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. Compute the design effect (DEFF) or effective sample size from sampling weights. Five methods are available for two use cases:

Usage

design_effect(x = NULL, ...)

effective_n(x = NULL, ...)

# S3 method for class 'tbl_sample'
design_effect(x, ..., y = NULL, x_cal = NULL, method = "kish")

# S3 method for class 'tbl_sample'
effective_n(x, ..., y = NULL, x_cal = NULL, method = "kish")

Arguments

x

A numeric weight vector, a tbl_sample, or NULL (for the "cluster" planning method).

...

Passed to the svyplan method. For method = "cluster", pass delta (measure of homogeneity, scalar or svyplan_varcomp) and psu_size (mean cluster size). See svyplan::design_effect().

y

<data-masking> Outcome variable (column name). Required for Henry, Spencer, and CR methods.

x_cal

<data-masking> Calibration covariate (column name). Required for the Henry method.

method

Design effect method. For diagnostic use (with weights): one of "kish" (default), "henry", "spencer", or "cr". For planning (no weights): "cluster".

Value

design_effect() returns a numeric svyplan_design_effect object. Use as.double() for the overall value and as.data.frame() for the Chen-Rust decomposition. effective_n() returns a numeric scalar.

Details

After data collection (diagnostic): assess how much precision was lost due to the complex design.

• "kish" (default): weights only. Quick, outcome-independent summary.

• "henry": weights + outcome + calibration covariate. Accounts for calibration weighting.

• "spencer": weights + outcome + selection probabilities. Accounts for correlation between weights and the outcome.

• "cr": weights + outcome + strata/cluster IDs. Full Chen-Rust decomposition for multistage stratified designs.

Before data collection (planning): estimate an expected DEFF to inflate a simple-random-sample size calculation.

• "cluster": uses homogeneity (delta) and mean cluster size (psu_size) to compute DEFF = 1 + (psu_size - 1) * delta. Pass the result to svyplan::n_prop(), svyplan::n_mean(), or other sizing functions.

The tbl_sample methods extract what they can from the sample metadata. The user only needs to supply column names for variables that are not part of the sampling metadata.

• Weights from .weight

• Selection probabilities from 1 / .weight (for Spencer). Spencer (2000) derives his DEFF at the unit level, so the required probability is the overall inclusion probability \(\pi_i = 1/w_i\), i.e. the product of all per-stage inclusion probabilities for multi-stage designs. This matches the convention used by PracTools::deffS().

• Stratification and clustering variables from the stored design (for CR)

See also

svyplan::design_effect(), svyplan::effective_n(), svyplan::varcomp(), svyplan::n_cluster(), svyplan::prec_prop(), svyplan::prec_mean()

Examples

# Kish design effect (default)
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)),
  x_cal = runif(200, 0.5, 2)
)
samp <- sampling_design() |>
  stratify_by(stratum) |>
  draw(n = c(A = 10, B = 40)) |>
  execute(frame, seed = 1213)

design_effect(samp)
#> Design effect (Kish)
#> overall = 1.5625
effective_n(samp)
#> [1] 32

# Henry (calibration covariate)
design_effect(samp, y = income, x_cal = x_cal, method = "henry")
#> Design effect (Henry)
#> overall = 1.3808

# Spencer (selection probabilities extracted automatically)
design_effect(samp, y = income, method = "spencer")
#> Design effect (Spencer)
#> overall = 2.3287

# Chen-Rust (strata and clusters extracted from design)
design_effect(samp, y = income, method = "cr")
#> Design effect (Chen-Rust)
#> overall = 0.3181

# Cluster planning (no sample needed)
design_effect(delta = 0.05, psu_size = 25, method = "cluster")
#> Design effect (Cluster)
#> overall = 2.2000