Skip to contents

Simultaneous bound for confidence interval using combined rank sum statistic on stratified randomized experiment

Source: R/CMRSS_SRE.R
com_block_conf_quant_larger.Rd

Computes simultaneous confidence intervals for quantiles of individual treatment effects in stratified randomized experiments.

Usage

com_block_conf_quant_larger(
  Z,
  Y,
  block,
  set = "all",
  methods.list.all = NULL,
  weight.name = "asymp.opt",
  opt.method = "ILP_auto",
  comb.method = 1,
  stat.null = NULL,
  null.max = 10^4,
  Z.perm = NULL,
  tol = 0.01,
  alpha = 0.1
)

Arguments

Z

An \(n\) dimensional treatment assignment vector.

Y

An \(n\) dimensional observed outcome vector.

block

An \(n\) dimensional vector specifying block of each unit.

set

Set of quantiles of interest. Options:

  • "treat": Prediction intervals for effect quantiles among treated units

  • "control": Prediction intervals for effect quantiles among control units

  • "all": Confidence intervals for all effect quantiles

methods.list.all

A list of lists of lists. Corresponds to the method for each stratum for each different stratified rank sum statistic.

weight.name

Weighting method to be implemented. If "asymp.opt", asymptotically optimal scheme under a class of local alternatives is adjusted, if "dist.free", design-free scheme is adjusted.

opt.method

Optimization method. Options include:

  • "ILP_gurobi": Integer linear programming with Gurobi solver

  • "LP_gurobi": Linear programming relaxation with Gurobi solver

  • "ILP_highs": Integer linear programming with HiGHS solver (open-source)

  • "LP_highs": Linear programming relaxation with HiGHS solver

  • "ILP" or "ILP_auto": Integer LP with auto-selected solver

  • "LP" or "LP_auto": Linear programming with auto-selected solver

HiGHS is recommended for users without a Gurobi license. Both solvers produce equivalent results.

comb.method

Integer specifying the combination method:

  • 1: Combine statistics across strata first, then take maximum across methods (default)

  • 2: Take maximum across methods within each stratum first, then combine across strata

stat.null

An vector whose empirical distribution approximates the randomization distribution of the combined stratified rank sum statistic.

null.max

A positive integer representing the number of permutations for approximating the randomization distribution of the rank sum statistic.

Z.perm

Optional pre-computed n x null.max matrix of permuted treatment assignments. If provided, this matrix will be used instead of generating new permutations. Can be generated using assign_block(summary_block(Z, block), null.max).

tol

A numerical object specifying the precision of the obtained confidence intervals. For example, if tol = 10^(-3), then the confidence limits are precise up to 3 digits.

alpha

A numerical object, where 1-alpha indicates the confidence level.

Value

A vector specifying lower limits of prediction (confidence) intervals for quantiles k = 1 ~ m (or n - m, or n).

See also

com_conf_quant_larger_cre for completely randomized experiments, pval_comb_block for hypothesis testing

Examples

if (FALSE) { # \dontrun{
# Load the electric teachers dataset
data(electric_teachers)

# Set up treatment, outcome, and blocking variable
Z <- electric_teachers$TxAny
Y <- electric_teachers$gain
block <- factor(electric_teachers$Site)
s <- length(levels(block))  # number of strata (7 sites)

# Define polynomial rank statistics with different r values
# For SRE, methods must be specified for EACH stratum within EACH statistic
r.vec <- c(2, 6, 10)
methods.list.all <- list()
for (j in seq_along(r.vec)) {
  methods.list.all[[j]] <- lapply(1:s, function(i) {
    list(name = "Polynomial", r = r.vec[j], std = TRUE, scale = FALSE)
  })
}

# Prediction intervals for effect quantiles among treated units
# Uses asymptotically optimal weighting across strata
ci.treat <- com_block_conf_quant_larger(Z, Y, block,
                                        set = "treat",
                                        methods.list.all = methods.list.all,
                                        weight.name = "asymp.opt",
                                        opt.method = "ILP",
                                        null.max = 10000,
                                        tol = 0.01,
                                        alpha = 0.05)

# Prediction intervals for control units
ci.control <- com_block_conf_quant_larger(Z, Y, block,
                                          set = "control",
                                          methods.list.all = methods.list.all,
                                          opt.method = "ILP",
                                          alpha = 0.05)

# Confidence intervals for all effect quantiles
ci.all <- com_block_conf_quant_larger(Z, Y, block,
                                      set = "all",
                                      methods.list.all = methods.list.all,
                                      opt.method = "ILP",
                                      alpha = 0.10)

# Using stratum-level combination (comb.method = 2)
# Takes maximum across methods within each stratum first
ci.treat.m2 <- com_block_conf_quant_larger(Z, Y, block,
                                           set = "treat",
                                           methods.list.all = methods.list.all,
                                           opt.method = "ILP",
                                           comb.method = 2,
                                           alpha = 0.05)

# Using LP relaxation for faster computation
ci.treat.lp <- com_block_conf_quant_larger(Z, Y, block,
                                           set = "treat",
                                           methods.list.all = methods.list.all,
                                           opt.method = "LP",
                                           alpha = 0.05)
} # }