stratallo (version 3.0.1)

check_rdca: 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

if (FALSE) {
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)
}

if (FALSE) {
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)
}

if (FALSE) {
(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`
}