that it predicts a named input y using a named input X. args Optional arguments to be passed to what. If stacking with multiple learners is used, learners is a list of lists, each containing four named elements: fun The base learner function. The function must be such that it predicts a named input y using a named input X. args Optional arguments to be passed to fun. assign_X An optional vector of column indices corresponding to control variables in X that are passed to the base learner. assign_Z An optional vector of column indices corresponding to instruments in Z that are passed to the base learner. Omission of the args element results in default arguments being used in fun. Omission of assign_X (and/or assign_Z) results in inclusion of all variables in X (and/or Z).
learners_DXZ, learners_DX	Optional arguments to allow for different estimators of $E[D \vert X, Z]$, $E[D \vert X]$. Setup is identical to learners.
sample_folds	Number of cross-fitting folds.
ensemble_type	Ensemble method to combine base learners into final estimate of the conditional expectation functions. Possible values are: "nnls" Non-negative least squares. "nnls1" Non-negative least squares with the constraint that all weights sum to one. "singlebest" Select base learner with minimum MSPE. "ols" Ordinary least squares. "average" Simple average over base learners. Multiple ensemble types may be passed as a vector of strings.
shortstack	Boolean to use short-stacking.
cv_folds	Number of folds used for cross-validation in ensemble construction.
enforce_LIE	Indicator equal to 1 if the law of iterated expectations is enforced in the first stage.
custom_ensemble_weights	A numerical matrix with user-specified ensemble weights. Each column corresponds to a custom ensemble specification, each row corresponds to a base learner in learners (in chronological order). Optional column names are used to name the estimation results corresponding the custom ensemble specification.
custom_ensemble_weights_DXZ, custom_ensemble_weights_DX	Optional arguments to allow for different custom ensemble weights for learners_DXZ,learners_DX. Setup is identical to custom_ensemble_weights. Note: custom_ensemble_weights and custom_ensemble_weights_DXZ,custom_ensemble_weights_DX must have the same number of columns.
cluster_variable	A vector of cluster indices.
subsamples	List of vectors with sample indices for cross-fitting.
cv_subsamples_list	List of lists, each corresponding to a subsample containing vectors with subsample indices for cross-validation.
silent	Boolean to silence estimation updates.

Details

ddml_fpliv provides a double/debiased machine learning estimator for the parameter of interest $\theta_0$ in the partially linear IV model given by

$Y = \theta_0D + g_0(X) + U,$

where $(Y, D, X, Z, U)$ is a random vector such that $E[U\vert X, Z] = 0$ and $E[Var(E[D\vert X, Z]\vert X)] \neq 0$, and $g_0$ is an unknown nuisance function.

Value

ddml_fpliv returns an object of S3 class ddml_fpliv. An object of class ddml_fpliv is a list containing the following components:

coef

A vector with the $\theta_0$ estimates.

weights

A list of matrices, providing the weight assigned to each base learner (in chronological order) by the ensemble procedure.

mspe

A list of matrices, providing the MSPE of each base learner (in chronological order) computed by the cross-validation step in the ensemble construction.

iv_fit

Object of class ivreg from the IV regression of $Y - \hat{E}[Y\vert X]$ on $D - \hat{E}[D\vert X]$ using $\hat{E}[D\vert X,Z] - \hat{E}[D\vert X]$ as the instrument.

learners,learners_DX,learners_DXZ, cluster_variable,subsamples, cv_subsamples_list,ensemble_type

Pass-through of selected user-provided arguments. See above.

References

Ahrens A, Hansen C B, Schaffer M E, Wiemann T (2023). "ddml: Double/debiased machine learning in Stata." https://arxiv.org/abs/2301.09397

Chernozhukov V, Chetverikov D, Demirer M, Duflo E, Hansen C B, Newey W, Robins J (2018). "Double/debiased machine learning for treatment and structural parameters." The Econometrics Journal, 21(1), C1-C68.

Wolpert D H (1992). "Stacked generalization." Neural Networks, 5(2), 241-259.

See Also

summary.ddml_fpliv(), AER::ivreg()

Other ddml: ddml_ate(), ddml_late(), ddml_pliv(), ddml_plm()

Examples

# Construct variables from the included Angrist & Evans (1998) data
y = AE98[, "worked"]
D = AE98[, "morekids"]
Z = AE98[, "samesex", drop = FALSE]
X = AE98[, c("age","agefst","black","hisp","othrace","educ")]

# Estimate the partially linear IV model using a single base learner: Ridge.
fpliv_fit <- ddml_fpliv(y, D, Z, X,
                        learners = list(what = mdl_glmnet,
                                        args = list(alpha = 0)),
                        sample_folds = 2,
                        silent = TRUE)
summary(fpliv_fit)

---

Estimator of the Local Average Treatment Effect.

