Package 'evalITR'

Estimation of the Area Under Prescription Evaluation Curve (AUPEC) in Randomized Experiments

Description

This function estimates AUPEC. The details of the methods for this design are given in Imai and Li (2019).

Usage

AUPEC(T, tau, Y, centered = TRUE)

Arguments

T	A vector of the unit-level binary treatment receipt variable for each sample.
tau	A vector of the unit-level continuous score for treatment assignment. We assume those that have tau<0 should not have treatment. Conditional Average Treatment Effect is one possible measure.
Y	A vector of the outcome variable of interest for each sample.
centered	If TRUE, the outcome variables would be centered before processing. This minimizes the variance of the estimator. Default is TRUE.

Value

A list that contains the following items:

aupec	The estimated Area Under Prescription Evaluation Curve
sd	The estimated standard deviation of AUPEC.
vec	A vector of points outlining the AUPEC curve across each possible budget point for the dataset. Each step increases the budget by 1/n where n is the number of data points.

Author(s)

Michael Lingzhi Li, Technology and Operations Management, Harvard Business School [email protected], https://www.michaellz.com/;

References

Imai and Li (2019). “Experimental Evaluation of Individualized Treatment Rules”,

Examples

T = c(1,0,1,0,1,0,1,0)
tau = c(0,0.1,0.2,0.3,0.4,0.5,0.6,0.7)
Y = c(4,5,0,2,4,1,-4,3)
aupeclist <- AUPEC(T,tau,Y)
aupeclist$aupec
aupeclist$sd
aupeclist$vec

---

Estimation of the Area Under Prescription Evaluation Curve (AUPEC) in Randomized Experiments Under Cross Validation

Description

This function estimates AUPEC. The details of the methods for this design are given in Imai and Li (2019).

Usage

AUPECcv(T, tau, Y, ind, centered = TRUE)

Arguments

T	A vector of the unit-level binary treatment receipt variable for each sample.
tau	A matrix where the ith column is the unit-level continuous score for treatment assignment generated in the ith fold.
Y	The outcome variable of interest.
ind	A vector of integers (between 1 and number of folds inclusive) indicating which testing set does each sample belong to.
centered	If TRUE, the outcome variables would be centered before processing. This minimizes the variance of the estimator. Default is TRUE.

Value

A list that contains the following items:

aupec	The estimated AUPEC.
sd	The estimated standard deviation of AUPEC.

Author(s)

Michael Lingzhi Li, Technology and Operations Management, Harvard Business School [email protected], https://www.michaellz.com/;

References

Imai and Li (2019). “Experimental Evaluation of Individualized Treatment Rules”,

Examples

T = c(1,0,1,0,1,0,1,0)
tau = matrix(c(0,0.1,0.2,0.3,0.4,0.5,0.6,0.7,-0.5,-0.3,-0.1,0.1,0.3,0.5,0.7,0.9),nrow = 8, ncol = 2)
Y = c(4,5,0,2,4,1,-4,3)
ind = c(rep(1,4),rep(2,4))
aupeclist <- AUPECcv(T, tau, Y, ind)
aupeclist$aupec
aupeclist$sd

---

Compute Quantities of Interest (PAPE, PAPEp, PAPDp, AUPEC, GATE, GATEcv)

Description

Compute Quantities of Interest (PAPE, PAPEp, PAPDp, AUPEC, GATE, GATEcv)

Usage

compute_qoi(fit_obj, algorithms)

Arguments

fit_obj	An output object from fit_itr function.
algorithms	Machine learning algorithms

---

Compute Quantities of Interest (PAPE, PAPEp, PAPDp, AUPEC, GATE, GATEcv) with user defined functions

Description

Compute Quantities of Interest (PAPE, PAPEp, PAPDp, AUPEC, GATE, GATEcv) with user defined functions

Usage

compute_qoi_user(user_itr, Tcv, Ycv, data, ngates, budget, ...)

