Cluster bootstrap interval for shares

Resamples clusters (sources) with replacement and returns percentile intervals and bootstrap standard errors of the share of every key.

Usage

cluster_boot_share(
  counts,
  key_cols,
  cluster_col = "source",
  B = 1000L,
  conf = 0.95,
  cluster_totals = NULL,
  x_col = "x",
  n_col = "n"
)

Arguments

counts

data.frame or data.table with one row per key and cluster, holding the count x_col and (when cluster_totals is NULL) the cluster denominator n_col.

key_cols

Character vector of key columns (e.g. the code).

cluster_col

Name of the cluster column (default "source").

B

Number of bootstrap replicates (default 1000).

conf

Confidence level, default 0.95.

cluster_totals

Optional data.frame with one row per cluster and columns cluster_col and n_col. When given, the denominator of every cluster is taken from it and every cluster with a positive denominator enters the variance of every key, also when the key has no row (zero count) for that cluster. Recommended.

x_col

Name of the count column (default "x").

n_col

Name of the denominator column (default "n"), in counts or in cluster_totals.

Value

A data.table with one row per key and columns key_cols, quota, lo_boot, hi_boot, se_boot.

Details

Let X be the sparse key x cluster count matrix and n_s the cluster denominators. The multiplicities of the S clusters in B replicates form the matrix M (S x B, columns drawn from a multinomial with S trials and equal probabilities); the replicate counts are X M and the replicate denominators n_s M, so all replicates are computed with two matrix products (processed in blocks of keys to bound memory). The interval is the percentile interval of the replicate shares; replicates with a zero denominator are dropped. Set the seed with set.seed() before the call; the function does not set it. The bootstrap of the clusters is the resampling counterpart of the linearised variance of cluster_deff() and shares its assumptions: clusters are treated as a sample of sources.

References

Davison, A. C. and Hinkley, D. V. (1997). Bootstrap Methods and their Application. Cambridge University Press, section 3.8.

Examples

counts <- data.frame(
  code = rep(c("a", "b"), each = 4),
  source = rep(c("s1", "s2", "s3", "s4"), 2),
  x = c(10, 40, 5, 25, 3, 2, 4, 1)
)
totals <- data.frame(source = c("s1", "s2", "s3", "s4"),
                     n = c(200, 400, 100, 300))
set.seed(1)
cluster_boot_share(counts, "code", B = 200, cluster_totals = totals)
#>      code quota     lo_boot    hi_boot     se_boot
#>    <char> <num>       <num>      <num>       <num>
#> 1:      a  0.08 0.050000000 0.09616667 0.011088630
#> 2:      b  0.01 0.004285714 0.02333333 0.005436773