Description

Estimator of the local average treatment effect.

Usage

ddml_late(
  y,
  D,
  Z,
  X,
  learners,
  learners_DXZ = learners,
  learners_ZX = learners,
  sample_folds = 10,
  ensemble_type = "nnls",
  shortstack = FALSE,
  cv_folds = 10,
  custom_ensemble_weights = NULL,
  custom_ensemble_weights_DXZ = custom_ensemble_weights,
  custom_ensemble_weights_ZX = custom_ensemble_weights,
  cluster_variable = seq_along(y),
  subsamples_byZ = NULL,
  cv_subsamples_byZ = NULL,
  trim = 0.01,
  silent = FALSE
)

Arguments

y	The outcome variable.
D	The binary endogenous variable of interest.
Z	Binary instrumental variable.
X	A (sparse) matrix of control variables.
learners	May take one of two forms, depending on whether a single learner or stacking with multiple learners is used for estimation of the conditional expectation functions. If a single learner is used, learners is a list with two named elements: what The base learner function. The function must be such that it predicts a named input y using a named input X. args Optional arguments to be passed to what. If stacking with multiple learners is used, learners is a list of lists, each containing four named elements: fun The base learner function. The function must be such that it predicts a named input y using a named input X. args Optional arguments to be passed to fun. assign_X An optional vector of column indices corresponding to control variables in X that are passed to the base learner. assign_Z An optional vector of column indices corresponding to instruments in Z that are passed to the base learner. Omission of the args element results in default arguments being used in fun. Omission of assign_X (and/or assign_Z) results in inclusion of all variables in X (and/or Z).
learners_DXZ, learners_ZX	Optional arguments to allow for different estimators of $E[D \vert X, Z]$, $E[Z \vert X]$. Setup is identical to learners.
sample_folds	Number of cross-fitting folds.
ensemble_type	Ensemble method to combine base learners into final estimate of the conditional expectation functions. Possible values are: "nnls" Non-negative least squares. "nnls1" Non-negative least squares with the constraint that all weights sum to one. "singlebest" Select base learner with minimum MSPE. "ols" Ordinary least squares. "average" Simple average over base learners. Multiple ensemble types may be passed as a vector of strings.
shortstack	Boolean to use short-stacking.
cv_folds	Number of folds used for cross-validation in ensemble construction.
custom_ensemble_weights	A numerical matrix with user-specified ensemble weights. Each column corresponds to a custom ensemble specification, each row corresponds to a base learner in learners (in chronological order). Optional column names are used to name the estimation results corresponding the custom ensemble specification.
custom_ensemble_weights_DXZ, custom_ensemble_weights_ZX	Optional arguments to allow for different custom ensemble weights for learners_DXZ,learners_ZX. Setup is identical to custom_ensemble_weights. Note: custom_ensemble_weights and custom_ensemble_weights_DXZ,custom_ensemble_weights_ZX must have the same number of columns.
cluster_variable	A vector of cluster indices.
subsamples_byZ	List of two lists corresponding to the two instrument levels. Each list contains vectors with sample indices for cross-fitting.
cv_subsamples_byZ	List of two lists, each corresponding to one of the two instrument levels. Each of the two lists contains lists, each corresponding to a subsample and contains vectors with subsample indices for cross-validation.
trim	Number in (0, 1) for trimming the estimated propensity scores at trim and 1-trim.
silent	Boolean to silence estimation updates.

Details

ddml_late provides a double/debiased machine learning estimator for the local average treatment effect in the interactive model given by

$Y = g_0(D, X) + U,$

where $(Y, D, X, Z, U)$ is a random vector such that $\operatorname{supp} D = \operatorname{supp} Z = \{0,1\}$, $E[U\vert X, Z] = 0$, $E[Var(E[D\vert X, Z]\vert X)] \neq 0$, $\Pr(Z=1\vert X) \in (0, 1)$ with probability 1, $p_0(1, X) \geq p_0(0, X)$ with probability 1 where $p_0(Z, X) \equiv \Pr(D=1\vert Z, X)$, and $g_0$ is an unknown nuisance function.

In this model, the local average treatment effect is defined as

$\theta_0^{\textrm{LATE}} \equiv E[g_0(1, X) - g_0(0, X)\vert p_0(1, X) > p(0, X)]$.

Value

ddml_late returns an object of S3 class ddml_late. An object of class ddml_late is a list containing the following components:

late

A vector with the average treatment effect estimates.

weights

A list of matrices, providing the weight assigned to each base learner (in chronological order) by the ensemble procedure.

mspe

A list of matrices, providing the MSPE of each base learner (in chronological order) computed by the cross-validation step in the ensemble construction.

psi_a, psi_b

Matrices needed for the computation of scores. Used in summary.ddml_late().

oos_pred

List of matrices, providing the reduced form predicted values.

learners,learners_DXZ,learners_ZX, cluster_variable,subsamples_Z0, subsamples_Z1,cv_subsamples_list_Z0, cv_subsamples_list_Z1,ensemble_type

Pass-through of selected user-provided arguments. See above.

