Design effect and bias of point sampling by simulation — point_design

Repeats the whole area-frame design, selecting cells with select_units(), placing points with select_points(), letting each point hit the establishment whose land it falls on (with probability equal to the establishment's share of the cell), and estimating the total with point_estimator(). Returns the empirical variance of the estimator, its bias, the mean number of interviews, and the design effect relative to a simple random sample of establishments with the same number of interviews: the deff_a that dual_frame_allocation() asks for.

Usage

point_design_effect(
  cells,
  areas,
  n,
  points_per_cell,
  cell_size,
  size = NULL,
  strata = NULL,
  method = c("lpm", "systematic", "srs"),
  replicates = 1,
  n_sim = 200,
  seed = 1
)

Arguments

cells: Data frame of cells as in select_units() (with unit, coordinates and, when used, strata and size columns).
areas: Data frame with one row per (establishment, cell) pair: establishment, unit, area (land of the establishment inside the cell, in the square units of cell_size) and y (the study variable of the whole establishment, repeated across its cells).
n: Sample size: a single number (allocated to strata in proportion to the sum of size, or to the number of units when size is NULL), or a vector named by stratum.
points_per_cell: Points per sampled cell: a single number, a vector named by stratum (for example more points where agricultural use is more intense), or the name of a column of the sample.
cell_size: Side of the square cells, in the units of the coordinates (one number, or c(dx, dy)).
size: Column of the size measure for probability-proportional-to-size selection, or NULL for equal probabilities within stratum.
strata: Column with the stratum of each unit, or NULL.
method: "lpm", "systematic", "srs" or "cube" (balanced sampling by the cube method of Deville and Tillé 2004, with the fast flight phase and landing by suppression of variables).
replicates: Number of independent interpenetrating replicates for "systematic" (each a systematic sample of about n / replicates units; replicates may share units). Ignored by the other methods.
n_sim: Number of simulated surveys.
seed: Seed.

Value

A one-row tibble of class fieldopt_point_deff: n_sim, total, mean_estimate, bias, variance, cv, mean_variance_estimate (the mean of the point_estimator() variance estimates, to be compared with variance), interviews, variance_srs, deff; attribute estimates holds the simulated values.

Details

Hits are attributed by the establishments' shares of the cell area, not by the geometry of their fields, so the simulator does not distinguish the random and systematic point layouts; it captures the cell design, the point intensity and the multiplicity, which is what drives the design effect at the cell level.

Examples

set.seed(4)
cells <- expand.grid(x = 1:10, y = 1:10)
cells$unit <- paste0("c", 1:100)
areas <- rbind(
  data.frame(establishment = paste0(cells$unit, "-1"), unit = cells$unit, area = 0.5),
  data.frame(establishment = paste0(cells$unit, "-2"), unit = cells$unit, area = 0.2)
)
areas$y <- round(rgamma(nrow(areas), 3, 3 / (10 * areas$area)), 1)
point_design_effect(cells, areas, n = 15, points_per_cell = 6, cell_size = 1, n_sim = 20)
#> # A tibble: 1 × 10
#>   n_sim total mean_estimate  bias variance    cv mean_variance_estimate
#> * <dbl> <dbl>         <dbl> <dbl>    <dbl> <dbl>                  <dbl>
#> 1    20  711.          694. -16.3    7923. 0.125                 12187.
#> # ℹ 3 more variables: interviews <dbl>, variance_srs <dbl>, deff <dbl>