Optimum Sample Allocation in Stratified Sampling with stratallo
The stratallo package provides algorithms for computing optimum sample
allocations in stratified sampling designs. The implemented methods
solve several classical optimization problems arising in survey design
using exact analytical algorithms, rather than relying on numerical
approximations.
The package supports a variety of practical constraints, including lower and upper bounds on stratum sample sizes, cost constraints, and multi-domain precision control.
Installation
install.packages("stratallo")
# Development version
# install.packages("remotes")
remotes::install_github("wwojciech/stratallo")User functions
The package provides three main user functions for solving optimum allocation problems:
| Function | Description |
|---|---|
opt() | Optimum allocation with a fixed total sample size. |
optcost() | Minimum-cost allocation under a variance constraint. |
dopt() | Multi-domain optimum allocation with controlled precision. |
The package also includes several helper functions:
| Function | Description |
|---|---|
var_st() | Computes the value of the variance of the stratified $\pi$ estimator of a population total. |
var_stsi() | Computes the value of the variance of the stratified $\pi$ estimator of a population total under simple random sampling without replacement within each stratum. |
alloc_summary() | Summarizes an allocation produced by opt() or optcost(). |
round_oric() | Deterministic rounding procedure for non-integer allocations, preserving integer constraints. |
round_ran() | Randomized rounding procedure for non-integer allocations. |
For a detailed description of the allocation problems and algorithms, see the package vignette.
Example datasets
The package includes several artificial populations that can be used for examples and benchmarking. The available datasets can be listed with
data(package = "stratallo")Examples
library(stratallo)Optimum allocation with fixed sample size
N <- c(3000, 4000, 5000, 2000) # Strata sizes.
S <- c(48, 79, 76, 16) # Standard deviations of a study variable in strata.
A <- N * S
m <- c(100, 90, 500, 50) # Lower bounds.
M <- c(300, 400, 800, 90) # Upper bounds.
n <- 1284 # Total sample size.
x <- opt(n = n, A = A, m = m, M = M)
x
#> [1] 228.9496 400.0000 604.1727 50.8777
x_int <- round_oric(x)
x_int
#> [1] 229 400 604 51
var_stsi(x, N, S)
#> [1] 538073357
var_stsi(x_int, N, S)
#> [1] 538073497Multi-domain optimal allocation with controlled precision
# Three domains with 2, 2, and 3 strata, respectively.
H_counts <- c(2, 2, 3)
N <- c(140, 110, 135, 190, 200, 40, 70)
S <- c(180, 20, 5, 4, 35, 9, 40)
total <- c(2, 3, 5)
kappa <- c(0.5, 0.2, 0.3)
n <- 828
dopt(n, H_counts, N, S, total, kappa)
#> [1] 140.00000 108.06261 135.00000 154.02807 200.00000 20.90933 70.00000