Allocation that equalises anticipated coefficients of variation

For a multivariate design built on mpps_size(), searches for the per-variable sample-size factors under which every auxiliary variable's total is anticipated with the same coefficient of variation, so no estimate is quietly sacrificed to another. At each step the anticipated CVs are computed under the design the current factors imply and the factors move against their spread, damped, until the spread falls within tolerance.

Usage

eqcv_allocation(
  frame,
  variables,
  n,
  max_iterations = 300,
  tolerance = 0.001,
  damping = 0.5
)

Arguments

frame

Data frame with one row per unit.

variables

Names of the auxiliary columns, non-negative numeric. Columns that sum to zero carry no information and are ignored.

n

The sample size, at most the number of units.

max_iterations, tolerance, damping

The search: at most max_iterations steps, stopping when the largest anticipated CV exceeds the smallest by less than tolerance (relative), each step damped by the exponent damping.

Value

A numeric vector of factors, one per variable, normalised to geometric mean one over the informative variables, with attributes cv (the anticipated CVs reached), iterations and converged. A converged of FALSE warns but still returns the best factors reached.

Examples

set.seed(1)
frame <- data.frame(a = rlnorm(100), b = rlnorm(100, sdlog = 2))
n_j <- eqcv_allocation(frame, c("a", "b"), n = 20)
n_j
#>         a         b 
#> 0.8886081 1.1253555 
#> attr(,"cv")
#>          a          b 
#> 0.08893883 0.08898617 
#> attr(,"iterations")
#> [1] 8
#> attr(,"converged")
#> [1] TRUE
attr(n_j, "cv")
#>          a          b 
#> 0.08893883 0.08898617