Type: Package
Title: Estimation of Conditional Average Treatment Effects with High-Dimensional Data
Version: 0.1.0
Imports: KernSmooth, R6, hdm, locpol, caret
Description: A two-step double-robust method to estimate the conditional average treatment effects (CATE) with potentially high-dimensional covariate(s). In the first stage, the nuisance functions necessary for identifying CATE are estimated by machine learning methods, allowing the number of covariates to be comparable to or larger than the sample size. The second stage consists of a low-dimensional local linear regression, reducing CATE to a function of the covariate(s) of interest. The CATE estimator implemented in this package not only allows for high-dimensional data, but also has the “double robustness” property: either the model for the propensity score or the models for the conditional means of the potential outcomes are allowed to be misspecified (but not both). This package is based on the paper by Fan et al., "Estimation of Conditional Average Treatment Effects With High-Dimensional Data" (2022), Journal of Business & Economic Statistics <doi:10.1080/07350015.2020.1811102>.
License: GPL (≥ 3)
Encoding: UTF-8
RoxygenNote: 7.2.3
Suggests: knitr, rmarkdown, xfun, randomForest, dplyr, ggplot2, ggthemes
VignetteBuilder: knitr
NeedsCompilation: no
Packaged: 2022-12-13 19:08:51 UTC; hengzhaohong
Author: Qingliang Fan [aut, cre], Hengzhao Hong [aut]
Maintainer: Qingliang Fan <michaelqfan@cuhk.edu.hk>
Repository: CRAN
Date/Publication: 2022-12-14 11:50:02 UTC

High-Dimensional Conditional Average Treatment Effects (HDCATE) Estimator

Description

Use a two-step procedure to estimate the conditional average treatment effects (CATE) with potentially high-dimensional covariate(s). Run browseVignettes('hdcate') to browse the user manual of this package.

Usage

HDCATE(data, y_name, d_name, x_formula)

Arguments

data

data frame of the observed data

y_name

variable name of the observed outcomes

d_name

variable name of the treatment indicators

x_formula

formula of the covariates

Value

An initialized HDCATE model (object), ready for estimation.

Examples

# get simulation data
n_obs <- 500  # Num of observations
n_var <- 100  # Num of observed variables
n_rel_var <- 4  # Num of relevant variables
data <- HDCATE.get_sim_data(n_obs, n_var, n_rel_var)
# conditional expectation model is misspecified
x_formula <- paste(paste0('X', c(2:n_var)), collapse ='+')
# for example, and alternatively, the propensity score model is misspecified
# x_formula <- paste(paste0('X', c(1:(n_var-1))), collapse ='+')

# Example 1: full-sample estimator
# create a new HDCATE model
model <- HDCATE(data=data, y_name='Y', d_name='D', x_formula=x_formula)

# estimate HDCATE function, inference, and plot
HDCATE.set_condition_var(model, 'X2', min=-1, max=1, step=0.01)

HDCATE.fit(model)
HDCATE.inference(model)
HDCATE.plot(model)


# Example 2: cross-fitting estimator
# change above estimator to cross-fitting mode, 5 folds, for example.
HDCATE.use_cross_fitting(model, k_fold=5)

# estimate HDCATE function, inference, and plot
HDCATE.set_condition_var(model, 'X2', min=-1, max=1, step=0.01)

HDCATE.fit(model)
HDCATE.inference(model)
HDCATE.plot(model)

Fit the HDCATE function

Description

Fit the HDCATE function

Usage

HDCATE.fit(HDCATE_model, verbose = TRUE)

Arguments

HDCATE_model

an object created via HDCATE

verbose

whether the verbose message is displayed, the default is TRUE

Value

None. The HDCATE_model is fitted.

