Help for package RCT2

Version:

0.0.1

Date:

2022-10-16

Title:

Designing and Analyzing Two-Stage Randomized Experiments

Maintainer:

Kosuke Imai <imai@harvard.edu>

Depends:

R (≥ 3.1.0)

Description:

Provides various statistical methods for designing and analyzing two-stage randomized controlled trials using the methods developed by Imai, Jiang, and Malani (2021) <doi:10.1080/01621459.2020.1775612> and (2022+) <doi:10.48550/arXiv.2011.07677>. The package enables the estimation of direct and spillover effects, conduct hypotheses tests, and conduct sample size calculation for two-stage randomized controlled trials.

License:

GPL-2 | GPL-3 [expanded from: GPL (≥ 2)]

URL:

https://github.com/kosukeimai/RCT2

BugReports:

https://github.com/kosukeimai/RCT2/issues

RoxygenNote:

7.2.1

Suggests:

testthat, knitr, rmarkdown

VignetteBuilder:

knitr

Imports:

sandwich, AER, stats, quadprog

NeedsCompilation:

Packaged:

2022-10-18 03:04:05 UTC; kosukeimai

Author:

Karissa Huang [aut], Zhichao Jiang [aut], Kosuke Imai [aut, cre]

Repository:

CRAN

Date/Publication:

2022-10-18 07:05:17 UTC

Regression-based method for the ITT effects and the complier average direct effect/spillover effect

Description

This function computes the point estimates and variance estimates of the direct effect and spillover effect for ITT and CADE/CASE

Usage

CADEparamreg(data, assign.prob, ci.level = 0.95)

Arguments

data

A data frame containing the relevant variables. The names for the variables should be: “Z” for the treatment assignment, “D” for the actual received treatment, “Y” for the outcome, “A” for the treatment assignment mechanism and “id” for the cluster ID. The variable for the cluster id should be a factor.

assign.prob

A double between 0 and 1 specifying the assignment probability to either assignment mechanism.

ci.level

A double between 0 and 1 specifying the confidence interval level to be output.

Details

For the details of the method implemented by this function, see the references.

Value

A list of class CADEparamreg which contains the following items:

ITT.DE

Estimate of direct effect under ITT regresion.

ITT.SE

Estimate of spillover effect under ITT regresion.

ITT.DE.CI

Confidence itnerval of direct effect under ITT regresion.

ITT.SE.CI

Confidence itnerval of spillover effect under ITT regresion.

IV.DE

Estimate of direct effect under IV regresion.

IV.SE

Estimate of spillover effect under IV regresion.

IV.DE.CI

Confidence interval of direct effect under IV regresion.

IV.SE.CI

Confidence interval of spillover effect under IV regresion.

IV.DE.CI

Confidence interval of direct effect under IV regresion.

ITT.tstat

t-stats from ITT regression.

IV.tstat

t-stats from IV regression.

ITT.pvals

p-values from ITT regression.

IV.pvals

p-values from IV regression.

data(india) india$id <- factor(india$id) CADEreg(india, ci.level = 0.90)

Author(s)

Kosuke Imai, Department of Statistics, Harvard University imai@harvard.edu, https://imai.fas.harvard.edu/; Zhichao Jiang, School of Public Health and Health Sciences, University of Massachusetts Amherst zhichaojiang@umass.edu; Karissa Huang, Department of Statistics, Harvard College krhuang@college.harvard.edu

References

Kosuke Imai, Zhichao Jiang and Anup Malani (2018). “Causal Inference with Interference and Noncompliance in the Two-Stage Randomized Experiments”, Technical Report. Department of Politics, Princeton University.

Randomization-based method for the complier average direct effect and the complier average spillover effect

Description

This function computes the point estimates and variance estimates of the complier average direct effect (CADE) and the complier average spillover effect (CASE). The estimators calculated using this function are either individual weighted or cluster-weighted. The point estimates and variances of ITT effects are also included.

Usage

CADErand(data, individual = 1, ci = 0.95)

Arguments

data

individual

A binary variable with TRUE for individual-weighted estimators and FALSE for cluster-weighted estimators.

ci

A numeric variable between 0 and 1 for the level of the confidence interval to be returned.

Details

For the details of the method implemented by this function, see the references.

Value

A list of class CADErand which contains the following items:

CADE

The point estimates of the CADE for each assignment mechanism.

CASE

The point estimate of CASE for each assignment mechanism.

var.CADE1

The variance estimate of CADE for each assignment mechanism.

var.CASE1

The variance estimate of CASE for each assignment mechanism.

DEY1

The point estimate of DEY for each assignment mechanism.

DED1

The point estimate of DED for each assignment mechanism.

var.DEY1

The variance estimate of DEY for each assignment mechanism.

var.DED1

The variance estimate of DED for each assignment mechanism.

SEY1

The point estimate of SEY for each pairwise groups of assignment mechanisms.

