two_stage_allocation: Two-stage allocation with a field cost function

In fieldopt: Area-Frame and Dual-Frame Survey Design under Real Field Cost

Two-stage allocation with a field cost function

Description

n primary units (segments, grid cells) are visited and m secondary units (points, tracts, establishments) are observed in each, at a cost c1 * n + c2 * n * m. With s2_between the variance among primary-unit means and s2_within the variance within primary units, the variance of the estimated mean per secondary unit is ⁠(1 - n/N) s2_between / n + (1 - m/M) s2_within / (n m)⁠ and the cost-optimal m is ⁠sqrt(c1 s2_within / (c2 (s2_between - s2_within / M)))⁠ (Cochran 1977, Section 10.6). The cost c1 of visiting a primary unit is where the routing enters: it is not a constant but depends on how spread the sample is; take it from cost_variance_frontier() at the candidate n and iterate.

Usage

two_stage_allocation(
  n_primary,
  m_secondary,
  s2_between,
  s2_within,
  c1,
  c2,
  target_variance = NULL,
  target_cv = NULL,
  budget = NULL,
  mean = NULL
)

Arguments

n_primary, m_secondary	Primary units in the population and secondary units per primary unit (an average when they differ; need not be a whole number). The allocation tries every whole m up to m_secondary and keeps the cheapest pair meeting the target (or the least variance within the budget), so small populations are handled exactly.
s2_between, s2_within	Variance among primary-unit means and within primary units.
c1, c2	Cost per primary unit visited and per secondary unit observed.
target_variance, target_cv, budget	Exactly one: target variance of the estimated total, target coefficient of variation (needs mean), or budget.
mean	Population mean per secondary unit, for target_cv.

Value

A list of class fieldopt_two_stage: n, m, m_optimal, cost, variance_mean, variance_total, se_total, cv (when mean is given), bounded.

Examples

two_stage_allocation(
  n_primary = 5000, m_secondary = 20, s2_between = 4, s2_within = 25,
  c1 = 300, c2 = 20, budget = 1e5
)
two_stage_allocation(5000, 20, 4, 25, c1 = 300, c2 = 20, target_cv = 0.03, mean = 12)

fieldopt documentation built on Oct. 22, 2026, 1:07 a.m.