Arguments

user_itr	A user-defined function to create an ITR. The function should take the data as input and return an unit-level continuous score for treatment assignment. We assume those that have score less than 0 should not have treatment. The default is NULL, which means the ITR will be estimated from the estimate_itr.
Tcv	A vector of the unit-level binary treatment.
Ycv	A vector of the unit-level continuous outcome.
data	A data frame containing the variables of interest.
ngates	The number of gates to be used in the GATE function.
budget	The maximum percentage of population that can be treated under the budget constraint.
...	Additional arguments to be passed to the user-defined function.

---

The Consistency Test for Grouped Average Treatment Effects (GATEs) in Randomized Experiments

Description

This function calculates statistics related to the test of treatment effect consistency across groups.

Usage

consist.test(T, tau, Y, ngates = 5, nsim = 10000)

Arguments

T	A vector of the unit-level binary treatment receipt variable for each sample.
tau	A vector of the unit-level continuous score. Conditional Average Treatment Effect is one possible measure.
Y	A vector of the outcome variable of interest for each sample.
ngates	The number of groups to separate the data into. The groups are determined by tau. Default is 5.
nsim	Number of Monte Carlo simulations used to simulate the null distributions. Default is 10000.

Details

The details of the methods for this design are given in Imai and Li (2022).

Value

A list that contains the following items:

stat	The estimated statistic for the test of consistency
pval	The p-value of the null hypothesis (that the treatment effects are consistent)

Author(s)

Michael Lingzhi Li, Technology and Operations Management, Harvard Business School [email protected], https://www.michaellz.com/;

References

Imai and Li (2022). “Statistical Inference for Heterogeneous Treatment Effects Discovered by Generic Machine Learning in Randomized Experiments”,

Examples

T = c(1,0,1,0,1,0,1,0)
tau = c(0,0.1,0.2,0.3,0.4,0.5,0.6,0.7)
Y = c(4,5,0,2,4,1,-4,3)
consisttestlist <- consist.test(T,tau,Y,ngates=5)
consisttestlist$stat
consisttestlist$pval

---

The Consistency Test for Grouped Average Treatment Effects (GATEs) under Cross Validation in Randomized Experiments

Description

This function calculates statistics related to the test of treatment effect consistency across groups under cross-validation.

Usage

consistcv.test(T, tau, Y, ind, ngates = 5, nsim = 10000)

Arguments

T	A vector of the unit-level binary treatment receipt variable for each sample.
tau	A vector of the unit-level continuous score. Conditional Average Treatment Effect is one possible measure.
Y	A vector of the outcome variable of interest for each sample.
ind	A vector of integers (between 1 and number of folds inclusive) indicating which testing set does each sample belong to.
ngates	The number of groups to separate the data into. The groups are determined by tau. Default is 5.
nsim	Number of Monte Carlo simulations used to simulate the null distributions. Default is 10000.

Details

The details of the methods for this design are given in Imai and Li (2022).

Value

A list that contains the following items:

stat	The estimated statistic for the test of consistency under cross-validation.
pval	The p-value of the null hypothesis (that the treatment effects are consistent)

Author(s)

Michael Lingzhi Li, Technology and Operations Management, Harvard Business School [email protected], https://www.michaellz.com/;

References

Imai and Li (2022). “Statistical Inference for Heterogeneous Treatment Effects Discovered by Generic Machine Learning in Randomized Experiments”,

Examples

T = c(1,0,1,0,1,0,1,0)
tau = matrix(c(0,0.1,0.2,0.3,0.4,0.5,0.6,0.7,-0.5,-0.3,-0.1,0.1,0.3,0.5,0.7,0.9),nrow = 8, ncol = 2)
Y = c(4,5,0,2,4,1,-4,3)
ind = c(rep(1,4),rep(2,4))
consisttestlist <- consistcv.test(T,tau,Y,ind,ngates=2)
consisttestlist$stat
consisttestlist$pval

