ATEcluster {experiment}

Estimation of the Average Treatment Effects in Cluster-Randomized Experiments

Description

This function estimates various average treatment effect in cluster-randomized experiments without using pre-treatment covariates. The treatment variable is 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

ATEcluster(
  Y,
  Z,
  grp,
  data = parent.frame(),
  match = NULL,
  weights = NULL,
  fpc = TRUE
)

Arguments

Y

The outcome variable of interest.

Z

The (randomized) cluster-level treatment 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.

fpc

A logical variable indicating whether or not finite population correction should be used for estimating the lower bound of CACE variance. This is relevant only when weights are specified.

Value

A list of class ATEcluster which contains the following items:

call

The matched call.

n

The total number of units.

n1

The total number of units in the treatment group.

n0

The total number of units in the control group.

Y

The outcome variable.

Y1bar

The cluster-specific (unweighted) average value of the observed outcome for the treatment group.

Y0bar

The cluster-specific (unweighted) average value of the observed outcome for the treatment group.

Y1var

The cluster-specific sample variance of the observed outcome for the treatment group.

Y0var

The cluster-specific sample variance of the observed outcome for the control group.

Z

The treatment variable.

grp

The cluster-indicator variable.

match

The matched-pair indicator variable.

weights

The weight variable in its original form.

est

The estimated average treatment effect based on the arithmetic mean weights.

var

The estimated variance of the average treatment effect estimator based on the arithmetic mean weights. This uses the variance formula provided in Imai, King, and Nall (2007).

var.lb

The estimated sharp lower bound of the cluster average treatment effect estimator using the arithmetic mean weights.

est.dk

The estimated average treatment effect based on the harmonic mean weights.

var.dk

The estimated variance of the average treatment effect estimator based on the harmonic mean weights. This uses the variance formula provided in Donner and Klar (1993).

dkvar

The estimated variance of the average treatment effect estimator based on the harmonic mean weights. This uses the variance formula provided in Imai, King, and Nall (2007).

eff

The estimated relative efficiency of the matched-pair design over the completely randomized design (the ratio of two estimated variances).

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.

w1

Cluster-specific weights for the treatment group.

w0

Cluster-specific weights 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.

w.dk

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

diff

Within-pair differences if the matched-pair design is analyzed. This equals the difference between Y1bar and Y0bar.

Author(s)

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

References

Donner, A. and N. Klar (1993). “Confidence interval construction for effect measures arising from cluster randomized trials.” Journal of Clinical Epidemiology. Vol. 46, No. 2, pp. 123-131.

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.