Examples

# get simulation data
n_obs <- 500  # Num of observations
n_var <- 100  # Num of observed variables
n_rel_var <- 4  # Num of relevant variables
data <- HDCATE.get_sim_data(n_obs, n_var, n_rel_var)
# conditional expectation model is misspecified
x_formula <- paste(paste0('X', c(2:n_var)), collapse ='+')
# propensity score model is misspecified
# x_formula <- paste(paste0('X', c(1:(n_var-1))), collapse ='+')

# create a new HDCATE model
model <- HDCATE(data=data, y_name='Y', d_name='D', x_formula=x_formula)

HDCATE.set_condition_var(model, 'X2', min=-1, max=1, step=0.01)


HDCATE.fit(model)

Get simulation data

Description

Get simulation data

Usage

HDCATE.get_sim_data(
  n_obs = 500,
  n_var = 100,
  n_rel_var = 4,
  sig_strength_propensity = 0.5,
  sig_strength_outcome = 1,
  intercept = 10
)

Arguments

n_obs

Num of observations

n_var

Num of covariates

n_rel_var

Num of relevant variables, only the first n_rel_var covariates are actually present in the expectation function of potential outcome, and only the last n_rel_var covariates are present in the propensity score function.

sig_strength_propensity

signal strength in propensity score functions

sig_strength_outcome

signal strength in outcome functions

intercept

value of intercept in outcome functions

Value

a data.frame, which is the simulated observed data.

Examples

HDCATE.get_sim_data()
HDCATE.get_sim_data(n_obs=50, n_var=4, n_rel_var=2)

Construct uniform confidence bands

Description

Construct uniform confidence bands

Usage

HDCATE.inference(
  HDCATE_model,
  sig_level = 0.01,
  n_rep_boot = 1000,
  verbose = FALSE
)

Arguments

HDCATE_model

an object created via HDCATE

sig_level

a (vector of) significant level, such as 0.01, or c(0.01, 0.05, 0.10)

n_rep_boot

repeat n times for bootstrap, the default is 1000

verbose

whether the verbose message is displayed, the default is FALSE

Value

None. The HDCATE confidence bands are constructed.

Examples

# get simulation data
n_obs <- 500  # Num of observations
n_var <- 100  # Num of observed variables
n_rel_var <- 4  # Num of relevant variables
data <- HDCATE.get_sim_data(n_obs, n_var, n_rel_var)
# conditional expectation model is misspecified
x_formula <- paste(paste0('X', c(2:n_var)), collapse ='+')
# propensity score model is misspecified
# x_formula <- paste(paste0('X', c(1:(n_var-1))), collapse ='+')

# create a new HDCATE model
model <- HDCATE(data=data, y_name='Y', d_name='D', x_formula=x_formula)

HDCATE.set_condition_var(model, 'X2', min=-1, max=1, step=0.01)


HDCATE.fit(model)
HDCATE.inference(model)

Plot HDCATE function and the uniform confidence bands

Description

Plot HDCATE function and the uniform confidence bands

Usage

HDCATE.plot(
  HDCATE_model,
  output_pdf = FALSE,
  pdf_name = "hdcate_plot.pdf",
  include_band = TRUE,
  test_side = "both",
  y_axis_min = "auto",
  y_axis_max = "auto",
  display.hdcate = "HDCATEF",
  display.ate = "ATE",
  display.siglevel = "sig_level"
)

Arguments

HDCATE_model

an object created via HDCATE

output_pdf

if TRUE, the plot will be saved as a PDF file, the default is FALSE

pdf_name

file name when output_pdf=TRUE

include_band

if TRUE, plot the uniform confidence bands (need: HDCATE.inference was called before)

test_side

'both', 'left' or 'right', i.e. 2-side test or one-side test

y_axis_min

minimum value of the Y axis to plot in the graph, the default is auto

y_axis_max

maximum value of the Y axis to plot in the graph, the default is auto

display.hdcate

the name of HDCATE function in the legend, the default is 'HDCATEF'

display.ate

the name of average treatment effect in the legend, the default is 'ATE'

display.siglevel

the name of the significant level for confidence bands in the legend, the default is 'sig_level'

Value

None. A plot will be shown or saved as PDF.