---

Create general arguments

Description

Create general arguments

Usage

create_ml_args(data)

Arguments

data

A dataset

---

Create arguments for bartMachine

Description

Create arguments for bartMachine

Usage

create_ml_args_bart(data)

Arguments

data

A dataset

---

Create arguments for bartCause

Description

Create arguments for bartCause

Usage

create_ml_args_bartc(data)

Arguments

data

A dataset

---

Create arguments for causal forest

Description

Create arguments for causal forest

Usage

create_ml_args_causalforest(data)

Arguments

data

A dataset

---

Create arguments for LASSO

Description

Create arguments for LASSO

Usage

create_ml_args_lasso(data)

Arguments

data

A dataset

---

Create arguments for super learner

Description

Create arguments for super learner

Usage

create_ml_args_superLearner(data)

Arguments

data

A dataset

---

Create arguments for SVM

Description

Create arguments for SVM

Usage

create_ml_args_svm(data)

Arguments

data

A dataset

---

Create arguments for SVM classification

Description

Create arguments for SVM classification

Usage

create_ml_args_svm_cls(data)

Arguments

data

A dataset

---

Create arguments for ML algorithms

Description

Create arguments for ML algorithms

Usage

create_ml_arguments(outcome, treatment, data)

Arguments

outcome	Outcome of interests
treatment	Treatment variable
data	A dataset

---

Estimate individual treatment rules (ITR)

Description

Estimate individual treatment rules (ITR)

Usage

estimate_itr(
  treatment,
  form,
  data,
  algorithms,
  budget,
  n_folds = 5,
  split_ratio = 0,
  ngates = 5,
  preProcess = NULL,
  weights = NULL,
  trControl = caret::trainControl(method = "none"),
  tuneGrid = NULL,
  tuneLength = ifelse(trControl$method == "none", 1, 3),
  user_model = NULL,
  SL_library = NULL,
  ...
)

Arguments

treatment	Treatment variable
form	a formula object that takes the form y ~ T + x1 + x2 + ....
data	A data frame that contains the outcome y and the treatment T.
algorithms	List of machine learning algorithms to be used.
budget	The maximum percentage of population that can be treated under the budget constraint.
n_folds	Number of cross-validation folds. Default is 5.
split_ratio	Split ratio between train and test set under sample splitting. Default is 0.
ngates	The number of groups to separate the data into. The groups are determined by tau. Default is 5.
preProcess	caret parameter
weights	caret parameter
trControl	caret parameter
tuneGrid	caret parameter
tuneLength	caret parameter
user_model	A user-defined function to create an ITR. The function should take the data as input and return a model to estimate the ITR.
SL_library	A list of machine learning algorithms to be used in the super learner.
...	Additional arguments passed to caret::train

Value

An object of itr class

---

Evaluate ITR

Description

Evaluate ITR

Usage

evaluate_itr(
  fit = NULL,
  user_itr = NULL,
  outcome = c(),
  treatment = c(),
  data = list(),
  budget = 1,
  ngates = 5,
  ...
)

Arguments

fit	Fitted model. Usually an output from estimate_itr
user_itr	A user-defined function to create an ITR. The function should take the data as input and return an unit-level continuous score for treatment assignment. We assume those that have score less than 0 should not have treatment. The default is NULL, which means the ITR will be estimated from the estimate_itr.
outcome	A character string of the outcome variable name.
treatment	A character string of the treatment variable name.
data	A data frame containing the variables specified in outcome, treatment, and tau.
budget	The maximum percentage of population that can be treated under the budget constraint.
ngates	The number of gates to use for the ITR. The default is 5. A user-defined function to create an ITR. The function should take the data as input and return an ITR. The output is a vector of the unit-level binary treatment that would have been assigned by the individualized treatment rule. The default is NULL, which means the ITR will be estimated from the estimate_itr. See ?evaluate_itr for an example.
...	Further arguments passed to the function.

