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Simultaneous lower bounds using multiple rank sum statistics in CRE

Source: R/CMRSS_CRE.R
com_conf_quant_larger_cre.Rd

Computes simultaneous confidence/prediction intervals for quantiles of individual treatment effects in completely randomized experiments (CRE) by combining multiple rank sum statistics.

Usage

com_conf_quant_larger_cre(
  Z,
  Y,
  methods.list,
  nperm = 10^4,
  set = "treat",
  Z.perm = NULL,
  alpha = 0.05,
  tol = 10^(-3)
)

Arguments

Z

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

Y

An \(n\) dimensional observed outcome vector.

methods.list

A list of lists specifying the choice of multiple rank sum test statistics. Each element should be a list with:

  • name: "Wilcoxon", "Stephenson", or "Polynomial"

  • s: (for Stephenson) parameter s controlling sensitivity to upper ranks

  • r: (for Polynomial) power parameter

  • std: (for Polynomial) logical, use Puri(1965) normalization

  • scale: logical, standardize scores to mean 0 and sd 1

nperm

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

set

Set of quantiles of interest:

  • "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

Z.perm

A \(n \times nperm\) matrix that specifies the permuted assignments for approximating the null distribution of the test statistic. If NULL, generated automatically.

alpha

A numeric value where 1-alpha indicates the confidence level.

tol

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

Value

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

Details

This function implements the combined rank sum test approach for inference about quantiles of individual treatment effects. By combining multiple rank statistics (e.g., Stephenson statistics with different s values), the method can achieve better power across a range of effect distributions.

When set = "all", the function combines inference from both treated and control units using the approach described in Chen and Li (2024), with a Bonferroni-style adjustment (alpha/2 for each direction).

See also

com_block_conf_quant_larger for stratified experiments, comb_p_val_cre for p-value computation

Examples

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

# Set up treatment and outcome (treating as CRE, ignoring sites)
Z <- electric_teachers$TxAny
Y <- electric_teachers$gain

# Define multiple Stephenson statistics with different s values
# Larger s focuses more on upper ranks (larger treatment effects)
s.vec <- c(2, 6, 10, 30)
methods.list <- lapply(s.vec, function(s) {
  list(name = "Stephenson", s = s, std = TRUE, scale = TRUE)
})

# Prediction intervals for treated units (90% confidence)
ci.treat <- com_conf_quant_larger_cre(Z, Y,
                                      methods.list = methods.list,
                                      nperm = 10000,
                                      set = "treat",
                                      alpha = 0.05)

# Prediction intervals for control units
ci.control <- com_conf_quant_larger_cre(Z, Y,
                                        methods.list = methods.list,
                                        nperm = 10000,
                                        set = "control",
                                        alpha = 0.05)

# Confidence intervals for all effect quantiles
ci.all <- com_conf_quant_larger_cre(Z, Y,
                                    methods.list = methods.list,
                                    nperm = 10000,
                                    set = "all",
                                    alpha = 0.10)
} # }