References

Ahrens A, Hansen C B, Schaffer M E, Wiemann T (2023). "ddml: Double/debiased machine learning in Stata." https://arxiv.org/abs/2301.09397

Chernozhukov V, Chetverikov D, Demirer M, Duflo E, Hansen C B, Newey W, Robins J (2018). "Double/debiased machine learning for treatment and structural parameters." The Econometrics Journal, 21(1), C1-C68.

Imbens G, Angrist J (1004). "Identification and Estimation of Local Average Treatment Effects." Econometrica, 62(2), 467-475.

Wolpert D H (1992). "Stacked generalization." Neural Networks, 5(2), 241-259.

See Also

summary.ddml_late()

Other ddml: ddml_ate(), ddml_fpliv(), ddml_pliv(), ddml_plm()

Examples

# Construct variables from the included Angrist & Evans (1998) data
y = AE98[, "worked"]
D = AE98[, "morekids"]
Z = AE98[, "samesex"]
X = AE98[, c("age","agefst","black","hisp","othrace","educ")]

# Estimate the local average treatment effect using a single base learner,
#     ridge.
late_fit <- ddml_late(y, D, Z, X,
                      learners = list(what = mdl_glmnet,
                                      args = list(alpha = 0)),
                      sample_folds = 2,
                      silent = TRUE)
summary(late_fit)

# Estimate the local average treatment effect using short-stacking with base
#     learners ols, lasso, and ridge. We can also use custom_ensemble_weights
#     to estimate the ATE using every individual base learner.
weights_everylearner <- diag(1, 3)
colnames(weights_everylearner) <- c("mdl:ols", "mdl:lasso", "mdl:ridge")
late_fit <- ddml_late(y, D, Z, X,
                      learners = list(list(fun = ols),
                                      list(fun = mdl_glmnet),
                                      list(fun = mdl_glmnet,
                                           args = list(alpha = 0))),
                      ensemble_type = 'nnls',
                      custom_ensemble_weights = weights_everylearner,
                      shortstack = TRUE,
                      sample_folds = 2,
                      silent = TRUE)
summary(late_fit)

---

Estimator for the Partially Linear IV Model.

Description

Estimator for the partially linear IV model.

Usage

ddml_pliv(
  y,
  D,
  Z,
  X,
  learners,
  learners_DX = learners,
  learners_ZX = learners,
  sample_folds = 10,
  ensemble_type = "nnls",
  shortstack = FALSE,
  cv_folds = 10,
  custom_ensemble_weights = NULL,
  custom_ensemble_weights_DX = custom_ensemble_weights,
  custom_ensemble_weights_ZX = custom_ensemble_weights,
  cluster_variable = seq_along(y),
  subsamples = NULL,
  cv_subsamples_list = NULL,
  silent = FALSE
)

Arguments

y	The outcome variable.
D	A matrix of endogenous variables.
Z	A matrix of instruments.
X	A (sparse) matrix of control variables.
learners	May take one of two forms, depending on whether a single learner or stacking with multiple learners is used for estimation of the conditional expectation functions. If a single learner is used, learners is a list with two named elements: what The base learner function. The function must be such that it predicts a named input y using a named input X. args Optional arguments to be passed to what. If stacking with multiple learners is used, learners is a list of lists, each containing four named elements: fun The base learner function. The function must be such that it predicts a named input y using a named input X. args Optional arguments to be passed to fun. assign_X An optional vector of column indices corresponding to control variables in X that are passed to the base learner. assign_Z An optional vector of column indices corresponding to instruments in Z that are passed to the base learner. Omission of the args element results in default arguments being used in fun. Omission of assign_X (and/or assign_Z) results in inclusion of all variables in X (and/or Z).
learners_DX, learners_ZX	Optional arguments to allow for different base learners for estimation of $E[D|X]$, $E[Z|X]$. Setup is identical to learners.
sample_folds	Number of cross-fitting folds.
ensemble_type	Ensemble method to combine base learners into final estimate of the conditional expectation functions. Possible values are: "nnls" Non-negative least squares. "nnls1" Non-negative least squares with the constraint that all weights sum to one. "singlebest" Select base learner with minimum MSPE. "ols" Ordinary least squares. "average" Simple average over base learners. Multiple ensemble types may be passed as a vector of strings.
shortstack	Boolean to use short-stacking.
cv_folds	Number of folds used for cross-validation in ensemble construction.
custom_ensemble_weights	A numerical matrix with user-specified ensemble weights. Each column corresponds to a custom ensemble specification, each row corresponds to a base learner in learners (in chronological order). Optional column names are used to name the estimation results corresponding the custom ensemble specification.
custom_ensemble_weights_DX, custom_ensemble_weights_ZX	Optional arguments to allow for different custom ensemble weights for learners_DX,learners_ZX. Setup is identical to custom_ensemble_weights. Note: custom_ensemble_weights and custom_ensemble_weights_DX,custom_ensemble_weights_ZX must have the same number of columns.
cluster_variable	A vector of cluster indices.
subsamples	List of vectors with sample indices for cross-fitting.
cv_subsamples_list	List of lists, each corresponding to a subsample containing vectors with subsample indices for cross-validation.
silent	Boolean to silence estimation updates.

