PER {ivdesign}

Two-sided test for the pooled effect ratio estimand

Description

PER returns the two-sided p-value testing the pooled effect ratio equal to lambda_0 in a cluster-randomized encouragement experiment.

Usage

PER(lambda_0, R_t, R_c, d_t, d_c, Q = NULL)

Arguments

lambda_0

The magnitude of the pooled effect ratio estimand to be tested.

R_t

A length-K vector where K is equal to the number of clusters and the kth entry equal to the sum of unit-level outcomes in the encouraged cluster of the kth matched pair of two clusters.

R_c

A length-K vector where K is equal to the number of clusters and the kth entry equal to the sum of unit-level outcomes in the control cluster of the kth matched pair of two clusters.

d_t

A length-K vector where K is equal to the number of clusters and the kth entry equal to the sum of unit-level treatment received in the encouraged cluster of the kth matched pair of two clusters.

d_c

A length-K vector where K is equal to the number of clusters and the kth entry equal to the sum of unit-level treatment received in the control cluster of the kth matched pair of two clusters.

Q

A K times p design matrix containing the covariate information. See Details.

Details

Q is used to construct a regression-assisted variance estimator. Q is can in principle be any K times p design matrix such that p < K. When Q is a column vector of 1's, the variance estimator is the classical sample variance estimator. More generally, Q may contain any cluster-level or even unit-level covariate information that are predictive of the encouraged-minus-control difference in the observed aggregated outcomes.

Value

A list of five elements: two-sided p-value, deviate, test statistics, expectation of the test statistic under the null hypothesis, and variance of the test statistic under the null hypothesis.

Examples

R_t = encouraged_clusters$aggregated_outcome
R_c = control_clusters$aggregated_outcome
d_t = encouraged_clusters$aggregated_treatment
d_c = control_clusters$aggregated_treatment


# Test the pooled effect ratio estimand lambda = 0 using
# the default sample variance estimator, i.e., setting Q = NULL.
res = PER(0, R_t, R_c, d_t, d_c)

# We may leverage observed covariates from both the encouraged
# and control clusters to construct less conservative variance
# estimator. The variance estimator will be less conservative if
# these covariate predict the treated-minus-control difference
# in the outcome. In this illustrated dataset, V1-V10 are simulated
# white noise; it is not surprising that they do not help
# reduce the variance.
Q = cbind(encouraged_clusters[,1:10], control_clusters[,1:10])
res_2 = PER(0, R_t, R_c, d_t, d_c, Q)