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Sampling precision for a multistage cluster allocation

Source: R/prec_cluster.R
prec_cluster.Rd

Compute the sampling error (SE, MOE, CV) for a given multistage sample allocation. This is the inverse of n_cluster().

Usage

prec_cluster(n, ...)

# Default S3 method
prec_cluster(
  n,
  ...,
  icc = NULL,
  unit_relvar = 1,
  var_ratio = 1,
  resp_rate_psu = 1,
  resp_rate_ssu = 1,
  resp_rate = 1,
  plan = NULL
)

# S3 method for class 'svyplan_cluster'
prec_cluster(n, ...)

Arguments

n

For the default method: numeric vector of per-stage sample sizes (c(n_psu, n_per_psu) for 2-stage or c(n_psu, n_per_psu, n_per_ssu) for 3-stage). Named vectors are accepted with stage names n_psu, n_per_psu, n_per_ssu. For svyplan_cluster objects: a cluster allocation from n_cluster().

...

Additional arguments passed to methods. Unused arguments are rejected.

icc

Numeric vector of homogeneity measures (length = stages - 1), or a svyplan_varcomp object.

unit_relvar

Unit relvariance (default 1).

var_ratio

Ratio of the stage components' unit variance to the analysis variable's, default 1. A scalar names var_ratio_psu; for three stages var_ratio_ssu = var_ratio_psu * (1 - icc_psu) follows from the decomposition. See design_effect().

resp_rate_psu

Expected PSU-level response rate, in (0, 1]. Default 1 (no adjustment). The effective stage-1 size is n * resp_rate_psu. It describes clusters that cannot be worked, not nonresponse among the ultimate units inside a cluster.

resp_rate_ssu

Expected SSU-level response rate, in (0, 1]. Three-stage designs only; default 1. The effective stage-2 size is n[2] * resp_rate_ssu.

resp_rate

Expected ultimate-unit response rate, in (0, 1]. Default 1. It scales the final stage, so it also shrinks the realized cluster and therefore the clustering penalty. See n_cluster() for the decomposition.

plan

Optional svyplan() object providing design defaults.

Value

A svyplan_prec object with components $se, $moe, and $cv. Because the cluster model is parameterized with unit relvariance (unit_relvar = S^2 / Y_bar^2), only $cv is computable. The $se and $moe components are NA.

Details

prec_cluster() is the inverse of n_cluster(): given per-stage sample sizes, it computes the achieved precision. You can pass the result of n_cluster() directly: prec_cluster(n_cluster(...)).

Stage count is determined by length(n).

2-stage (Valliant et al., 2018, Eq. 9.2.23): $$CV = \sqrt{\frac{V \cdot k}{n_1 \cdot n_2} (1 + \delta (n_2 - 1))}$$

3-stage: $$CV = \sqrt{\frac{V}{n_1 \cdot n_2 \cdot n_3} (k_1 \delta_1 n_2 n_3 + k_2 (1 + \delta_2 (n_3 - 1)))}$$

References

Valliant, R., Dever, J. A., and Kreuter, F. (2018). Practical Tools for Designing and Weighting Survey Samples (2nd ed.). Springer. Ch. 9.

See also

n_cluster() for the inverse operation, varcomp() for estimating variance components.

Other precision functions: prec_alloc(), prec_change(), prec_mean(), prec_multi(), prec_multi_cluster(), prec_panel(), prec_pooled(), prec_prop(), prec_twophase()

Examples

# Direct usage
prec_cluster(n = c(50, 12), icc = 0.05)
#> Sampling precision for 2-stage cluster
#> n_psu = 50 | n_per_psu = 12 -> total n = 600
#> cv = 0.0508
prec_cluster(n = c(50, 12, 8), icc = c(0.01, 0.05))
#> Sampling precision for 3-stage cluster
#> n_psu = 50 | n_per_psu = 12 | n_per_ssu = 8 -> total n = 4800
#> cv = 0.0219

# Round-trip from n_cluster
res <- n_cluster(stage_cost = c(500, 50), icc = 0.05, cv = 0.05)
prec_cluster(res)
#> Sampling precision for 2-stage cluster
#> n_psu = 48 | n_per_psu = 14 -> total n = 672
#> cv = 0.0500