Details

ddml_pliv provides a double/debiased machine learning estimator for the parameter of interest $\theta_0$ in the partially linear IV model given by

$Y = \theta_0D + g_0(X) + U,$

where $(Y, D, X, Z, U)$ is a random vector such that $E[Cov(U, Z\vert X)] = 0$ and $E[Cov(D, Z\vert X)] \neq 0$, and $g_0$ is an unknown nuisance function.

Value

ddml_pliv returns an object of S3 class ddml_pliv. An object of class ddml_pliv is a list containing the following components:

coef

A vector with the $\theta_0$ estimates.

weights

A list of matrices, providing the weight assigned to each base learner (in chronological order) by the ensemble procedure.

mspe

A list of matrices, providing the MSPE of each base learner (in chronological order) computed by the cross-validation step in the ensemble construction.

iv_fit

Object of class ivreg from the IV regression of $Y - \hat{E}[Y\vert X]$ on $D - \hat{E}[D\vert X]$ using $Z - \hat{E}[Z\vert X]$ as the instrument. See also AER::ivreg() for details.

learners,learners_DX,learners_ZX, cluster_variable, subsamples, cv_subsamples_list,ensemble_type

Pass-through of selected user-provided arguments. See above.

References

Ahrens A, Hansen C B, Schaffer M E, Wiemann T (2023). "ddml: Double/debiased machine learning in Stata." https://arxiv.org/abs/2301.09397

Chernozhukov V, Chetverikov D, Demirer M, Duflo E, Hansen C B, Newey W, Robins J (2018). "Double/debiased machine learning for treatment and structural parameters." The Econometrics Journal, 21(1), C1-C68.

Kleiber C, Zeileis A (2008). Applied Econometrics with R. Springer-Verlag, New York.

Wolpert D H (1992). "Stacked generalization." Neural Networks, 5(2), 241-259.

See Also

summary.ddml_pliv(), AER::ivreg()

Other ddml: ddml_ate(), ddml_fpliv(), ddml_late(), ddml_plm()

Examples

# Construct variables from the included Angrist & Evans (1998) data
y = AE98[, "worked"]
D = AE98[, "morekids"]
Z = AE98[, "samesex"]
X = AE98[, c("age","agefst","black","hisp","othrace","educ")]

# Estimate the partially linear IV model using a single base learner, ridge.
pliv_fit <- ddml_pliv(y, D, Z, X,
                      learners = list(what = mdl_glmnet,
                                      args = list(alpha = 0)),
                      sample_folds = 2,
                      silent = TRUE)
summary(pliv_fit)

---

Estimator for the Partially Linear Model.

Description

Estimator for the partially linear model.

Usage

ddml_plm(
  y,
  D,
  X,
  learners,
  learners_DX = learners,
  sample_folds = 10,
  ensemble_type = "nnls",
  shortstack = FALSE,
  cv_folds = 10,
  custom_ensemble_weights = NULL,
  custom_ensemble_weights_DX = custom_ensemble_weights,
  cluster_variable = seq_along(y),
  subsamples = NULL,
  cv_subsamples_list = NULL,
  silent = FALSE
)

