Chen and Li Combination Method

Method combining treated and control inference using Bonferroni correction, based on Chen and Li (2024).

Usage

method_chen_li(
  Z,
  Y,
  N,
  k_vec,
  control.method.list = list(name = "Stephenson", s = 6),
  treat.method.list = list(name = "Stephenson", s = 6),
  simul = TRUE,
  stat.null = NULL,
  score = NULL,
  Z.perm = NULL,
  alpha = 0.05,
  gamma = 0.5,
  alpha.ratio.treat = 0.5,
  ndraw = 10^5,
  nperm = 10^4,
  tol = 10^(-3)
)

Arguments

Z

An n-dimensional binary treatment assignment vector (1 = treated, 0 = control).

Y

An n-dimensional observed outcome vector.

N

Population size for generalization. Set to length(Z) for sample inference.

k_vec

Vector of quantile ranks to compute intervals for.

control.method.list

Method specification for control units.

treat.method.list

Method specification for treated units.

simul

Logical; if TRUE (default), compute simultaneous intervals.

stat.null

Optional pre-computed null distribution.

score

Optional pre-computed score vector.

Z.perm

Optional permutation matrix.

alpha

Significance level.

gamma

Proportion of alpha for hypergeometric correction.

alpha.ratio.treat

Proportion of alpha allocated to treated units.

ndraw

Number of Monte Carlo draws for hypergeometric correction.

nperm

Number of permutations for null distribution.

tol

Tolerance for root-finding.

Value

A data frame with columns k, lower, and upper.

Details

This method combines inference from both treated and control perspectives using a Bonferroni-style correction. It provides confidence intervals for all effect quantiles by separately computing prediction intervals for treated and control units, then combining them.

When N > n (the sample size), the method incorporates a hypergeometric correction to generalize inference to the larger population.

References

Chen, H. and Li, X. (2024). Randomization Inference for Quantile Treatment Effects with Varying Numbers of Treated and Control Units.

See also

method_caughey for single-direction inference, com_conf_quant_larger_cre for the CMRSS combined method

Examples

if (FALSE) { # \dontrun{
data(electric_teachers)
Z <- electric_teachers$TxAny
Y <- electric_teachers$gain
n <- length(Z)

# Confidence intervals for all effect quantiles
result <- method_chen_li(Z, Y,
                         N = n,  # sample inference
                         k_vec = 1:n,
                         treat.method.list = list(name = "Stephenson", s = 6),
                         control.method.list = list(name = "Stephenson", s = 6),
                         nperm = 10000,
                         alpha = 0.10)
print(head(result))
} # }