Design effect and effective sample size

These are the svyplan generics re-exported by samplyr. Samplyr adds tbl_sample methods rather than defining competing generics.

Usage

design_effect(x = NULL, ...)

effective_n(x = NULL, ...)

# S3 method for class 'tbl_sample'
design_effect(x, ...)

# S3 method for class 'tbl_sample'
effective_n(x, ...)

Arguments

x

A tbl_sample, or a numeric weight vector passed to the svyplan method.

...

Passed to the svyplan method: the planning arguments icc, n_per_psu, n_per_ssu and var_ratio are the useful ones here. Every argument must be named. svyplan reports any name it does not recognize.

Value

design_effect() returns a numeric svyplan_deff object. Use as.double() for the value. effective_n() returns a numeric scalar.

Details

The tbl_sample methods report the weighting loss: how much precision the realized weights cost relative to a self-weighting sample of the same size. This is Kish's design effect, \(n \sum w_i^2 / (\sum w_i)^2\), computed from the .weight column, so it equals 1 for a self-weighting design and rises with weight variability. It is outcome-independent, which is what makes it available from the sample alone.

It is one component of a full design effect and not a substitute for one. Clustering and stratification also move precision, and neither is visible in the weights. To estimate a design effect that reflects them, fit the design and ask the estimator: as_svydesign() then survey::svymean(deff = TRUE), which is outcome-specific by necessity. To anticipate the clustering component before collecting data, name the planning arguments in the same call: design_effect(x, icc = , n_per_psu = ) forwards them to svyplan::design_effect() and returns the weighting loss multiplied by the anticipated clustering component. Positional arguments are refused, since these methods take no outcome variable.

References

Kish, L. (1965). Survey Sampling. Wiley.

See also

svyplan::design_effect(), svyplan::effective_n(), svyplan::varcomp(), svyplan::n_cluster(), as_svydesign() to hand the design to survey for an outcome-specific design effect

Other diagnostics: compare_designs(), frame_summary(), joint_expectation(), sample_columns, summary.tbl_sample(), varcomp.tbl_sample()

Examples

set.seed(1207)
frame <- data.frame(
  id = 1:200,
  stratum = rep(c("A", "B"), each = 100),
  income = c(rnorm(100, 50, 10), rnorm(100, 80, 15))
)

# A disproportionate allocation costs precision through its weights
samp <- sampling_design() |>
  stratify_by(stratum) |>
  draw(n = c(A = 10, B = 40)) |>
  execute(frame, seed = 1213)

design_effect(samp)
#> Planning design effect: 1.5625
effective_n(samp)
#> [1] 32

# A proportional allocation is self-weighting, so the loss is 1
prop_samp <- sampling_design() |>
  stratify_by(stratum) |>
  draw(n = c(A = 25, B = 25)) |>
  execute(frame, seed = 1213)

design_effect(prop_samp)
#> Planning design effect: 1.0000

# Anticipating the clustering component: the weighting loss above,
# multiplied by the clustering component the planning arguments imply
design_effect(samp, icc = 0.05, n_per_psu = 25)
#> Planning design effect: 3.4375