Arguments

y	The outcome variable.
D	A matrix of endogenous variables.
X	A (sparse) matrix of control variables.
learners	May take one of two forms, depending on whether a single learner or stacking with multiple learners is used for estimation of the conditional expectation functions. If a single learner is used, learners is a list with two named elements: what The base learner function. The function must be such that it predicts a named input y using a named input X. args Optional arguments to be passed to what. If stacking with multiple learners is used, learners is a list of lists, each containing four named elements: fun The base learner function. The function must be such that it predicts a named input y using a named input X. args Optional arguments to be passed to fun. assign_X An optional vector of column indices corresponding to control variables in X that are passed to the base learner. Omission of the args element results in default arguments being used in fun. Omission of assign_X results in inclusion of all variables in X.
learners_DX	Optional argument to allow for different estimators of $E[D|X]$. Setup is identical to learners.
sample_folds	Number of cross-fitting folds.
ensemble_type	Ensemble method to combine base learners into final estimate of the conditional expectation functions. Possible values are: "nnls" Non-negative least squares. "nnls1" Non-negative least squares with the constraint that all weights sum to one. "singlebest" Select base learner with minimum MSPE. "ols" Ordinary least squares. "average" Simple average over base learners. Multiple ensemble types may be passed as a vector of strings.
shortstack	Boolean to use short-stacking.
cv_folds	Number of folds used for cross-validation in ensemble construction.
custom_ensemble_weights	A numerical matrix with user-specified ensemble weights. Each column corresponds to a custom ensemble specification, each row corresponds to a base learner in learners (in chronological order). Optional column names are used to name the estimation results corresponding the custom ensemble specification.
custom_ensemble_weights_DX	Optional argument to allow for different custom ensemble weights for learners_DX. Setup is identical to custom_ensemble_weights. Note: custom_ensemble_weights and custom_ensemble_weights_DX must have the same number of columns.
cluster_variable	A vector of cluster indices.
subsamples	List of vectors with sample indices for cross-fitting.
cv_subsamples_list	List of lists, each corresponding to a subsample containing vectors with subsample indices for cross-validation.
silent	Boolean to silence estimation updates.

Details

ddml_plm provides a double/debiased machine learning estimator for the parameter of interest $\theta_0$ in the partially linear model given by

$Y = \theta_0D + g_0(X) + U,$

where $(Y, D, X, U)$ is a random vector such that $E[Cov(U, D\vert X)] = 0$ and $E[Var(D\vert X)] \neq 0$, and $g_0$ is an unknown nuisance function.

Value

ddml_plm returns an object of S3 class ddml_plm. An object of class ddml_plm is a list containing the following components:

coef

A vector with the $\theta_0$ estimates.

weights

A list of matrices, providing the weight assigned to each base learner (in chronological order) by the ensemble procedure.

mspe

A list of matrices, providing the MSPE of each base learner (in chronological order) computed by the cross-validation step in the ensemble construction.

ols_fit

Object of class lm from the second stage regression of $Y - \hat{E}[Y|X]$ on $D - \hat{E}[D|X]$.

learners,learners_DX,cluster_variable, subsamples, cv_subsamples_list, ensemble_type

Pass-through of selected user-provided arguments. See above.

References

Ahrens A, Hansen C B, Schaffer M E, Wiemann T (2023). "ddml: Double/debiased machine learning in Stata." https://arxiv.org/abs/2301.09397

Chernozhukov V, Chetverikov D, Demirer M, Duflo E, Hansen C B, Newey W, Robins J (2018). "Double/debiased machine learning for treatment and structural parameters." The Econometrics Journal, 21(1), C1-C68.

Wolpert D H (1992). "Stacked generalization." Neural Networks, 5(2), 241-259.

See Also

summary.ddml_plm()

Other ddml: ddml_ate(), ddml_fpliv(), ddml_late(), ddml_pliv()

Examples

# Construct variables from the included Angrist & Evans (1998) data
y = AE98[, "worked"]
D = AE98[, "morekids"]
X = AE98[, c("age","agefst","black","hisp","othrace","educ")]

# Estimate the partially linear model using a single base learner, ridge.
plm_fit <- ddml_plm(y, D, X,
                    learners = list(what = mdl_glmnet,
                                    args = list(alpha = 0)),
                    sample_folds = 2,
                    silent = TRUE)
summary(plm_fit)

# Estimate the partially linear model using short-stacking with base learners
#     ols, lasso, and ridge. We can also use custom_ensemble_weights
#     to estimate the ATE using every individual base learner.
weights_everylearner <- diag(1, 3)
colnames(weights_everylearner) <- c("mdl:ols", "mdl:lasso", "mdl:ridge")
plm_fit <- ddml_plm(y, D, X,
                    learners = list(list(fun = ols),
                                    list(fun = mdl_glmnet),
                                    list(fun = mdl_glmnet,
                                         args = list(alpha = 0))),
                    ensemble_type = 'nnls',
                    custom_ensemble_weights = weights_everylearner,
                    shortstack = TRUE,
                    sample_folds = 2,
                    silent = TRUE)
summary(plm_fit)

---

Wrapper for stats::glm().

Description

Simple wrapper for stats::glm().

Usage

mdl_glm(y, X, ...)

Arguments

y	The outcome variable.
X	The feature matrix.
...	Additional arguments passed to glm. See stats::glm() for a complete list of arguments.

Value

mdl_glm returns an object of S3 class mdl_glm as a simple mask of the return object of stats::glm().

See Also

stats::glm()

Other ml_wrapper: mdl_glmnet(), mdl_ranger(), mdl_xgboost(), ols()

Examples

glm_fit <- mdl_glm(sample(0:1, 100, replace = TRUE),
                   matrix(rnorm(1000), 100, 10))
class(glm_fit)

---

Wrapper for glmnet::glmnet().