Value

An object of itr class

---

Estimate ITR for Single Outcome

Description

Estimate ITR for Single Outcome

Usage

fit_itr(data, algorithms, params, folds, budget, user_model, ...)

Arguments

data	A dataset.
algorithms	Machine learning algorithms.
params	A list of parameters.
folds	Number of folds.
budget	The maximum percentage of population that can be treated under the budget constraint.
user_model	User's own function to estimated the ITR.
...	Additional arguments passed to caret::train

Value

A list of estimates.

---

Estimation of the Grouped Average Treatment Effects (GATEs) in Randomized Experiments

Description

This function estimates the Grouped Average Treatment Effects (GATEs) where the groups are determined by a continuous score. The details of the methods for this design are given in Imai and Li (2022).

Usage

GATE(T, tau, Y, ngates = 5)

Arguments

T	A vector of the unit-level binary treatment receipt variable for each sample.
tau	A vector of the unit-level continuous score. Conditional Average Treatment Effect is one possible measure.
Y	A vector of the outcome variable of interest for each sample.
ngates	The number of groups to separate the data into. The groups are determined by tau. Default is 5.

Value

A list that contains the following items:

gate	The estimated vector of GATEs of length ngates arranged in order of increasing tau.
sd	The estimated vector of standard deviation of GATEs.

Author(s)

Michael Lingzhi Li, Technology and Operations Management, Harvard Business School [email protected], https://www.michaellz.com/;

References

Imai and Li (2022). “Statistical Inference for Heterogeneous Treatment Effects Discovered by Generic Machine Learning in Randomized Experiments”,

Examples

T = c(1,0,1,0,1,0,1,0)
tau = c(0,0.1,0.2,0.3,0.4,0.5,0.6,0.7)
Y = c(4,5,0,2,4,1,-4,3)
gatelist <- GATE(T,tau,Y,ngates=5)
gatelist$gate
gatelist$sd

---

Estimation of the Grouped Average Treatment Effects (GATEs) in Randomized Experiments Under Cross Validation

Description

This function estimates the Grouped Average Treatment Effects (GATEs) under cross-validation where the groups are determined by a continuous score. The details of the methods for this design are given in Imai and Li (2022).

Usage

GATEcv(T, tau, Y, ind, ngates = 5)

Arguments

T	A vector of the unit-level binary treatment receipt variable for each sample.
tau	A matrix where the ith column is the unit-level continuous score for treatment assignment generated in the ith fold. Conditional Average Treatment Effect is one possible measure.
Y	A vector of the outcome variable of interest for each sample.
ind	A vector of integers (between 1 and number of folds inclusive) indicating which testing set does each sample belong to.
ngates	The number of groups to separate the data into. The groups are determined by tau. Default is 5.

Value

A list that contains the following items:

gate	The estimated vector of GATEs under cross-validation of length ngates arranged in order of increasing tau.
sd	The estimated vector of standard deviation of GATEs under cross-validation.

Author(s)

Michael Lingzhi Li, Technology and Operations Management, Harvard Business School [email protected], https://www.michaellz.com/;

References

Imai and Li (2022). “Statistical Inference for Heterogeneous Treatment Effects Discovered by Generic Machine Learning in Randomized Experiments”,

Examples

T = c(1,0,1,0,1,0,1,0)
tau = matrix(c(0,0.1,0.2,0.3,0.4,0.5,0.6,0.7,-0.5,-0.3,-0.1,0.1,0.3,0.5,0.7,0.9),nrow = 8, ncol = 2)
Y = c(4,5,0,2,4,1,-4,3)
ind = c(rep(1,4),rep(2,4))
gatelist <- GATEcv(T, tau, Y, ind, ngates = 2)
gatelist$gate
gatelist$sd

---

The Heterogeneity Test for Grouped Average Treatment Effects (GATEs) in Randomized Experiments

Description

This function calculates statistics related to the test of heterogeneous treatment effects across groups.

