Sampling Precision for a Multistage Cluster Allocation

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, delta, rel_var = 1, k = 1, resp_rate = 1, ...)

# 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, psu_size) for 2-stage or c(n_psu, psu_size, ssu_size) for 3-stage). For svyplan_cluster objects: a cluster allocation from n_cluster().

...

Additional arguments passed to methods.

delta

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

rel_var

Unit relvariance (default 1).

k

Ratio parameter(s). Scalar for 2-stage, length-2 vector for 3-stage (default 1).

resp_rate

Expected response rate, in (0, 1]. Default 1 (no adjustment). The effective stage-1 size is deflated by resp_rate.

Value

A svyplan_prec object with components $se, $moe, and $cv.

Details

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.

Examples

prec_cluster(n = c(50, 12), delta = 0.05)
#> Sampling precision for 2-stage cluster
#> n_psu = 50 | psu_size = 12 -> total n = 600
#> cv = 0.0508
prec_cluster(n = c(50, 12, 8), delta = c(0.01, 0.05))
#> Sampling precision for 3-stage cluster
#> n_psu = 50 | psu_size = 12 | ssu_size = 8 -> total n = 4800
#> cv = 0.0219