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Dual-frame estimate of a total

Source: R/dualframe.R
dual_frame_estimator.Rd

Combines the sample of frame A (the area frame) and the sample of frame B (the list) into one estimate of the population total of y. Each sampled unit carries its domain: "a" or "ab" in the A sample, "b" or "ab" in the B sample. Two estimators:

Usage

dual_frame_estimator(
  sample_a,
  sample_b,
  y,
  domain = "domain",
  theta = NULL,
  estimator = c("hartley", "fuller-burmeister")
)

Arguments

sample_a, sample_b

select_units() samples of frame A and frame B with columns y and domain (unsampled rows may hold NA).

y

Column of the study variable.

domain

Column with the domain of each unit.

theta

Mixing weight of the overlap for Hartley: a number in [0, 1], "screening", or NULL to estimate it.

estimator

"hartley" or "fuller-burmeister".

Value

A one-row tibble: total, variance, se, cv, estimator, theta (Hartley) or beta_1, beta_2 (Fuller-Burmeister), the domain totals y_a, y_ab_a, y_ab_b, y_b, and n_a, n_b.

Details

  • Hartley (1962): Y_a + theta * Y_ab(A) + (1 - theta) * Y_ab(B) + Y_b, with theta fixed, "screening" (theta = 0: overlap units found in the area sample are dropped, as when the list is enumerated completely) or estimated as the value that minimises the variance;

  • Fuller and Burmeister (1972): adds a second term in the difference between the two estimates of the overlap size, with coefficients chosen to minimise the variance.

Variances and covariances of the domain totals come from the variance estimator of each sample's design (design_variance()), the two samples being independent. The estimated theta and the Fuller-Burmeister coefficients make the variances slightly optimistic in small samples.

References

Hartley, H. O. (1962). Multiple frame surveys. Proceedings of the Social Statistics Section, ASA, 203-206. Fuller, W. A. and Burmeister, L. F. (1972). Estimators for samples selected from two overlapping frames. Proceedings of the Social Statistics Section, ASA, 245-249. Lohr, S. L. (2009). Multiple-frame surveys. In Handbook of Statistics 29A, 71-88.

Examples

set.seed(7)
cells <- expand.grid(x = 1:12, y = 1:12)
cells$unit <- paste0("c", 1:144)
cells$domain <- ifelse(runif(144) < 0.2, "ab", "a")
cells$y <- ifelse(cells$domain == "ab", 80, 10) + rnorm(144, sd = 3)
# the list holds the overlap units (same values) plus units of its own
ab <- cells[cells$domain == "ab", ]
list <- data.frame(
  unit = c(paste0("l", seq_len(nrow(ab))), paste0("b", 1:11)),
  x = runif(nrow(ab) + 11), y = c(ab$y, 120 + rnorm(11, sd = 5)),
  domain = rep(c("ab", "b"), c(nrow(ab), 11))
)
list$lon <- runif(nrow(list))
list$lat <- runif(nrow(list))
sa <- select_units(cells, n = 30, seed = 1)
sb <- select_units(list, n = 15, coords = c("lat", "lon"), method = "srs", seed = 2)
dual_frame_estimator(sa, sb, y = "y", domain = "domain")
#> # A tibble: 1 × 13
#>   total variance    se     cv estimator theta theta_fixed   y_a y_ab_a y_ab_b
#>   <dbl>    <dbl> <dbl>  <dbl> <chr>     <dbl> <lgl>       <dbl>  <dbl>  <dbl>
#> 1 4510.   18687.  137. 0.0303 hartley       0 FALSE       1169.  2300.  2167.
#> # ℹ 3 more variables: y_b <dbl>, n_a <int>, n_b <int>
dual_frame_estimator(sa, sb, y = "y", domain = "domain", theta = "screening")
#> # A tibble: 1 × 13
#>   total variance    se     cv estimator theta theta_fixed   y_a y_ab_a y_ab_b
#>   <dbl>    <dbl> <dbl>  <dbl> <chr>     <dbl> <lgl>       <dbl>  <dbl>  <dbl>
#> 1 4510.   18687.  137. 0.0303 hartley       0 TRUE        1169.  2300.  2167.
#> # ℹ 3 more variables: y_b <dbl>, n_a <int>, n_b <int>
dual_frame_estimator(sa, sb, y = "y", domain = "domain", estimator = "fuller-burmeister")
#> # A tibble: 1 × 13
#>   total variance    se      cv estimator beta_1 beta_2   y_a y_ab_a y_ab_b   y_b
#>   <dbl>    <dbl> <dbl>   <dbl> <chr>      <dbl>  <dbl> <dbl>  <dbl>  <dbl> <dbl>
#> 1 4445.    1167.  34.2 0.00769 fuller-b…  0.309  -63.8 1169.  2300.  2167. 1174.
#> # ℹ 2 more variables: n_a <int>, n_b <int>