Xleaners: X-Learners
In soerenkuenzel/causalToolbox: Toolbox for Causal Inference with emphasize on Heterogeneous Treatment Effect Estimator

Description Usage Arguments Details Value Author(s) References See Also Examples

X_RF is an implementation of the X-learner with Random Forests (Breiman 2001) in the first and second stage.

X_BART is an implementation of the X-learner with Bayesian Additive Regression Trees (Chipman et al. 2010) at the first and second stage

X_RF(feat, tr, yobs, predmode = "propmean", nthread = 0,
  verbose = FALSE, mu.forestry = list(relevant.Variable = 1:ncol(feat),
  ntree = 1000, replace = TRUE, sample.fraction = 0.8, mtry =
  round(ncol(feat) * 13/20), nodesizeSpl = 2, nodesizeAvg = 1, splitratio =
  1, middleSplit = TRUE), tau.forestry = list(relevant.Variable =
  1:ncol(feat), ntree = 1000, replace = TRUE, sample.fraction = 0.7, mtry =
  round(ncol(feat) * 17/20), nodesizeSpl = 5, nodesizeAvg = 6, splitratio =
  0.8, middleSplit = TRUE), e.forestry = list(relevant.Variable =
  1:ncol(feat), ntree = 500, replace = TRUE, sample.fraction = 0.5, mtry =
  ncol(feat), nodesizeSpl = 11, nodesizeAvg = 33, splitratio = 0.5,
  middleSplit = FALSE))

X_BART(feat, tr, yobs, predmode = "pscore", nthread = 1,
  ndpost = 1200, ntree = 200, mu.BART = list(sparse = FALSE, theta =
  0, omega = 1, a = 0.5, b = 1, augment = FALSE, rho = NULL, usequants =
  FALSE, cont = FALSE, sigest = NA, sigdf = 3, sigquant = 0.9, k = 2, power
  = 2, base = 0.95, sigmaf = NA, lambda = NA, numcut = 100L, nskip = 100L),
  tau.BART = list(sparse = FALSE, theta = 0, omega = 1, a = 0.5, b = 1,
  augment = FALSE, rho = NULL, usequants = FALSE, cont = FALSE, sigest =
  NA, sigdf = 3, sigquant = 0.9, k = 2, power = 2, base = 0.95, sigmaf =
  NA, lambda = NA, numcut = 100L, nskip = 100L), e.BART = list(sparse =
  FALSE, theta = 0, omega = 1, a = 0.5, b = 1, augment = FALSE, rho = NULL,
  usequants = FALSE, cont = FALSE, sigest = NA, sigdf = 3, sigquant = 0.9,
  k = 2, power = 2, base = 0.95, sigmaf = NA, lambda = NA, numcut = 100L,
  nskip = 100L))

`feat`	A data frame containing the features.
`tr`	A numeric vector with 0 for control and 1 for treated variables.
`yobs`	A numeric vector containing the observed outcomes.
`predmode`	Specifies how the two estimators of the second stage should be aggregated. Possible types are "propmean," "control," and "treated." The default is "propmean," which refers to propensity score weighting.
`nthread`	Number of threads which should be used to work in parallel.
`verbose`	TRUE for detailed output, FALSE for no output.
`mu.forestry, tau.forestry, e.forestry`	A list containing the hyperparameters for the `forestry` package that are used for estimating the response functions, the CATE, and the propensity score. These hyperparameters are passed to the `forestry` package. (Please refer to the forestry package for a more detailed documentation of the hyperparamters.) `relevant.Variable` Variables that are only used in the first stage. `ntree` Numbers of trees used in the first stage. `replace` Sample with or without replacement in the first stage. `sample.fraction` The size of total samples to draw for the training data in the first stage. `mtry` The number of variables randomly selected in each splitting point. `nodesizeSpl` Minimum nodesize in the first stage for the observations in the splitting set. (See the details of the `forestry` package) `nodesizeAvg` Minimum nodesize in the first stage for the observations in the averaging set. `splitratio` Proportion of the training data used as the splitting dataset in the first stage. `middleSplit` If true, the split value will be exactly in the middle of two observations. Otherwise, it will take a point based on a uniform distribution between the two observations.
`ndpost`	Number of posterior draws.
`ntree`	Number of trees.
`mu.BART, tau.BART, e.BART`	hyperparameters of the BART functions for the estimates of the first and second stage and the propensity score. Use `?BART::mc.wbart` for a detailed explanation of their effects.