Description

Simple wrapper for glmnet::glmnet() and glmnet::cv.glmnet().

Usage

mdl_glmnet(y, X, cv = TRUE, ...)

Arguments

y	The outcome variable.
X	The (sparse) feature matrix.
cv	Boolean to indicate use of lasso with cross-validated penalty.
...	Additional arguments passed to glmnet. See glmnet::glmnet() and glmnet::cv.glmnet() for a complete list of arguments.

Value

mdl_glmnet returns an object of S3 class mdl_glmnet as a simple mask of the return object of glmnet::glmnet() or glmnet::cv.glmnet().

References

Friedman J, Hastie T, Tibshirani R (2010). "Regularization Paths for Generalized Linear Models via Coordinate Descent." Journal of Statistical Software, 33(1), 1–22.

Simon N, Friedman J, Hastie T, Tibshirani R (2011). "Regularization Paths for Cox's Proportional Hazards Model via Coordinate Descent." Journal of Statistical Software, 39(5), 1–13.

See Also

glmnet::glmnet(),glmnet::cv.glmnet()

Other ml_wrapper: mdl_glm(), mdl_ranger(), mdl_xgboost(), ols()

Examples

glmnet_fit <- mdl_glmnet(rnorm(100), matrix(rnorm(1000), 100, 10))
class(glmnet_fit)

---

Wrapper for ranger::ranger().

Description

Simple wrapper for ranger::ranger(). Supports regression (default) and probability forests (set probability = TRUE).

Usage

mdl_ranger(y, X, ...)

Arguments

y	The outcome variable.
X	The feature matrix.
...	Additional arguments passed to ranger. See ranger::ranger() for a complete list of arguments.

Value

mdl_ranger returns an object of S3 class ranger as a simple mask of the return object of ranger::ranger().

References

Wright M N, Ziegler A (2017). "ranger: A fast implementation of random forests for high dimensional data in C++ and R." Journal of Statistical Software 77(1), 1-17.

See Also

ranger::ranger()

Other ml_wrapper: mdl_glmnet(), mdl_glm(), mdl_xgboost(), ols()

Examples

ranger_fit <- mdl_ranger(rnorm(100), matrix(rnorm(1000), 100, 10))
class(ranger_fit)

---

Wrapper for xgboost::xgboost().

Description

Simple wrapper for xgboost::xgboost() with some changes to the default arguments.

Usage

mdl_xgboost(y, X, nrounds = 500, verbose = 0, ...)

Arguments

y	The outcome variable.
X	The (sparse) feature matrix.
nrounds	max number of boosting iterations.
verbose	If 0, xgboost will stay silent. If 1, it will print information about performance. If 2, some additional information will be printed out. Note that setting verbose > 0 automatically engages the cb.print.evaluation(period=1) callback function.
...	Additional arguments passed to xgboost. See xgboost::xgboost() for a complete list of arguments.

Value

mdl_xgboost returns an object of S3 class mdl_xgboost as a simple mask to the return object of xgboost::xgboost().

References

Chen T, Guestrin C (2011). "Xgboost: A Scalable Tree Boosting System." Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, 785–794.

See Also

xgboost::xgboost()

Other ml_wrapper: mdl_glmnet(), mdl_glm(), mdl_ranger(), ols()

Examples

xgboost_fit <- mdl_xgboost(rnorm(50), matrix(rnorm(150), 50, 3),
                           nrounds = 1)
class(xgboost_fit)

---

Ordinary least squares.

Description

Simple implementation of ordinary least squares that computes with sparse feature matrices.

Usage

ols(y, X, const = TRUE, w = NULL)

Arguments

y	The outcome variable.
X	The feature matrix.
const	Boolean equal to TRUE if a constant should be included.
w	A vector of weights for weighted least squares.

Value

ols returns an object of S3 class ols. An object of class ols is a list containing the following components:

coef

A vector with the regression coefficents.

y, X, const, w

Pass-through of the user-provided arguments. See above.

See Also

Other ml_wrapper: mdl_glmnet(), mdl_glm(), mdl_ranger(), mdl_xgboost()

Examples

ols_fit <- ols(rnorm(100), cbind(rnorm(100), rnorm(100)), const = TRUE)
ols_fit$coef

---

Print Methods for Treatment Effect Estimators.

Description

Print methods for treatment effect estimators.

Usage

## S3 method for class 'summary.ddml_ate'
print(x, digits = 3, ...)

## S3 method for class 'summary.ddml_att'
print(x, digits = 3, ...)

## S3 method for class 'summary.ddml_late'
print(x, digits = 3, ...)

Arguments

x	An object of class summary.ddml_ate, summary.ddml_att, and ddml_late, as returned by summary.ddml_ate(), summary.ddml_att(), and summary.ddml_late(), respectively.
digits	The number of significant digits used for printing.
...	Currently unused.