Usage

het.test(T, tau, Y, ngates = 5)

Arguments

T	A vector of the unit-level binary treatment receipt variable for each sample.
tau	A vector of the unit-level continuous score. Conditional Average Treatment Effect is one possible measure.
Y	A vector of the outcome variable of interest for each sample.
ngates	The number of groups to separate the data into. The groups are determined by tau. Default is 5.

Details

The details of the methods for this design are given in Imai and Li (2022).

Value

A list that contains the following items:

stat	The estimated statistic for the test of heterogeneity.
pval	The p-value of the null hypothesis (that the treatment effects are homogeneous)

Author(s)

Michael Lingzhi Li, Technology and Operations Management, Harvard Business School [email protected], https://www.michaellz.com/;

References

Imai and Li (2022). “Statistical Inference for Heterogeneous Treatment Effects Discovered by Generic Machine Learning in Randomized Experiments”,

Examples

T = c(1,0,1,0,1,0,1,0)
tau = c(0,0.1,0.2,0.3,0.4,0.5,0.6,0.7)
Y = c(4,5,0,2,4,1,-4,3)
hettestlist <- het.test(T,tau,Y,ngates=5)
hettestlist$stat
hettestlist$pval

---

The Heterogeneity Test for Grouped Average Treatment Effects (GATEs) under Cross Validation in Randomized Experiments

Description

This function calculates statistics related to the test of heterogeneous treatment effects across groups under cross-validation.

Usage

hetcv.test(T, tau, Y, ind, ngates = 5)

Arguments

T	A vector of the unit-level binary treatment receipt variable for each sample.
tau	A vector of the unit-level continuous score. Conditional Average Treatment Effect is one possible measure.
Y	A vector of the outcome variable of interest for each sample.
ind	A vector of integers (between 1 and number of folds inclusive) indicating which testing set does each sample belong to.
ngates	The number of groups to separate the data into. The groups are determined by tau. Default is 5.

Details

The details of the methods for this design are given in Imai and Li (2022).

Value

A list that contains the following items:

stat	The estimated statistic for the test of heterogeneity under cross-validation.
pval	The p-value of the null hypothesis (that the treatment effects are homogeneous)

Author(s)

Michael Lingzhi Li, Technology and Operations Management, Harvard Business School [email protected], https://www.michaellz.com/;

References

Imai and Li (2022). “Statistical Inference for Heterogeneous Treatment Effects Discovered by Generic Machine Learning in Randomized Experiments”,

Examples

T = c(1,0,1,0,1,0,1,0)
tau = matrix(c(0,0.1,0.2,0.3,0.4,0.5,0.6,0.7,-0.5,-0.3,-0.1,0.1,0.3,0.5,0.7,0.9),nrow = 8, ncol = 2)
Y = c(4,5,0,2,4,1,-4,3)
ind = c(rep(1,4),rep(2,4))
hettestlist <- hetcv.test(T,tau,Y,ind,ngates=2)
hettestlist$stat
hettestlist$pval

---

Estimation of the Population Average Prescription Difference in Randomized Experiments

Description

This function estimates the Population Average Prescription Difference with a budget constraint. The details of the methods for this design are given in Imai and Li (2019).

Usage

PAPD(T, Thatfp, Thatgp, Y, budget, centered = TRUE)

Arguments

T	A vector of the unit-level binary treatment receipt variable for each sample.
Thatfp	A vector of the unit-level binary treatment that would have been assigned by the first individualized treatment rule. Please ensure that the percentage of treatment units of That is lower than the budget constraint.
Thatgp	A vector of the unit-level binary treatment that would have been assigned by the second individualized treatment rule. Please ensure that the percentage of treatment units of That is lower than the budget constraint.
Y	A vector of the outcome variable of interest for each sample.
budget	The maximum percentage of population that can be treated under the budget constraint. Should be a decimal between 0 and 1.
centered	If TRUE, the outcome variables would be centered before processing. This minimizes the variance of the estimator. Default is TRUE.

