Draw a choice-based sample stratified by the chosen alternative

Subsamples whole choice situations from a population data set according to fixed per-stratum quotas, where strata are defined by the chosen alternative. The input data set is treated as the population, so the population shares \(Q(j)\) are known exactly; the returned sample carries a ready-to-use WESML weight column (see wesml_weights).

Usage

sample_by_choice(
  data,
  id_col,
  alt_col,
  choice_col,
  n_per_alt = NULL,
  frac_per_alt = NULL,
  seed = NULL,
  weight_name = ".wesml_weight",
  outside_opt_label = NULL,
  include_outside_option = FALSE
)

Arguments

data, id_col, alt_col, choice_col: As in wesml_weights.
n_per_alt: Either a single integer applied to every stratum, or a named integer vector of per-stratum counts (names matched to as.character(alt), covering all strata). Mutually exclusive with frac_per_alt.
frac_per_alt: Either a single fraction in [0, 1] applied to every stratum, or a named numeric vector of per-stratum fractions. Mutually exclusive with n_per_alt.
seed: Optional integer seed for reproducible sampling.
weight_name: Name of the attached weight column (default ".wesml_weight").
outside_opt_label, include_outside_option: As in wesml_weights (for an implicit outside good).

Value

A data.table subsample with the weight column appended and "Q", "H", and "choice_sampling" attributes (the last records the scheme, shares, quotas, and meat = "robust").

Details

Sampling is by choice situation (id), never by row: all alternative-rows of a sampled situation are kept together. Sampling is without replacement.

References

Manski, C. F. and Lerman, S. R. (1977). Econometrica 45(8), 1977-1988.

Examples

library(data.table)
set.seed(1)
N <- 600L; J <- 3L
pop <- data.table(id = rep(seq_len(N), each = J), alt = rep(1:J, N))
pop[, x1 := rnorm(.N)]
#>          id   alt         x1
#>       <int> <int>      <num>
#>    1:     1     1 -0.6264538
#>    2:     1     2  0.1836433
#>    3:     1     3 -0.8356286
#>    4:     2     1  1.5952808
#>    5:     2     2  0.3295078
#>   ---                       
#> 1796:   599     2  1.9363973
#> 1797:   599     3 -1.4558838
#> 1798:   600     1  1.4819057
#> 1799:   600     2  1.0761196
#> 1800:   600     3 -0.7574884
pop[, w1 := rnorm(.N)]
#>          id   alt         x1         w1
#>       <int> <int>      <num>      <num>
#>    1:     1     1 -0.6264538  0.7140855
#>    2:     1     2  0.1836433  0.5813846
#>    3:     1     3 -0.8356286 -0.1467239
#>    4:     2     1  1.5952808  1.5069818
#>    5:     2     2  0.3295078 -0.2795326
#>   ---                                  
#> 1796:   599     2  1.9363973 -0.5294766
#> 1797:   599     3 -1.4558838  0.7047356
#> 1798:   600     1  1.4819057 -0.9388858
#> 1799:   600     2  1.0761196  0.8752661
#> 1800:   600     3 -0.7574884 -0.7443670
pop[, choice := as.integer(seq_len(.N) == sample.int(.N, 1L)), by = id]
#>          id   alt         x1         w1 choice
#>       <int> <int>      <num>      <num>  <int>
#>    1:     1     1 -0.6264538  0.7140855      0
#>    2:     1     2  0.1836433  0.5813846      0
#>    3:     1     3 -0.8356286 -0.1467239      1
#>    4:     2     1  1.5952808  1.5069818      1
#>    5:     2     2  0.3295078 -0.2795326      0
#>   ---                                         
#> 1796:   599     2  1.9363973 -0.5294766      0
#> 1797:   599     3 -1.4558838  0.7047356      0
#> 1798:   600     1  1.4819057 -0.9388858      1
#> 1799:   600     2  1.0761196  0.8752661      0
#> 1800:   600     3 -0.7574884 -0.7443670      0

s <- sample_by_choice(pop, "id", "alt", "choice", n_per_alt = 50L, seed = 1L)
attr(s, "choice_sampling")$H   # realized sample shares
#>         3         1         2 
#> 0.3333333 0.3333333 0.3333333 
head(s[[".wesml_weight"]])
#> [1] 0.970 0.970 0.970 0.985 0.985 0.985