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Effective sample size

Source: R/effective_n.R
effective_n.Rd

Convert a planned sample size into the simple-random-sample size that would give the same precision, n * resp_rate / deff. This is the mirror of design_effect() and takes the same arguments.

Usage

effective_n(x = NULL, ...)

# Default S3 method
effective_n(
  x = NULL,
  ...,
  n = NULL,
  deff = NULL,
  resp_rate = 1,
  eligibility_rate = 1,
  icc = NULL,
  n_per_psu = NULL,
  n_per_ssu = NULL,
  var_ratio = 1,
  weights = NULL,
  strata = NULL
)

# S3 method for class 'svyplan_deff'
effective_n(x, ..., n = NULL, resp_rate = 1, eligibility_rate = 1)

# S3 method for class 'svyplan_cluster'
effective_n(
  x,
  ...,
  n = NULL,
  resp_rate = NULL,
  eligibility_rate = NULL,
  weights = NULL,
  strata = NULL
)

# S3 method for class 'svyplan_prec'
effective_n(
  x,
  ...,
  n = NULL,
  resp_rate = NULL,
  eligibility_rate = NULL,
  weights = NULL,
  strata = NULL
)

# S3 method for class 'svyplan_varcomp'
effective_n(
  x,
  ...,
  n = NULL,
  resp_rate = 1,
  eligibility_rate = 1,
  n_per_psu = NULL,
  n_per_ssu = NULL,
  weights = NULL,
  strata = NULL
)

# S3 method for class 'svyplan_n'
effective_n(
  x,
  ...,
  n = NULL,
  resp_rate = NULL,
  eligibility_rate = NULL,
  weights = NULL
)

Arguments

x

A svyplan_deff from design_effect(), a n_cluster() or prec_cluster() allocation, a varcomp() estimate, an n_alloc() allocation, or NULL (default) to build the design effect from the component arguments. A n_prop() or n_mean() result is not one of these, since its design effect is the deff you supplied rather than something to be derived, so pass the two directly as effective_n(n = x$n, deff = x$params$deff).

...

Additional arguments passed to methods. Unused arguments are rejected.

n

Gross planned sample size, counted as units issued. Required unless it can be derived from weights, strata$n, or x.

deff

Design effect to apply directly, instead of building one from components. A published DEFT is squared first. See varcomp() for that and for removing the published survey's weighting loss.

resp_rate

Expected response rate among eligible units, in (0, 1]. Default 1. It nets n down to the units the design expects to analyze before the design effect is applied. When x is a plan, its own rate is used unless you override it here. An override re-evaluates the plan at that rate, so the take that responds and with it the clustering factor follow. On an allocation or a cluster plan it is the ultimate-unit rate, one value or one per stratum, and PSU and SSU response stay the plan's. See the nonresponse section of svyplan-package for what the rate counts.

eligibility_rate

Share of issued units in scope, in (0, 1]. Default 1. It nets n down with resp_rate. When x is a plan, its own value is used unless you override it here. An override re-evaluates the plan, so on an allocation the population weights and the population variance follow it too.

icc, n_per_psu, n_per_ssu, var_ratio, weights, strata

Design components, with the same meaning as in design_effect().

Value

A numeric scalar: the effective sample size, n * resp_rate / deff. It is not rounded, and it can exceed n when the design effect is below 1 (a stratification gain, for instance).

Details

The design effect is built exactly as in design_effect(), from whichever of the clustering, weighting, and stratification components you supply. n is the gross planned sample size. It is taken from the arguments when it can be (the length of weights, the total of strata$n, or the total of the plan you pass as x), and must be given explicitly otherwise.

Sizes are counted as units issued, so nonresponse has to be taken off before the design effect is applied. A design that issues n and analyzes n * resp_rate of them carries the information of n * resp_rate / deff simple random draws. This is the identity the allocation and precision functions plan on, and the one reported in the n_eff column of an n_alloc() table. Passing a plan as x picks up the response rate it was built with, so effective_n(plan) and that column agree. Supply resp_rate yourself when you pass a bare n that has not already been netted down.

The design effect it divides by is a without-FPC planning quantity, so for an n_alloc() result the effective size inherits that scale. It answers how many simple random draws carry the same information under the planning model, not how many the finite-population variance from prec_alloc() would imply once sampling fractions are material. A generalized allocation has no single design effect and is refused here for the same reason it is in design_effect().

effective_n() is a planning tool. To compute the effective sample size realized by collected data, use survey::svymean(..., deff = TRUE) with the actual weights, strata, and clusters.

Methods (by class)

  • effective_n(default): Build the design effect from planning components.

  • effective_n(svyplan_deff): Apply a design effect already built by design_effect().

  • effective_n(svyplan_cluster): Use the total sample size and design features of a n_cluster() or prec_cluster() allocation. The total is netted by every stage's response rate and by eligible_per_unit, so the result counts eligible respondents, as the cv does.

  • effective_n(svyplan_prec): Use the total and design features of a prec_cluster() result, or the stratum counts of a prec_alloc() result as for an allocation. prec_alloc(x, n = x$detail$n_int) gives the whole stratum counts. On a cluster frame it keeps the plan's takes. Other svyplan_prec types carry the deff you supplied rather than one to be derived, and are rejected.

  • effective_n(svyplan_varcomp): Use the design features of a varcomp() estimate. n and the stage takes are your design choice.

  • effective_n(svyplan_n): Use the total and design features of an n_alloc() allocation, dividing by the allocation's own variance ratio. The frame needs mean alongside N and sd, since without the stratum means the population variance that ratio divides by is not identified. Each stratum's response, eligibility and PSU response rates, from the arguments or the frame, net its own count down, so the result is the population variance over the plan's variance without FPC. A scalar n rescales the continuous allocation and keeps its stratum shares. To evaluate the whole stratum counts, pass prec_alloc(x, n = x$detail$n_int) as x. An allocation from stratum sizes alone reads its whole counts throughout, as its design effect does.

See also

design_effect() for the design effect itself.

Other design input functions: design_df(), design_effect(), svyplan()

Examples

# From a design effect you already built
effective_n(design_effect(icc = 0.05, n_per_psu = 25), n = 1200)
#> [1] 545.4545

# Straight from the components
effective_n(n = 1200, icc = 0.05, n_per_psu = 25)
#> [1] 545.4545

# From planned weights, where n is the number of units
effective_n(weights = rep(c(1, 4), c(300, 100)))
#> [1] 257.8947

# From a planned allocation
effective_n(strata = data.frame(N = c(50000, 120000), n = c(600, 400)))
#> [1] 719.5021

# From an optimized cluster plan
effective_n(n_cluster(stage_cost = c(500, 50), icc = 0.05, cv = 0.05))
#> [1] 400