Value

A list that contains the following items:

papd	The estimated Population Average Prescription Difference
sd	The estimated standard deviation of PAPD.

Author(s)

Michael Lingzhi Li, Technology and Operations Management, Harvard Business School [email protected], https://www.michaellz.com/;

References

Imai and Li (2019). “Experimental Evaluation of Individualized Treatment Rules”,

Examples

T = c(1,0,1,0,1,0,1,0)
That = c(0,1,1,0,0,1,1,0)
That2 = c(1,0,0,1,1,0,0,1)
Y = c(4,5,0,2,4,1,-4,3)
papdlist <- PAPD(T,That,That2,Y,budget = 0.5)
papdlist$papd
papdlist$sd

---

Estimation of the Population Average Prescription Difference in Randomized Experiments Under Cross Validation

Description

This function estimates the Population Average Prescription Difference with a budget constaint under cross validation. The details of the methods for this design are given in Imai and Li (2019).

Usage

PAPDcv(T, Thatfp, Thatgp, Y, ind, budget, centered = TRUE)

Arguments

T	A vector of the unit-level binary treatment receipt variable for each sample.
Thatfp	A matrix where the ith column is the unit-level binary treatment that would have been assigned by the first individualized treatment rule generated in the ith fold. Please ensure that the percentage of treatment units of That is lower than the budget constraint.
Thatgp	A matrix where the ith column is the unit-level binary treatment that would have been assigned by the second individualized treatment rule generated in the ith fold. Please ensure that the percentage of treatment units of That is lower than the budget constraint.
Y	The outcome variable of interest.
ind	A vector of integers (between 1 and number of folds inclusive) indicating which testing set does each sample belong to.
budget	The maximum percentage of population that can be treated under the budget constraint. Should be a decimal between 0 and 1.
centered	If TRUE, the outcome variables would be centered before processing. This minimizes the variance of the estimator. Default is TRUE.

Value

A list that contains the following items:

papd	The estimated Population Average Prescription Difference.
sd	The estimated standard deviation of PAPD.

Author(s)

Michael Lingzhi Li, Technology and Operations Management, Harvard Business School [email protected], https://www.michaellz.com/;

References

Imai and Li (2019). “Experimental Evaluation of Individualized Treatment Rules”,

Examples

T = c(1,0,1,0,1,0,1,0)
That = matrix(c(0,1,1,0,0,1,1,0,1,0,0,1,1,0,0,1), nrow = 8, ncol = 2)
That2 = matrix(c(0,0,1,1,0,0,1,1,1,1,0,0,1,1,0,0), nrow = 8, ncol = 2)
Y = c(4,5,0,2,4,1,-4,3)
ind = c(rep(1,4),rep(2,4))
papdlist <- PAPDcv(T, That, That2, Y, ind, budget = 0.5)
papdlist$papd
papdlist$sd

---

Estimation of the Population Average Prescription Effect in Randomized Experiments

Description

This function estimates the Population Average Prescription Effect with and without a budget constraint. The details of the methods for this design are given in Imai and Li (2019).

Usage

PAPE(T, That, Y, budget = NA, centered = TRUE)

Arguments

T	A vector of the unit-level binary treatment receipt variable for each sample.
That	A vector of the unit-level binary treatment that would have been assigned by the individualized treatment rule. If budget is specified, please ensure that the percentage of treatment units of That is lower than the budget constraint.
Y	A vector of the outcome variable of interest for each sample.
budget	The maximum percentage of population that can be treated under the budget constraint. Should be a decimal between 0 and 1. Default is NA which assumes no budget constraint.
centered	If TRUE, the outcome variables would be centered before processing. This minimizes the variance of the estimator. Default is TRUE.