The X-Learner estimates the CATE in three steps:

Estimate the response functions

μ_0(x) = E[Y(0) | X = x]

μ_1(x) = E[Y(1) | X = x]

using the base learner and denote the estimates as \hat μ_0 and \hat μ_1.
Impute the treatment effects for the individuals in the treated group, based on the control outcome estimator, and the treatment effects for the individuals in the control group, based on the treatment outcome estimator, that is,

D^1_i = Y_i(1) - \hat μ_0(X_i)

D^0_i = \hat μ_1(X_i) - Y_i(0).

Now employ the base learner in two ways: using D^1_i as the dependent variable to obtain \hat τ_1(x), and using D^0_i as the dependent variable to obtain \hat τ_0(x).
Define the CATE estimate by a weighted average of the two estimates at Stage 2:

τ(x) = g(x) \hat τ_0(x) + (1 - g(x)) \hat τ_1(x).

If predmode = "propmean", then g(x) = e(x), where e(x) is an estimate of the propensity score using the forestry Random Forests version with the hyperparameters specified in e.forestry. If predmode = "control", then g(x) = 1, and if predmode = "treated", then g(x) = 0.

An object from a class that contains the CATEestimator class. It should be used with one of the following functions: EstimateCATE, CateCI, and CateBIAS. The object has at least the following slots:

`feature_train`	A copy of feat.
`tr_train`	A copy of tr.
`yobs_train`	A copy of yobs.
`creator`	Function call that creates the CATE estimator. This is used for different bootstrap procedures.

Soeren R. Kuenzel

Sören Künzel, Jasjeet Sekhon, Peter Bickel, and Bin Yu (2017). MetaLearners for Estimating Heterogeneous Treatment Effects using Machine Learning. https://www.pnas.org/content/116/10/4156
Sören Künzel, Simon Walter, and Jasjeet Sekhon (2018). Causaltoolbox—Estimator Stability for Heterogeneous Treatment Effects. https://arxiv.org/pdf/1811.02833.pdf
Sören Künzel, Bradly Stadie, Nikita Vemuri, Varsha Ramakrishnan, Jasjeet Sekhon, and Pieter Abbeel (2018). Transfer Learning for Estimating Causal Effects using Neural Networks. https://arxiv.org/pdf/1808.07804.pdf

Other metalearners: M-Learner, S-Learner, T-Learner

require(causalToolbox)

# create example data set
simulated_experiment <- simulate_causal_experiment(
  ntrain = 1000,
  ntest = 1000,
  dim = 10
)
feat <- simulated_experiment$feat_tr
tr <- simulated_experiment$W_tr
yobs <- simulated_experiment$Yobs_tr
feature_test <- simulated_experiment$feat_te

# create the CATE estimator using Random Forests (RF)
xl_rf <- X_RF(feat = feat, tr = tr, yobs = yobs)
tl_rf <- T_RF(feat = feat, tr = tr, yobs = yobs)
sl_rf <- S_RF(feat = feat, tr = tr, yobs = yobs)
ml_rf <- M_RF(feat = feat, tr = tr, yobs = yobs)
xl_bt <- X_BART(feat = feat, tr = tr, yobs = yobs)
tl_bt <- T_BART(feat = feat, tr = tr, yobs = yobs)
sl_bt <- S_BART(feat = feat, tr = tr, yobs = yobs)
ml_bt <- M_BART(feat = feat, tr = tr, yobs = yobs)
  
cate_esti_xrf <- EstimateCate(xl_rf, feature_test)

# evaluate the performance.
cate_true <- simulated_experiment$tau_te
mean((cate_esti_xrf - cate_true) ^ 2)
## Not run: 
# create confidence intervals via bootstrapping. 
xl_ci_rf <- CateCI(xl_rf, feature_test, B = 500)

## End(Not run)