Value

NULL.

Examples

# Construct variables from the included Angrist & Evans (1998) data
y = AE98[, "worked"]
D = AE98[, "morekids"]
X = AE98[, c("age","agefst","black","hisp","othrace","educ")]

# Estimate the average treatment effect using a single base learner, ridge.
ate_fit <- ddml_ate(y, D, X,
                    learners = list(what = mdl_glmnet,
                                    args = list(alpha = 0)),
                    sample_folds = 2,
                    silent = TRUE)
summary(ate_fit)

---

Print Methods for Treatment Effect Estimators.

Description

Print methods for treatment effect estimators.

Usage

## S3 method for class 'summary.ddml_fpliv'
print(x, digits = 3, ...)

## S3 method for class 'summary.ddml_pliv'
print(x, digits = 3, ...)

## S3 method for class 'summary.ddml_plm'
print(x, digits = 3, ...)

Arguments

x	An object of class summary.ddml_plm, summary.ddml_pliv, and summary.ddml_fpliv, as returned by summary.ddml_plm(), summary.ddml_pliv(), and summary.ddml_fpliv(), respectively.
digits	Number of significant digits used for priniting.
...	Currently unused.

Value

NULL.

Examples

# Construct variables from the included Angrist & Evans (1998) data
y = AE98[, "worked"]
D = AE98[, "morekids"]
X = AE98[, c("age","agefst","black","hisp","othrace","educ")]

# Estimate the partially linear model using a single base learner, ridge.
plm_fit <- ddml_plm(y, D, X,
                    learners = list(what = mdl_glmnet,
                                    args = list(alpha = 0)),
                    sample_folds = 2,
                    silent = TRUE)
summary(plm_fit)

---

Predictions using Short-Stacking.

Description

Predictions using short-stacking.

Usage

shortstacking(
  y,
  X,
  Z = NULL,
  learners,
  sample_folds = 2,
  ensemble_type = "average",
  custom_ensemble_weights = NULL,
  compute_insample_predictions = FALSE,
  subsamples = NULL,
  silent = FALSE,
  progress = NULL,
  auxiliary_X = NULL,
  shortstack_y = y
)

Arguments

y	The outcome variable.
X	A (sparse) matrix of predictive variables.
Z	Optional additional (sparse) matrix of predictive variables.
learners	May take one of two forms, depending on whether a single learner or stacking with multiple learners is used for estimation of the predictor. If a single learner is used, learners is a list with two named elements: what The base learner function. The function must be such that it predicts a named input y using a named input X. args Optional arguments to be passed to what. If stacking with multiple learners is used, learners is a list of lists, each containing four named elements: fun The base learner function. The function must be such that it predicts a named input y using a named input X. args Optional arguments to be passed to fun. assign_X An optional vector of column indices corresponding to predictive variables in X that are passed to the base learner. assign_Z An optional vector of column indices corresponding to predictive in Z that are passed to the base learner. Omission of the args element results in default arguments being used in fun. Omission of assign_X (and/or assign_Z) results in inclusion of all variables in X (and/or Z).
sample_folds	Number of cross-fitting folds.
ensemble_type	Ensemble method to combine base learners into final estimate of the conditional expectation functions. Possible values are: "nnls" Non-negative least squares. "nnls1" Non-negative least squares with the constraint that all weights sum to one. "singlebest" Select base learner with minimum MSPE. "ols" Ordinary least squares. "average" Simple average over base learners. Multiple ensemble types may be passed as a vector of strings.
custom_ensemble_weights	A numerical matrix with user-specified ensemble weights. Each column corresponds to a custom ensemble specification, each row corresponds to a base learner in learners (in chronological order). Optional column names are used to name the estimation results corresponding the custom ensemble specification.
compute_insample_predictions	Indicator equal to 1 if in-sample predictions should also be computed.
subsamples	List of vectors with sample indices for cross-fitting.
silent	Boolean to silence estimation updates.
progress	String to print before learner and cv fold progress.
auxiliary_X	An optional list of matrices of length sample_folds, each containing additional observations to calculate predictions for.
shortstack_y	Optional vector of the outcome variable to form short-stacking predictions for. Base learners are always trained on y.

Value

shortstack returns a list containing the following components:

oos_fitted

A matrix of out-of-sample predictions, each column corresponding to an ensemble type (in chronological order).

weights

An array, providing the weight assigned to each base learner (in chronological order) by the ensemble procedures.

is_fitted

When compute_insample_predictions = T. a list of matrices with in-sample predictions by sample fold.

auxiliary_fitted

When auxiliary_X is not NULL, a list of matrices with additional predictions.

oos_fitted_bylearner

A matrix of out-of-sample predictions, each column corresponding to a base learner (in chronological order).

is_fitted_bylearner

When compute_insample_predictions = T, a list of matrices with in-sample predictions by sample fold.

auxiliary_fitted_bylearner

When auxiliary_X is not NULL, a list of matrices with additional predictions for each learner.