Examples

# get simulation data
n_obs <- 500  # Num of observations
n_var <- 100  # Num of observed variables
n_rel_var <- 4  # Num of relevant variables
data <- HDCATE.get_sim_data(n_obs, n_var, n_rel_var)
# conditional expectation model is misspecified
x_formula <- paste(paste0('X', c(2:n_var)), collapse ='+')
# propensity score model is misspecified
# x_formula <- paste(paste0('X', c(1:(n_var-1))), collapse ='+')

# create a new HDCATE model
model <- HDCATE(data=data, y_name='Y', d_name='D', x_formula=x_formula)

HDCATE.set_condition_var(model, 'X2', min=-1, max=1, step=0.01)

HDCATE.fit(model)
HDCATE.inference(model)
HDCATE.plot(model)

Set bandwidth

Description

Set user-defined bandwidth.

Usage

HDCATE.set_bw(model, bandwidth = "default")

Arguments

model

an object created via HDCATE

bandwidth

the value of bandwidth

Value

None.

Examples

# get simulation data
n_obs <- 500  # Num of observations
n_var <- 100  # Num of observed variables
n_rel_var <- 4  # Num of relevant variables
data <- HDCATE.get_sim_data(n_obs, n_var, n_rel_var)
# conditional expectation model is misspecified
x_formula <- paste(paste0('X', c(2:n_var)), collapse ='+')
# propensity score model is misspecified
# x_formula <- paste(paste0('X', c(1:(n_var-1))), collapse ='+')

# create a new HDCATE model
model <- HDCATE(data=data, y_name='Y', d_name='D', x_formula=x_formula)

# Set user-defined bandwidth, e.g., 0.15.
HDCATE.set_bw(model, 0.15)

Set the conditional variable in CATE

Description

Set the conditional variable in CATE

Usage

HDCATE.set_condition_var(
  HDCATE_model,
  name = NA,
  min = NA,
  max = NA,
  step = NA
)

Arguments

HDCATE_model

an object created via HDCATE

name

name of the conditional variable

min

minimum value of the conditional variable for evaluation

max

maximum value of the conditional variable for evaluation

step

minimum distance between two evaluation points

Value

None. The HDCATE_model is ready to fit.

Examples

# get simulation data
n_obs <- 500  # Num of observations
n_var <- 100  # Num of observed variables
n_rel_var <- 4  # Num of relevant variables
data <- HDCATE.get_sim_data(n_obs, n_var, n_rel_var)
# conditional expectation model is misspecified
x_formula <- paste(paste0('X', c(2:n_var)), collapse ='+')
# propensity score model is misspecified
# x_formula <- paste(paste0('X', c(1:(n_var-1))), collapse ='+')

# create a new HDCATE model
model <- HDCATE(data=data, y_name='Y', d_name='D', x_formula=x_formula)

HDCATE.set_condition_var(model, 'X2', min=-1, max=1, step=0.01)

Set user-defined first-stage estimating methods

Description

Set user-defined ML methods (such as random forests, elastic-net, boosting) to run the first-stage estimation.

Usage

HDCATE.set_first_stage(
  model,
  fit.treated,
  fit.untreated,
  fit.propensity,
  predict.treated,
  predict.untreated,
  predict.propensity
)

Arguments

model

an object created via HDCATE

fit.treated

function that accepts a data.frame as the only argument, fits the treated expectation function, and returns a fitted object

fit.untreated

function that accepts a data.frame as the only argument, fits the untreated expectation function, and returns a fitted object

fit.propensity

function that accepts a data.frame as the only argument, fits the propensity function, and return a fitted object

predict.treated

function that accepts the returned object of fit.treated and a data.frame as arguments, and returns the predicted vector of that data.frame

predict.untreated

function that accepts the returned object of fit.untreated and a data.frame as arguments, and returns the predicted vector that data.frame

predict.propensity

function that accepts the returned object of fit.propensity and a data.frame as arguments, and returns the predicted vector that data.frame

Value

None.

