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Create a Two-Phase Survey Design

Source: R/core-constructors.R
as_survey_twophase.Rd

Creates a two-phase (double) sampling design from an existing survey_taylor Phase 1 object. Phase 1 covers all rows; Phase 2 is a strict subset indicated by a logical column. Uses a tidy-select interface for all Phase 2 design variable arguments.

Usage

as_survey_twophase(
  phase1,
  ids2 = NULL,
  strata2 = NULL,
  probs2 = NULL,
  fpc2 = NULL,
  subset,
  method = c("full", "approx", "simple")
)

Arguments

phase1

A survey design object (inheriting from survey_base) representing the Phase 1 design. Accepts a survey_taylor object. A survey_replicate object is refused: the phase-1 variance for a replicate design is not implemented. Its @data must contain ALL rows from both phases, plus a logical indicator column for Phase 2 membership. Create with as_survey().

ids2

<tidy-select> Phase 2 cluster ID column: a single column, such as ids2 = psu2. Omit if Phase 2 has no within-stratum clustering. Without probs2 or fpc2, the Phase 2 inclusion probability is the fraction of clusters selected within each Phase 2 stratum, not the fraction of rows.

Multi-stage Phase 2 is not supported. The two-phase variance uses one Phase 2 sampling stage, so selecting more than one column, such as ids2 = c(psu2, ssu2), is an error (surveycore_error_twophase_multistage_phase2) rather than a standard error that silently ignores the later stages.

strata2

<tidy-select> Phase 2 stratification column (a single column; more than one is an error, as Phase 2 has one sampling stage). Optional.

probs2

<tidy-select> Phase 2 inclusion probability column (a single column, values in (0, 1]). Optional.

fpc2

<tidy-select> Phase 2 finite population correction column (a single column; more than one is an error, as Phase 2 has one sampling stage). Optional.

subset

<tidy-select> Single logical column in phase1@data. TRUE = row selected into Phase 2; FALSE = Phase 1 only. Required. Must contain both TRUE and FALSE values (non-degenerate).

method

Character. Variance estimation method for combining Phase 1 and Phase 2 variability. One of "full" (default), "approx", or "simple". Case-sensitive. See Details.

"full" and "approx" both match survey::twophase(), and both can give standard errors that are too large (conservative) for some designs:

  • "full" without an fpc on the Phase 1 design treats the Phase 1 sampling units (clusters, or rows when Phase 1 is unclustered) as Poisson-sampled. For a fixed-size Phase 1 sample that is very conservative for totals: in a simulation of a stratified cluster sample, about 13 times the true variance, or 3.7 times the standard error, and an unclustered, unstratified Phase 1 was overstated by a similar amount. Means are much less affected when Phase 1 is unstratified, but are still overstated when it is stratified. Supply fpc to as_survey() for Phase 1; a weighted Phase 1 with no fpc raises a warning; see Details.

  • "approx" (and so "simple") is conservative when Phase 1 is clustered and Phase 2 subsamples rows within the Phase 1 clusters, that is, when ids2 is absent or finer than the Phase 1 cluster: in a simulation, about 2.4 times the true variance, or 1.55 times the standard error. It is close to unbiased when Phase 2 draws whole Phase 1 clusters or Phase 1 is unclustered. For the first kind of design, method = "full" with a Phase 1 fpc is the alternative.

Value

A survey_twophase object. Columns imported with haven-style value labels are stored as their underlying type: the label and labels attributes are kept, and the value labels are also recorded in the metadata system, but the haven_labelled class is not stored. Use survey_data(x, haven_class = TRUE) to read the data back with that class rebuilt.

Details

Variance methods

  • "full" — Full two-phase variance formula: the double-expansion Horvitz-Thompson estimator of survey::twophase(method = "full") (Breslow and Chatterjee, 1999). Accounts for variability in both phases, using the Phase 1 weights as inclusion probabilities, and treats a Phase 1 with no weights, strata or fpc as an iid sample. Requires Phase 2 design information (probs2, ids2, strata2) when Phase 2 is not a simple random subsample. If none of these are provided, an error is raised.

  • "approx" — The two-phase variance formula from survey 3.14 and earlier: a Phase 1 term plus a Phase 2 term. Needs less memory than "full", and is exact for some special cases, most importantly Phase 1 simple random sampling with stratified random sampling at Phase 2.

  • "simple" — The same method as "approx", as in survey::twophase(). The design records "simple", and every estimate and standard error equals the "approx" one.

Phase 1 fpc and method = "full"

The "full" variance needs the Phase 1 sampling probabilities and, for a fixed-size sample, the Phase 1 population sizes. Without a Phase 1 fpc it treats each Phase 1 sampling unit as drawn independently with probability 1 / weight (Poisson sampling), so it never centres the unit totals. For a fixed-size Phase 1 sample the resulting standard error of a total can be several times too large, whether or not Phase 1 is clustered or stratified. With an fpc, the variance is that of a fixed-size sample in each Phase 1 stratum, and is close to unbiased.

as_survey_twophase() raises a warning of class surveycore_warning_twophase_full_no_fpc when all three hold: method = "full", the Phase 1 design has no fpc, and the Phase 1 weights are not all 1. Phase 1 weights of all 1 mean the design was built with no weights, which "full" treats as an iid sample, or is a census, which contributes no Phase 1 variance; neither is overstated. The warning fires once, when the design is built. from_svydesign() raises the same warning for a twophase2 object under the same rule.

References

Sarndal, C-E., Swensson, B. and Wretman, J. (1992) Model Assisted Survey Sampling. Springer.

Breslow, N.E. and Chatterjee, N. (1999) Design and analysis of two-phase studies with binary outcome applied to Wilms tumour prognosis. Applied Statistics 48, 457–468.

Breslow, N., Lumley, T., Ballantyne, C.M., Chambless, L.E. and Kulick, M. (2009) Improved Horvitz-Thompson estimation of model parameters from two-phase stratified samples: applications in epidemiology. Statistics in Biosciences. doi:10.1007/s12561-009-9001-6

See also

as_survey() for Taylor series designs

Other constructors: as_caldata(), as_survey(), as_survey_nonprob(), as_survey_replicate(), survey_glm(), survey_glm_fit(), survey_nonprob(), survey_replicate(), survey_taylor(), survey_twophase()

Examples

# Minimal two-phase design: Phase 1 = a sample of 20 from 40, Phase 2 =
# random subset. The Phase 1 fpc gives method = "full" the population size.
df <- data.frame(
  id = 1:20,
  wt = rep(2, 20),
  pop = rep(40, 20),
  in_phase2 = c(rep(TRUE, 10), rep(FALSE, 10)),
  y = rnorm(20)
)
phase1 <- as_survey(df, ids = id, weights = wt, fpc = pop)
d2 <- as_survey_twophase(phase1, subset = in_phase2)

# With Phase 2 stratification and inclusion probabilities
df2 <- data.frame(
  id = 1:30,
  wt = rep(3, 30),
  pop = rep(90, 30),
  in_phase2 = c(rep(TRUE, 15), rep(FALSE, 15)),
  arm = rep(c("A", "B", "C"), 10),
  subsamprate = rep(c(0.5, 0.7, 0.3), 10),
  y = rnorm(30)
)
phase1b <- as_survey(df2, ids = id, weights = wt, fpc = pop)
d2b <- as_survey_twophase(
  phase1b,
  strata2 = arm,
  probs2 = subsamprate,
  subset = in_phase2,
  method = "full"
)