ddml_plm: Estimator for the Partially Linear Model.

In ddml: Double/Debiased Machine Learning

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)

ddml documentation built on Oct. 3, 2024, 1:13 a.m.