Examples

# get simulation data
n_obs <- 500  # Num of observations
n_var <- 100  # Num of observed variables
n_rel_var <- 4  # Num of relevant variables
data <- HDCATE.get_sim_data(n_obs, n_var, n_rel_var)
# conditional expectation model is misspecified
x_formula <- paste(paste0('X', c(2:n_var)), collapse ='+')
# propensity score model is misspecified
# x_formula <- paste(paste0('X', c(1:(n_var-1))), collapse ='+')

# create a new HDCATE model
model <- HDCATE(data=data, y_name='Y', d_name='D', x_formula=x_formula)

# manually define a lasso method
my_lasso_fit_exp <- function(df) {
  hdm::rlasso(as.formula(paste0('Y', "~", x_formula)), df)
}
my_lasso_predict_exp <- function(fitted_model, df) {
  predict(fitted_model, df)
}
my_lasso_fit_ps <- function(df) {
  hdm::rlassologit(as.formula(paste0('D', "~", x_formula)), df)
}
my_lasso_predict_ps <- function(fitted_model, df) {
  predict(fitted_model, df, type="response")
}

# Apply the "my-lasso" apporach to the first stage
HDCATE.set_first_stage(
  model,
  my_lasso_fit_exp,
  my_lasso_fit_exp,
  my_lasso_fit_ps,
  my_lasso_predict_exp,
  my_lasso_predict_exp,
  my_lasso_predict_ps
)

Clear the user-defined first-stage estimating methods

Description

Inverse operation of HDCATE.set_first_stage

Usage

HDCATE.unset_first_stage(model)

Arguments

model

an object created via HDCATE

Value

None.

Examples

# get simulation data
n_obs <- 500  # Num of observations
n_var <- 100  # Num of observed variables
n_rel_var <- 4  # Num of relevant variables
data <- HDCATE.get_sim_data(n_obs, n_var, n_rel_var)
# conditional expectation model is misspecified
x_formula <- paste(paste0('X', c(2:n_var)), collapse ='+')
# propensity score model is misspecified
# x_formula <- paste(paste0('X', c(1:(n_var-1))), collapse ='+')

# create a new HDCATE model
model <- HDCATE(data=data, y_name='Y', d_name='D', x_formula=x_formula)

# ... manually set user-defined first-stage estimating methods via `HDCATE.set_first_stage`

# Clear those user-defined methods and use the built-in method
HDCATE.unset_first_stage(model)

Use k-fold cross-fitting estimator

Description

Use k-fold cross-fitting estimator

Usage

HDCATE.use_cross_fitting(model, k_fold = 5, folds = NULL)

Arguments

model

an object created via HDCATE

k_fold

number of folds

folds

you can manually set the folds, should be a list of index vector

Value

None.

Examples

# get simulation data
n_obs <- 500  # Num of observations
n_var <- 100  # Num of observed variables
n_rel_var <- 4  # Num of relevant variables
data <- HDCATE.get_sim_data(n_obs, n_var, n_rel_var)
# conditional expectation model is misspecified
x_formula <- paste(paste0('X', c(2:n_var)), collapse ='+')
# propensity score model is misspecified
# x_formula <- paste(paste0('X', c(1:(n_var-1))), collapse ='+')

# create a new HDCATE model
model <- HDCATE(data=data, y_name='Y', d_name='D', x_formula=x_formula)

# for example, use 5-fold cross-fitting estimator
HDCATE.use_cross_fitting(model, k_fold=5)

# alternatively, pass a list of index vector to the third argument to set the folds manually,
# in this case, the second argument k_fold is auto detected, you can pass any value to it.
HDCATE.use_cross_fitting(model, k_fold=2, folds=list(c(1:250), c(251:500)))

Use full-sample estimator

Description

This is the default mode when creating a model via HDCATE

Usage

HDCATE.use_full_sample(model)

Arguments

model

an object created via HDCATE

Value

None.