Value

A list that contains the following items:

pape	The estimated Population Average Prescription Effect.
sd	The estimated standard deviation of PAPE.

Author(s)

Michael Lingzhi Li, Technology and Operations Management, Harvard Business School [email protected], https://www.michaellz.com/;

References

Imai and Li (2019). “Experimental Evaluation of Individualized Treatment Rules”,

Examples

T = c(1,0,1,0,1,0,1,0)
That = c(0,1,1,0,0,1,1,0)
Y = c(4,5,0,2,4,1,-4,3)
papelist <- PAPE(T,That,Y)
papelist$pape
papelist$sd

---

Estimation of the Population Average Prescription Effect in Randomized Experiments Under Cross Validation

Description

This function estimates the Population Average Prescription Effect with and without a budget constraint. The details of the methods for this design are given in Imai and Li (2019).

Usage

PAPEcv(T, That, Y, ind, budget = NA, centered = TRUE)

Arguments

T	A vector of the unit-level binary treatment receipt variable for each sample.
That	A matrix where the ith column is the unit-level binary treatment that would have been assigned by the individualized treatment rule generated in the ith fold. If budget is specified, please ensure that the percentage of treatment units of That is lower than the budget constraint.
Y	The outcome variable of interest.
ind	A vector of integers (between 1 and number of folds inclusive) indicating which testing set does each sample belong to.
budget	The maximum percentage of population that can be treated under the budget constraint. Should be a decimal between 0 and 1. Default is NA which assumes no budget constraint.
centered	If TRUE, the outcome variables would be centered before processing. This minimizes the variance of the estimator. Default is TRUE.

Value

A list that contains the following items:

pape	The estimated Population Average Prescription Effect.
sd	The estimated standard deviation of PAPE.

Author(s)

Michael Lingzhi Li, Technology and Operations Management, Harvard Business School [email protected], https://www.michaellz.com/;

References

Imai and Li (2019). “Experimental Evaluation of Individualized Treatment Rules”,

Examples

T = c(1,0,1,0,1,0,1,0)
That = matrix(c(0,1,1,0,0,1,1,0,1,0,0,1,1,0,0,1), nrow = 8, ncol = 2)
Y = c(4,5,0,2,4,1,-4,3)
ind = c(rep(1,4),rep(2,4))
papelist <- PAPEcv(T, That, Y, ind)
papelist$pape
papelist$sd

---

Estimation of the Population Average Value in Randomized Experiments

Description

This function estimates the Population Average Value. The details of the methods for this design are given in Imai and Li (2019).

Usage

PAV(T, That, Y, centered = TRUE)

Arguments

T	A vector of the unit-level binary treatment receipt variable for each sample.
That	A vector of the unit-level binary treatment that would have been assigned by the individualized treatment rule. If budget is specified, please ensure that the percentage of treatment units of That is lower than the budget constraint.
Y	A vector of the outcome variable of interest for each sample.
centered	If TRUE, the outcome variables would be centered before processing. This minimizes the variance of the estimator. Default is TRUE.

Value

A list that contains the following items:

pav	The estimated Population Average Value.
sd	The estimated standard deviation of PAV.

Author(s)

Michael Lingzhi Li, Technology and Operations Management, Harvard Business School [email protected], https://www.michaellz.com/;

References

Imai and Li (2019). “Experimental Evaluation of Individualized Treatment Rules”,

Examples

T = c(1,0,1,0,1,0,1,0)
That = c(0,1,1,0,0,1,1,0)
Y = c(4,5,0,2,4,1,-4,3)
pavlist <- PAV(T,That,Y)
pavlist$pav
pavlist$sd

---

Estimation of the Population Average Value in Randomized Experiments Under Cross Validation

Description

This function estimates the Population Average Value. The details of the methods for this design are given in Imai and Li (2019).

