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Stratified and Clustered Random Sampling

Source: R/strata_and_cluster_rs.R
strata_and_cluster_rs.Rd

strata_and_cluster_rs draws whole clusters, sampling separately within each stratum. Use it when the sampling unit is a group rather than an individual and the groups fall into categories you want represented in fixed proportion. Sampling by cluster costs precision, since the effective sample size is the number of clusters rather than the number of units; stratifying buys some of it back by fixing how many clusters come from each stratum.

Usage

strata_and_cluster_rs(
  strata = NULL,
  clusters = NULL,
  prob = NULL,
  prob_unit = NULL,
  n = NULL,
  n_unit = NULL,
  strata_n = NULL,
  strata_prob = NULL,
  check_inputs = TRUE
)

Arguments

strata

A vector of length N indicating which stratum each unit belongs to. Every unit in a cluster must belong to the same stratum. (required)

clusters

A vector of length N indicating which cluster each unit belongs to. (required)

prob

Use for a design in which either floor(N_clusters_stratum*prob) or ceiling(N_clusters_stratum*prob) clusters are sampled within each stratum. Which of the two is used is itself random: the ceiling is drawn with probability equal to the fractional part of N_clusters_stratum*prob and the floor otherwise, which makes each cluster's probability of inclusion exactly prob. Must be a real number between 0 and 1 inclusive. (optional)

prob_unit

Must be of length N. tapply(prob_unit, strata, unique) will be passed to strata_prob, so it must be constant within each stratum. (optional)

n

Use for a design in which the scalar n gives the fixed number of clusters to sample in every stratum. This count does not vary across strata. (optional)

n_unit

Must be of length N. tapply(n_unit, strata, unique) will be passed to strata_n, so it must be constant within each stratum. (optional)

strata_n

Use for a design in which strata_n gives the number of clusters to sample within each stratum. Must be as long as the number of strata, in the same order as sort(unique(strata)). (optional)

strata_prob

Use for a design in which strata_prob gives the probability of being sampled within each stratum. Must be in the same order as sort(unique(strata)). Differs from prob in that the probability of being sampled can vary across strata. (optional)

check_inputs

Logical. Whether to verify before sampling that the arguments are internally consistent: that clusters nest within strata, that counts do not exceed the number of clusters in a stratum, that probabilities lie between 0 and 1, and so on. Defaults to TRUE. Set to FALSE to skip the checks when drawing many samples from arguments that have already been verified; declaring the design once with declare_rs() and drawing from it with draw_rs() does this for you. (optional)

Value

A numeric vector of length N indicating whether each unit is sampled (1) or not (0). Every unit in a cluster receives the same value.

Details

Clusters must nest within strata: every unit in a cluster has to belong to the same stratum.

See also

cluster_rs(), strata_rs(), block_and_cluster_ra()

Examples

# Twelve clusters, of sizes 1 through 12, nested in four strata of three
clusters <- rep(letters[1:12], times = 1:12)

strata <- rep(NA, length(clusters))
strata[clusters %in% letters[1:3]] <- "stratum_1"
strata[clusters %in% letters[4:6]] <- "stratum_2"
strata[clusters %in% letters[7:9]] <- "stratum_3"
strata[clusters %in% letters[10:12]] <- "stratum_4"

table(strata, clusters)
#>            clusters
#> strata       a  b  c  d  e  f  g  h  i  j  k  l
#>   stratum_1  1  2  3  0  0  0  0  0  0  0  0  0
#>   stratum_2  0  0  0  4  5  6  0  0  0  0  0  0
#>   stratum_3  0  0  0  0  0  0  7  8  9  0  0  0
#>   stratum_4  0  0  0  0  0  0  0  0  0 10 11 12

S <- strata_and_cluster_rs(strata = strata,
                          clusters = clusters)

table(S, strata)
#>    strata
#> S   stratum_1 stratum_2 stratum_3 stratum_4
#>   0         5         6         8        12
#>   1         1         9        16        21
table(S, clusters)
#>    clusters
#> S    a  b  c  d  e  f  g  h  i  j  k  l
#>   0  0  2  3  0  0  6  0  8  0  0  0 12
#>   1  1  0  0  4  5  0  7  0  9 10 11  0


S <- strata_and_cluster_rs(clusters = clusters,
                           strata = strata,
                           prob = 0.5)

table(S, clusters)
#>    clusters
#> S    a  b  c  d  e  f  g  h  i  j  k  l
#>   0  0  2  3  0  0  6  7  8  0  0  0 12
#>   1  1  0  0  4  5  0  0  0  9 10 11  0
table(S, strata)
#>    strata
#> S   stratum_1 stratum_2 stratum_3 stratum_4
#>   0         5         6        15        12
#>   1         1         9         9        21

S <- strata_and_cluster_rs(clusters = clusters,
                           strata = strata,
                           strata_n = c(1, 2, 1, 2))

table(S, clusters)
#>    clusters
#> S    a  b  c  d  e  f  g  h  i  j  k  l
#>   0  0  2  3  0  5  0  0  8  9 10  0  0
#>   1  1  0  0  4  0  6  7  0  0  0 11 12
table(S, strata)
#>    strata
#> S   stratum_1 stratum_2 stratum_3 stratum_4
#>   0         5         5        17        10
#>   1         1        10         7        23

S <- strata_and_cluster_rs(clusters = clusters,
                           strata = strata,
                           strata_prob = c(0.2, 0.4, 0.6, 0.8))

table(S, clusters)
#>    clusters
#> S    a  b  c  d  e  f  g  h  i  j  k  l
#>   0  1  2  3  0  5  6  0  8  0 10  0  0
#>   1  0  0  0  4  0  0  7  0  9  0 11 12
table(S, strata)
#>    strata
#> S   stratum_1 stratum_2 stratum_3 stratum_4
#>   0         6        11         8        10
#>   1         0         4        16        23