Minimum cost sum c_h n_h such that the variance of the estimated total
of every study variable is at most its target (Bethel 1989; Chromy 1987).
This is frame_allocation() with one constraint per variable: a survey
that must estimate several crops, or a crop and the number of farms, with
stated precisions. The multipliers tell which constraints bind.
Usage
multivariate_allocation(
strata,
sd,
target_variance = NULL,
target_cv = NULL,
totals = NULL
)Arguments
- strata
Data frame with columns
size,cost, optionallystratum, and one standard-deviation column per study variable.- sd
Names of the standard-deviation columns, one per variable.
- target_variance
Target variance of each variable's total, in the order of
sd(give this ortarget_cv).- target_cv
Target coefficient of variation of each total; needs
totals.- totals
Population totals of the variables, for
target_cv.
Value
The strata with a column n, of class
fieldopt_multi_allocation, with attributes cost, targets,
attained (variance of each variable), multipliers, bounded.
References
Bethel, J. (1989). Sample allocation in multivariate surveys. Survey Methodology, 15, 47-57. Chromy, J. R. (1987). Design optimization with multiple objectives. Proceedings of the Survey Research Methods Section, ASA, 194-199.
Examples
strata <- data.frame(
stratum = c("high", "mid", "low"), size = c(300, 800, 2000),
cost = c(250, 180, 150), sd_corn = c(40, 25, 8), sd_cattle = c(15, 30, 12)
)
multivariate_allocation(strata,
sd = c("sd_corn", "sd_cattle"),
target_cv = c(0.05, 0.08), totals = c(90000, 60000)
)
#>
#> ── Multivariate allocation ─────────────────────────────────────────────────────
#> Minimum cost 21150 for 2 targets.
#> sd_corn: target 20250000, attained 19910000 (binding).
#> sd_cattle: target 23040000, attained 22860000 (binding).
#> # A tibble: 3 × 4
#> stratum size cost n
#> <chr> <dbl> <dbl> <int>
#> 1 high 300 250 18
#> 2 mid 800 180 50
#> 3 low 2000 150 51