CACEcluster {experiment}

Estimation of the Complier Average Causal Effects in Cluster-Randomized Experiments with Unit-level Noncompliance

Description

This function estimates various complier average causal effect in cluster-randomized experiments without using pre-treatment covariates when unit-level noncompliance exists. Both the encouragement and treatment variables are assumed to be binary. Currently, only the matched-pair design is allowed. The details of the methods for this design are given in Imai, King, and Nall (2007).

Usage

CACEcluster(
  Y,
  D,
  Z,
  grp,
  data = parent.frame(),
  match = NULL,
  weights = NULL,
  ...
)

Arguments

Y

The outcome variable of interest.

D

The unit-level treatment receipt variable. This variable should be binary but can differ across units within each cluster.

Z

The (randomized) cluster-level encouragement variable. This variable should be binary. Two units in the same cluster should have the same value.

grp

A variable indicating clusters of units. Two units in the same cluster should have the same value.

data

A data frame containing the relevant variables.

match

A variable indicating matched-pairs of clusters. Two units in the same matched-pair of clusters should have the same value. The default is NULL (i.e., no matching).

weights

A variable indicating the population cluster sizes, which will be used to construct weights for each pair of clusters. Two units in the same cluster should have the same value. The default is NULL, in which case sample cluster sizes will be used for constructing weights.

...

Optional arguments passed to ATEcluster, which is called internally.

Value

A list of class CACEcluster which contains the following items:

call

The matched call.

ITTY

The output object from ATEcluster which is used to estimate the ITT effect of the encouragement on the outcome variable.

ITTD

The output object from ATEcluster which is used to estimate the ITT effect of the encouragement on the treatment receipt variable.

n1

The total number of units in the treatment group.

n0

The total number of units in the control group.

Z

The treatment variable.

est

The estimated complier average causal effect.

var

The estimated variance of the complier average causal effect estimator.

cov

The estimated covariance between two ITT estimator.

m

The number of pairs in the matched-pair design.

N1

The population cluster sizes for the treatment group.

N0

The population cluster sizes for the control group.

w

Pair-specific normalized arithmetic mean weights. These weights sum up to the total number of units in the sample, i.e., n.

Author(s)

Kosuke Imai, Department of Government and Department of Statistics, Harvard University [e-mail], https://imai.fas.harvard.edu;

References

Imai, Kosuke, Gary King, and Clayton Nall (2007). “The Essential Role of Pair Matching in Cluster-Randomized Experiments, with Application to the Mexican Universal Health Insurance Evaluation”, Technical Report. Department of Politics, Princeton University.