Note that unlike crosspred, shortstack always computes out-of-sample predictions for each base learner (at no additional computational cost).

References

Ahrens A, Hansen C B, Schaffer M E, Wiemann T (2023). "ddml: Double/debiased machine learning in Stata." https://arxiv.org/abs/2301.09397

Wolpert D H (1992). "Stacked generalization." Neural Networks, 5(2), 241-259.

See Also

Other utilities: crosspred(), crossval()

Examples

# Construct variables from the included Angrist & Evans (1998) data
y = AE98[, "worked"]
X = AE98[, c("morekids", "age","agefst","black","hisp","othrace","educ")]

# Compute predictions using shortstacking with base learners ols and lasso.
#     Two stacking approaches are simultaneously computed: Equally
#     weighted (ensemble_type = "average") and MSPE-minimizing with weights
#     in the unit simplex (ensemble_type = "nnls1"). Predictions for each
#     learner are also calculated.
shortstack_res <- shortstacking(y, X,
                                learners = list(list(fun = ols),
                                                list(fun = mdl_glmnet)),
                                ensemble_type = c("average",
                                                  "nnls1",
                                                  "singlebest"),
                                sample_folds = 2,
                                silent = TRUE)
dim(shortstack_res$oos_fitted) # = length(y) by length(ensemble_type)
dim(shortstack_res$oos_fitted_bylearner) # = length(y) by length(learners)

---

Inference Methods for Treatment Effect Estimators.

Description

Inference methods for treatment effect estimators. By default, standard errors are heteroskedasiticty-robust. If the ddml estimator was computed using a cluster_variable, the standard errors are also cluster-robust by default.

Usage

## S3 method for class 'ddml_ate'
summary(object, ...)

## S3 method for class 'ddml_att'
summary(object, ...)

## S3 method for class 'ddml_late'
summary(object, ...)

Arguments

object	An object of class ddml_ate, ddml_att, and ddml_late, as fitted by ddml_ate(), ddml_att(), and ddml_late(), respectively.
...	Currently unused.

Value

A matrix with inference results.

Examples

# Construct variables from the included Angrist & Evans (1998) data
y = AE98[, "worked"]
D = AE98[, "morekids"]
X = AE98[, c("age","agefst","black","hisp","othrace","educ")]

# Estimate the average treatment effect using a single base learner, ridge.
ate_fit <- ddml_ate(y, D, X,
                    learners = list(what = mdl_glmnet,
                                    args = list(alpha = 0)),
                    sample_folds = 2,
                    silent = TRUE)
summary(ate_fit)

---

Inference Methods for Partially Linear Estimators.

Description

Inference methods for partially linear estimators. Simple wrapper for sandwich::vcovHC() and sandwich::vcovCL(). Default standard errors are heteroskedasiticty-robust. If the ddml estimator was computed using a cluster_variable, the standard errors are also cluster-robust by default.

Usage

## S3 method for class 'ddml_fpliv'
summary(object, ...)

## S3 method for class 'ddml_pliv'
summary(object, ...)

## S3 method for class 'ddml_plm'
summary(object, ...)

Arguments

object	An object of class ddml_plm, ddml_pliv, or ddml_fpliv as fitted by ddml_plm(), ddml_pliv(), and ddml_fpliv(), respectively.
...	Additional arguments passed to vcovHC and vcovCL. See sandwich::vcovHC() and sandwich::vcovCL() for a complete list of arguments.

Value

An array with inference results for each ensemble_type.

References

Zeileis A (2004). "Econometric Computing with HC and HAC Covariance Matrix Estimators.” Journal of Statistical Software, 11(10), 1-17.

Zeileis A (2006). “Object-Oriented Computation of Sandwich Estimators.” Journal of Statistical Software, 16(9), 1-16.

Zeileis A, Köll S, Graham N (2020). “Various Versatile Variances: An Object-Oriented Implementation of Clustered Covariances in R.” Journal of Statistical Software, 95(1), 1-36.

See Also

sandwich::vcovHC(), sandwich::vcovCL()

Examples

# Construct variables from the included Angrist & Evans (1998) data
y = AE98[, "worked"]
D = AE98[, "morekids"]
X = AE98[, c("age","agefst","black","hisp","othrace","educ")]

# Estimate the partially linear model using a single base learner, ridge.
plm_fit <- ddml_plm(y, D, X,
                    learners = list(what = mdl_glmnet,
                                    args = list(alpha = 0)),
                    sample_folds = 2,
                    silent = TRUE)
summary(plm_fit)

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