SED1

The point estimate of SED for each pairwise groups of assignment mechanisms.

var.SEY1

The variance estimate of SEY for each pairwise groups of assignment mechanisms.

var.SED1

The variance estimate of SED for each pairwise groups of assignment mechanisms.

lci.CADE

The left endpoint for the confidence intervals for the CADE from each assignment mechanism.

rci.CADE

The right endpoint for the confidence intervals for the CADE from each assignment mechanism.

lci.CASE

The left endpoint for the confidence intervals for the CASE from each assignment mechanism.

rci.CASE

The left endpoint for the confidence intervals for the CASE from each assignment mechanism.

lci.DEY

The left endpoint for the confidence intervals for the DEY from each assignment mechanism.

rci.DEY

The left endpoint for the confidence intervals for the DEY from each assignment mechanism.

lci.SEY

The left endpoint for the confidence intervals for the SEY from each pairwise groups of assignment mechanisms.

rci.SEY

The left endpoint for the confidence intervals for the SEY from each pairwise groups of assignment mechanism.

lci.DED

The left endpoint for the confidence intervals for the DED from each assignment mechanism.

rci.DED

The left endpoint for the confidence intervals for the DED from each assignment mechanism.

lci.SED

The left endpoint for the confidence intervals for the SED from each pairwise groups of assignment mechanism.

rci.SED

The left endpoint for the confidence intervals for the SED from each pairwise groups of assignment mechanism.

Author(s)

References

Examples

data(india)
india$id <- factor(india$id)
CADErand(india, 0.95)

Regression-based method for the complier average direct effect

Description

This function computes the point estimates of the complier average direct effect (CADE) and four different variance estimates: the HC2 variance, the cluster-robust variance, the cluster-robust HC2 variance and the variance proposed in the reference. The estimators calculated using this function are cluster-weighted, i.e., the weights are equal for each cluster. To obtain the indivudal-weighted estimators, please multiply the recieved treatment and the outcome by n_jJ/N, where n_j is the number of individuals in cluster j, J is the number of clusters and N is the total number of individuals.

Usage

CADEreg(data, ci.level = 0.95)

Arguments

data

ci.level

A double between 0 and 1 specifying the confidence interval level to be output.

Details

For the details of the method implemented by this function, see the references.

Value

A list of class CADEreg which contains the following items:

CADE1

The point estimate of CADE(1).

CADE0

The point estimate of CADE(0).

var1.clu

The cluster-robust variance of CADE(1).

var0.clu

The cluster-robust variance of CADE(0).

var1.clu.hc2

The cluster-robust HC2 variance of CADE(1).

var0.clu.hc2

The cluster-robust HC2 variance of CADE(0).

var1.hc2

The HC2 variance of CADE(1).

var0.hc2

The HC2 variance of CADE(0).

var1.ind

The individual-robust variance of CADE(1).

var0.ind

The individual-robust variance of CADE(0).

var1.reg

The proposed variance of CADE(1).

var0.reg

The proposed variance of CADE(0).

Author(s)

References

Examples

data(india)
india$id <- factor(india$id)
CADEreg(india, ci.level = 0.90)

Point Estimation and Variance for the unit-level direct effect (ADE), marginal direct effect (MDE), and unit level spillover effect (ASE)

Description

This function calculates the estimated average potential outcomes Y(z,a), point estimates for the ADE, MDE, and ASE, and conservative covariance matrix estimates.

Usage

CalAPO(data)

Arguments

data

A data frame containing the relevant variables. The names for the variables should be “Z” for the treatment assignment, “Y” for the treatment outcome, “A” for the treatment assignment mechanism, and “id” for the cluster ID. The variable for the cluster ID should be a factor.

Details

For the details of the method implemented by this function, see the references.

Value

A list of class CalAPO which contains the following items:

Y.hat

Estimate of the average potential outcomes.

ADE.est

Estimate of the unit level direct effect.

MDE.est

Estimate of the marginal direct effect.

ASE.est

Estimate of the unti level spillover effect.

cov.hat

Conservative covariance matrix for the estimated potential outcomes.

var.hat.ADE

Estimated variance of the ADE.

var.hat.MDE

Estimated variance of the MDE.

var.hat.ASE

Estimated variance of the ASE.

Author(s)

References

Zhichao Jiang, Kosuke Imai (2020). “Statistical Inference and Power Analysis for Direct and Spillover Effects in Two-Stage Randomized Experiments”, Technical Report.

Examples

data(jd)
data_LTFC <- data.frame(jd$assigned, jd$pct0, jd$cdd6m, jd$anonale)
colnames(data_LTFC) <- c("Z", "A", "Y", "id")
test <- CalAPO(data_LTFC)
print(CalAPO(data_LTFC))

Sample size calculations for detecting a specific alternative

Description

This function calculates the sample size needed to detect a specific alternative hypothesis with a given power at a given significance level. For the details of the method implemented by this function, see the references.

