Cost-variance frontier of a design by simulation

For each sample size in n_grid, draws n_rep spatially balanced samples from the frame, routes the field work from the depot, prices it with the cost model and, when a study variable is given, estimates the variance of the total. The result is the trade-off a survey planner faces: how much the field work costs and how precise the estimate is at each sample size.

Usage

cost_variance_frontier(
  frame,
  depot,
  cost_model,
  n_grid,
  y = NULL,
  size = NULL,
  strata = NULL,
  selection = c("lpm", "systematic", "srs"),
  replicates = 1,
  matrix = NULL,
  method = c("haversine", "euclidean", "osrm"),
  max_length = Inf,
  max_stops = Inf,
  n_rep = 20,
  iterations = 100,
  seed = 1
)

Arguments

frame

Data frame of units as in select_units(), including the depot row named in depot.

depot

Name of the depot unit in frame$unit.

cost_model

A field_cost_model().

n_grid

Sample sizes to evaluate: a numeric vector of total sizes (allocated across strata as in select_units()), or a list of vectors named by stratum, one allocation per grid point.

y

Optional column of the study variable for the whole frame (a planning value); when given, the variance of the estimated total is computed with design_variance() on each simulated sample.

size

Optional size column for probability-proportional-to-size selection.

strata

Optional stratum column, passed to select_units().

selection

Selection method of select_units(): "lpm", "systematic" or "srs".

replicates

Replicates of a "systematic" selection.

matrix

Optional travel_matrix() of the frame (computed from the coordinates otherwise).

method

Distance method of travel_matrix() when matrix is NULL ("osrm" queries the road network once for the whole frame).

max_length, max_stops

Route limits passed to route_fieldwork().

n_rep

Replications per sample size.

iterations

GRASP iterations per routing.

seed

Seed.

Value

A tibble of class fieldopt_frontier with one row per sample size: n, cost_mean, cost_sd, cost_per_unit (the planning value for c1 in two_stage_allocation() or cost_a in dual_frame_allocation()), travel_mean, routes_mean, variance_mean and cv_mean (when y is given), n_rep, and allocation (a list column with the stratum sizes) when strata are used.

Examples

set.seed(3)
frame <- data.frame(
  unit = c("depot", paste0("s", 1:40)),
  x = c(5, runif(40, 0, 10)), y = c(5, runif(40, 0, 10))
)
frame$crop <- c(NA, 20 + 3 * frame$x[-1] + rnorm(40))
model <- field_cost_model(
  per_travel = 2, per_unit = 30, per_interview = 10,
  interviews_per_unit = 4
)
cost_variance_frontier(frame,
  depot = "depot", cost_model = model, n_grid = c(8, 16),
  y = "crop", method = "euclidean", n_rep = 3, iterations = 20
)
#> # A tibble: 2 × 9
#>       n cost_mean cost_sd cost_per_unit travel_mean routes_mean variance_mean
#> * <dbl>     <dbl>   <dbl>         <dbl>       <dbl>       <dbl>         <dbl>
#> 1     8      619.    2.88          77.4        29.6           1         7519.
#> 2    16     1196.    2.85          74.7        37.8           1         1267.
#> # ℹ 2 more variables: cv_mean <dbl>, n_rep <dbl>