Examples

# get simulation data
n_obs <- 500  # Num of observations
n_var <- 100  # Num of observed variables
n_rel_var <- 4  # Num of relevant variables
data <- HDCATE.get_sim_data(n_obs, n_var, n_rel_var)
# conditional expectation model is misspecified
x_formula <- paste(paste0('X', c(2:n_var)), collapse ='+')
# propensity score model is misspecified
# x_formula <- paste(paste0('X', c(1:(n_var-1))), collapse ='+')

# create a new HDCATE model
model <- HDCATE(data=data, y_name='Y', d_name='D', x_formula=x_formula)

HDCATE.use_full_sample(model)

High-Dimensional Conditional Average Treatment Effects (HDCATE) Estimator

Description

Use a two-step procedure to estimate the conditional average treatment effects (CATE) for all possible values of the covariate(s).

Format

R6::R6Class object.

Methods

Public methods

Method new()

Usage
HDCATE_R6Class$new(data, y_name, d_name, x_formula)

Method propensity_hd_estimate()

Usage
HDCATE_R6Class$propensity_hd_estimate(data = NA, verbose = F)

Method conditional_expectations_hd_estimate()

Usage
HDCATE_R6Class$conditional_expectations_hd_estimate(data = NA, verbose = F)

Method first_stage()

Usage
HDCATE_R6Class$first_stage(data = NA, verbose = F)

Method second_stage()

Usage
HDCATE_R6Class$second_stage(
  predictor_eta_hat = NA,
  eta_hat = NA,
  subsample_idx = NULL,
  local_weight = NULL,
  estimate_std = TRUE,
  verbose = FALSE,
  save_model = TRUE
)

Method get_bw()

Usage
HDCATE_R6Class$get_bw(phi, use_sample_idx)

Method fit()

Fit the HDCATE function

Usage
HDCATE_R6Class$fit(verbose = FALSE)
Returns

estimated HDCATE

Method inference()

Usage
HDCATE_R6Class$inference(
  sig_level = 0.01,
  boot_method = "normal",
  n_rep_boot = 1000,
  verbose = FALSE
)

Method plot()

Plot the results.

Usage
HDCATE_R6Class$plot(
  output_pdf = FALSE,
  pdf_name = "hdcate_plot.pdf",
  include_band = TRUE,
  test_side = "both",
  y_axis_min = "auto",
  y_axis_max = "auto",
  display.hdcate = "HDCATEF",
  display.ate = "ATE",
  display.siglevel = "sig_level"
)
Arguments
output_pdf

if TRUE, save image to a pdf file named as pdf_name

pdf_name

the name of the output PDF file

include_band

if TRUE, plot uniform confidence bands as well.

test_side

'both' for a 2-sided test, 'left' for a left-sided test or 'right' for a right-sided test

y_axis_min

the lowest value plotted in Y axis, the default is 'auto'

y_axis_max

the largest value plotted in Y axis, the default is 'auto'

display.hdcate

the name of HDCATE function in the legend, the default is 'HDCATEF'

display.ate

the name of average treatment effect in the legend, the default is 'ATE'

display.siglevel

the name of the significant level for confidence bands in the legend, the default is 'sig_level'

Method get_confidence_bands()

Usage
HDCATE_R6Class$get_confidence_bands(test_side = "both")

Method draw_weights()

Usage
HDCATE_R6Class$draw_weights(method, n_rep_boot, n_obs)

Method set_condition_var()

Usage
HDCATE_R6Class$set_condition_var(name = NA, min = NA, max = NA, step = NA)

Method clone()

The objects of this class are cloneable with this method.

Usage
HDCATE_R6Class$clone(deep = FALSE)
Arguments
deep

Whether to make a deep clone.