check_rdca: Internal Diagnostic Functions for Checking Optimality of...

In stratallo: Optimum Sample Allocation in Stratified Sampling

Internal Diagnostic Functions for Checking Optimality of rdca() Allocations

Description

Diagnostic tools to verify the objective function and constraint satisfaction for allocations computed by the rdca() algorithm.

Usage

rdca_obj_cnstr(x, n, H_counts, N, S, rho2, J = integer(0))

rdca_cnstr_check(x, n, H_counts, N, S, rho2, J = integer(0), tol_max = 0.1)

rdca_optcond_sU(H_counts, S, rho, s, U, return_diff = FALSE)

Arguments

x	(numeric) vector of sample allocations.
n	(integerish(1)) total sample size n. Must satisfy ⁠0 < n <= sum(N)⁠.
H_counts	(integerish) strata counts in each domain.
N	(integerish) strata sizes (N_{d,h},\, (d,h) \in \mathcal H).
S	(numeric) standard deviations (S_{d,h},\, (d,h) \in \mathcal H) of surveyed variable in strata.
rho2	(numeric) the square of rho (rho^2).
J	(integerish or NULL) vector of domain indices, a subset of \mathcal D. Specifies domains d \in \mathcal D for which values of constraint functions g_{dh} are computed. If integer(0), these values are not computed. If NULL, all domains are included.
tol_max	(integerish(1)) the maximum tolerance exponent (as a power of 10).
rho	(numeric) parameters (\rho_d,\, d \in \mathcal D) of the optimization problem.
s	(numeric) vector of values for function s(\mathcal U, \boldsymbol{v}, d \mid p) calculated only for domains included in U that are not fully blocked by the take-max assignment.
U	(integerish or NULL) a vector of indices identifying the take-max strata, i.e., the strata (d,h) for which the allocation is fixed to x_{d,h} = N_{d,h}. The indices refer to the positions of strata in the set \mathcal H, in the same order as in the input vectors (N, S, etc.). For example, if \mathcal H = \{(1,1),\, (2,1)\} and stratum (2,1) is a take-max stratum, then U = 2. If U contains all strata from a domain, the dimension of the D matrix is reduced accordingly. U must satisfy one of the following conditions: n > sum(N[U]), n = sum(N[U]) and n = sum(N).
return_diff	(logical(1)) If FALSE, the function returns a logical vector indicating whether the optimality condition s(\mathcal{U},\, \boldsymbol{v},\, d \mid p) \ge \rho_d / S_{d,h} is satisfied for each unblocked stratum (d,h) \in \mathcal U. If TRUE, the function returns the differences s(\mathcal{U},\, \boldsymbol{v},\, d \mid p) - \rho_d / S_{d,h} instead of a logical vector, which can be used to assess by how much the condition is satisfied or violated.

Functions

• rdca_obj_cnstr(): Compute the value of the objective function and constraint functions for a given allocation.

• rdca_cnstr_check(): Check whether the equality and inequality constraints are satisfied for a given allocation, within a specified tolerance. The tolerance applies to equality constraints only.

• rdca_optcond_sU(): Check the optimality condition related to s. Specifically, verifies whether s(\mathcal{U},\, \boldsymbol{v},\, d \mid p) \ge \rho_d / S_{d,h} for all (d,h) \in \mathcal{U} such that d is not fully blocked by \mathcal{U}.

Examples

H_counts <- c(2, 2) # 2 domains with 2 strata each
N <- c(140, 110, 135, 190)
S <- sqrt(c(180, 20, 5, 4))
total <- c(2, 3)
kappa <- c(0.4, 0.6)
rho <- total * sqrt(kappa)
rho2 <- total^2 * kappa
n <- 500

(x <- dca(n, H_counts, N, S, rho, rho2))

# internal functions (not exported) – examples skipped

## Not run: 
rdca_obj_cnstr(x, n, H_counts, N, S, rho2)
rdca_obj_cnstr(x, n, H_counts, N, S, rho2, 2)
rdca_obj_cnstr(x, n, H_counts, N, S, rho2, NULL)

## End(Not run)

## Not run: 
rdca_cnstr_check(x, n, H_counts, N, S, rho2)
rdca_cnstr_check(x, n, H_counts, N, S, rho2, 1)
rdca_cnstr_check(x, n, H_counts, N, S, rho2, 2)
rdca_cnstr_check(x, n, H_counts, N, S, rho2, NULL)

## End(Not run)

## Not run: 
(n <- dca_nmax(H_counts, N, S) - 1)

U <- 1
(x <- dca(n, H_counts, N, S, rho, rho2, U = U, details = TRUE))
rdca_optcond_sU(H_counts, S, rho, x$s, U) # TRUE

U <- 2
(x <- dca(n, H_counts, N, S, rho, rho2, U = U, details = TRUE))
rdca_optcond_sU(H_counts, S, rho, x$s, U) # FALSE

U <- 3
(x <- dca(n, H_counts, N, S, rho, rho2, U = U, details = TRUE))
rdca_optcond_sU(H_counts, S, rho, x$s, U) # TRUE

U <- 1:2 # domain 2 blocked
(x <- dca(n, H_counts, N, S, rho, rho2, U = U, details = TRUE))
rdca_optcond_sU(H_counts, S, rho, x$s, U) # no unblocked strata in `U`

## End(Not run)

stratallo documentation built on March 12, 2026, 5:06 p.m.