Usage

Calsamplesize(data, mu, qa, alpha = 0.05, beta = 0.2)

Arguments

data

mu

The effect size (i.e. the largest direct effect across treatment assignment mechanisms).

qa

The proportions of different treatment assignment mechanisms.

alpha

The given significance level (default 0.05).

beta

The given power level (default 0.2).

Value

A list of class sampleSRE which contains the following item:

samplesize

A list of the calculated necessary nubmer of clusters for each assignment mechanism in order to detect a specific alternative with a given power at a given significance level.

Author(s)

References

Zhichao Jiang, Kosuke Imai (2020). “Statistical Inference and Power Analysis for Direct and Spillover Effects in Two-Stage Randomized Experiments”, Technical Report.

Hypothesis testing for three null hypotheses

Description

This function tests the null hypotheses of no direct effect, no marginal direct effect, and no spillover effect.

Usage

Test2SRE(data, effect = "DE", alpha = 0.05)

Arguments

data

effect

Specify which null hypothesis to be tested. “DE” for direct effect, “ME” for marginal effect, and “SE” for spillover effect.

alpha

The level of significance at which the test is to be run (default is 0.05).

Details

For the details of the method implemented by this function, see the references.

Value

A list of class Test2SRE which contains the following item:

rej

Rejection region for test conducted.

Author(s)

References

Zhichao Jiang, Kosuke Imai (2020). “Statistical Inference and Power Analysis for Direct and Spillover Effects in Two-Stage Randomized Experiments”, Technical Report.

Examples

data(jd)
data_LTFC <- data.frame(jd$assigned, jd$pct0, jd$cdd6m, jd$anonale)
colnames(data_LTFC) <- c("Z", "A", "Y", "id")
Test2SRE(data_LTFC, effect="MDE", alpha=0.05)

Sample size parameter calculations for detecting a specific alternative

Description

This function calculates the parameters needed for the method to calculate sample size references.

Usage

calpara(data)

Arguments

data

Value

A list of class calpara which contains the following item:

sigmaw

The within-cluster variance of the potential outcomes, with the assumption that the all of the variances the same.

sigmab

The between-cluster variance of the potential outcomes, with the assumption that all of the variances are the same.

r

The intraclass correlation coefficient with respect to the potential outcomes.

sigma.tot

The total variance of the potential outcomes.

n.avg

The mean of the number of treated observations by cluster.

Author(s)

References

Zhichao Jiang, Kosuke Imai (2020). “Statistical Inference and Power Analysis for Direct and Spillover Effects in Two-Stage Randomized Experiments”, Technical Report.

Examples

data(jd)
data_LTFC <- data.frame(jd$assigned, jd$pct0, jd$cdd6m, jd$anonale)
colnames(data_LTFC) <- c("Z", "A", "Y", "id")
var.LTFC <- calpara(data_LTFC)

Replication Data for: Causal Inference with Interference and Noncompliance in Two-Stage Randomized Experiments.

Description

Replication Data for: Causal Inference with Interference and Noncompliance in Two-Stage Randomized Experiments.

Usage

data(india)

Format

A data frame with columns:

id: The id for the village.
DistrictId: The id for the district.
Z: The treatment status for the individual.
A: The treatment assignment mechanism.
D: Whether or not the individual enrolled.
Y: The hospital expenditure.
X: Enumeration of the patients.

Source

doi:10.7910/DVN/N7D9LS

Replication Data for: Statistical Inference and Power Analysis for Direct and Spillover Effects in Two-Stage Randomized Experiments

Description

Replication Data for: Statistical Inference and Power Analysis for Direct and Spillover Effects in Two-Stage Randomized Experiments

Usage

data(jd)

Format

A data frame with columns:

anonale: The local employment agency.
tempsc_av: Categorical variable for full-time work at time of assignment (1: 1-4 months, 2: 4-8 months, 3: 8-12 months, 4: 12+ months)
assigned: An indicator variable for whether or not the individual is assigned to treatment.
pct0: The share of the local population treated (as a decimal).
cdi: An indicator variable for whether the individual works on a permanent contract 8 months after assignment.
cdd6m: An indicator variable for whether the individual works in CDD (LTFC-time contract) for more than 6 months, 8 months after the assignment.
emploidur: An indicator variable for whether the individual works on a permanent or LTFC-term contract for more than 6 months, 8 months after the assignment.
tempsc: An indicator variable for whether the individual works full time, 8 months after the assignment.
salaire: The individual's salary in Euros.

Print Method for the RCT2 Package

Description

This function prints a nicely formatted summary of the three functions in the RCT2 package.

Usage

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

Arguments

x

A list object generated by running one of the analyses on a data set.

...

ignored

Details

For the details of the method implemented by this function, see the references.

Value

NULL