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Decompose a two-phase variance into V = V1 + V2

Source: R/variance.R
two_phase_variance.Rd

For a recipe containing step_subsample(), two_phase_variance() splits the recipe-aware bootstrap variance of an estimate into its first-phase and second-phase components, \(V = V_1 + V_2\). The per-unit coupling factor has variance \(d = (1-f_1)\pi_2 + (1-\pi_2)\), the sum of the phase-1 term \((1-f_1)\pi_2\) and the phase-2 conditional term \(1-\pi_2\); running the same bootstrap with each term in turn yields the two components.

Usage

two_phase_variance(
  object,
  variable,
  estimator = c("mean", "total"),
  replicates = 500L,
  seed = NULL,
  fpc = NULL
)

Arguments

object

a weighting_spec (or prepped) whose recipe contains step_subsample().

variable

name of the study variable (a single column).

estimator

"mean" (default) or "total".

replicates, seed, fpc

passed through to bootstrap_weights().

Value

An object of class weightflow_tp_variance: V1, V2, V, the matching standard errors se1, se2, se, and prop_phase2 = V2 / V.

Details

The share prop_phase2 = V2 / V is an operational read: a large share means the second-phase subsampling drives the uncertainty, so subsampling more would pay off; a small share means a denser (more expensive) subsample would buy little, and the first phase is the binding constraint.

See also

bootstrap_weights(), step_subsample().

Examples

df <- transform(sample_survey,
                in2 = as.integer(runif(nrow(sample_survey)) < 0.3), p2 = 0.3)
spec <- weighting_spec(df, base_weights = pw) |>
  step_subsample(selected = in2, prob = p2, psu = "household_id")
two_phase_variance(spec, "income", replicates = 100)
#> boot_mean(): with a two-phase design the phase-1 multiplier is uncentred. It self-centres for a ratio only to first order, so this SE is mildly conservative (measured +5-8% in simulation); read it as a slight upper bound.
#> boot_mean(): with a two-phase design the phase-1 multiplier is uncentred. It self-centres for a ratio only to first order, so this SE is mildly conservative (measured +5-8% in simulation); read it as a slight upper bound.
#> Two-phase variance of the mean of 'income'  (V = V1 + V2)
#>   V1  phase-1  = 731721   (SE 855.41)
#>   V2  phase-2  = 1.34677e+06   (SE 1160.5)
#>   V   total    = 2.07849e+06   (SE 1441.7)
#>   phase-2 share  V2/V = 64.8%