Usage

PAVcv(T, That, Y, ind, centered = TRUE)

Arguments

T	A vector of the unit-level binary treatment receipt variable for each sample.
That	A matrix where the ith column is the unit-level binary treatment that would have been assigned by the individualized treatment rule generated in the ith fold. If budget is specified, please ensure that the percentage of treatment units of That is lower than the budget constraint.
Y	The outcome variable of interest.
ind	A vector of integers (between 1 and number of folds inclusive) indicating which testing set does each sample belong to.
centered	If TRUE, the outcome variables would be centered before processing. This minimizes the variance of the estimator. Default is TRUE.

Value

A list that contains the following items:

pav	The estimated Population Average Value.
sd	The estimated standard deviation of PAV.

Author(s)

Michael Lingzhi Li, Technology and Operations Management, Harvard Business School [email protected], https://www.michaellz.com/;

References

Imai and Li (2019). “Experimental Evaluation of Individualized Treatment Rules”,

Examples

T = c(1,0,1,0,1,0,1,0)
That = matrix(c(0,1,1,0,0,1,1,0,1,0,0,1,1,0,0,1), nrow = 8, ncol = 2)
Y = c(4,5,0,2,4,1,-4,3)
ind = c(rep(1,4),rep(2,4))
pavlist <- PAVcv(T, That, Y, ind)
pavlist$pav
pavlist$sd

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Plot the GATE estimate

Description

Plot the GATE estimate

Usage

plot_estimate(x, type, ...)

Arguments

x	An table object. This is typically an output of evaluate_itr() function.
type	The metric that you wish to plot. One of GATE, PAPE, PAPEp, or PAPDp.
...	Further arguments passed to the function.

Value

A plot of ggplot2 object.

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Plot the AUPEC curve

Description

Plot the AUPEC curve

Usage

## S3 method for class 'itr'
plot(x, ...)

Arguments

x	An object of evaluate_itr() class. This is typically an output of evaluate_itr() function.
...	Further arguments passed to the function.

Value

A plot of ggplot2 object.

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Print

Description

Print

Usage

## S3 method for class 'summary.itr'
print(x, ...)

Arguments

x	An object of summary.itr class. This is typically an output of summary.itr() function.
...	Other parameters. Currently not supported.

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Print

Description

Print

Usage

## S3 method for class 'summary.test_itr'
print(x, ...)

Arguments

x	An object of summary.test_itr class. This is typically an output of summary.test_itr() function.
...	Other parameters.

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Tennessee’s Student/Teacher Achievement Ratio (STAR) project

Description

A longitudinal study experimentally evaluating the impacts of class size in early education on various outcomes (Mosteller, 1995)

Usage

star

Format

A data frame with 1911 observations and 14 variables:

treatment

A binary treatment indicating whether a student is assigned to small class and regular class without an aid

g3tlangss

A continous variable measuring student's writing scores

g3treadss

A continous variable measuring student's reading scores

g3tmathss

A continous variable measuring student's math scores

gender

Students' gender

race

Students' race

birthmonth

Students' birth month

birthyear

Students' birth year

SCHLURBN

Urban or rural

GKENRMNT

Enrollment size

GRDRANGE

Grade range

GKFRLNCH

Number of students on free lunch

GKBUSED

Number of students on school buses

GKWHITE

Percentage of white students

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Summarize estimate_itr output

Description

Summarize estimate_itr output

Usage

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

Arguments

object	An object of estimate_itr class (typically an output of estimate_itr() function).
...	Other parameters.

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Summarize test_itr output

Description

Summarize test_itr output

Usage

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

Arguments

object	An object of test_itr class (typically an output of test_itr() function).
...	Other parameters.

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Conduct hypothesis tests

Description

Conduct hypothesis tests

Usage

test_itr(fit, nsim = 1000, ...)

Arguments

fit	Fitted model. Usually an output from estimate_itr
nsim	Number of Monte Carlo simulations used to simulate the null distributions. Default is 1000.
...	Further arguments passed to the function.

Value

An object of test_itr class

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