Select a sample by Chromy's sequential method

Draws a probability-proportional-to-size sample by Chromy's (1979) method of sequential random sampling with probability minimum replacement: the frame is ordered, the head of the list is drawn with probability proportional to size, and the selection then walks the rotated list so that every unit's realised number of selections differs from its expected number by less than one and the sample size is always exact. This is the procedure behind PROC SURVEYSELECT METHOD=PPS_SEQ.

Usage

chromy_sample(
  frame,
  n,
  size = NULL,
  variables = NULL,
  n_j = c("eqcv", "equal"),
  order_by = NULL,
  method = c("serpentine", "nested"),
  head = c("all", "residual"),
  min_replacement = FALSE,
  seed = NULL
)

Arguments

frame: Data frame with one row per unit.
n: The sample size: the expected number of selections.
size: Name of the size column, or NULL.
variables: Names of auxiliary columns for the maximal size measure, or NULL. At most one of size and variables.
n_j: How the auxiliary variables share the sample: "eqcv" (equalise anticipated CVs, the default), "equal", or a numeric vector of factors, one per variable.
order_by: Names of sort key columns for implicit stratification (may include "chromy_size"), or NULL to keep the frame's order.
method: "serpentine" (the default) or "nested"; see serpentine_order().
head: Which units may be drawn as the head of the list: "all" (the default) randomises every hit; "residual" takes integer expected hits as fixed and randomises only the fractional remainder.
min_replacement: Allow expected hits above one (units selected more than once) instead of resolving certainties; see expected_hits().
seed: Seed passed to set.seed(), or NULL to use the session's random state.

Value

An object of class chromy_sample: a list with sample (a tibble of the selected units: unit the frame row, position in the selection list, expected_hits, hits, weight the sampling weight 1 / expected_hits, fixed_hits, random_hits, then the frame's columns — a frame column that clashes with one of these design names is kept under the suffix _frame, with a warning), expected_hits and effective_hits for the whole frame, size, n_j, order, head_position, and accounting (the floating-point adjustments the selection made, if any).

Details

The size comes from one of three places: a size column; several auxiliary variables combined by the maximal measure of mpps_size(), with factors from eqcv_allocation() (the default), equal, or supplied; or, with neither, equal sizes. With order_by the frame is listed in hierarchical serpentine (or nested) order first, so the selection is implicitly stratified by the keys; the computed size is available to the sort as the column chromy_size.

All randomness comes from R's own generator — one sample.int() for the head and one runif() per randomised unit — so set.seed() (or seed) makes the selection exactly reproducible.

References

Chromy, J. R. (1979). Sequential sample selection methods. Proceedings of the American Statistical Association, Survey Research Methods Section, 401–406.

Chauvet, G. and Le Gleut, R. (2021). Properties of Chromy's sampling procedure. Survey Methodology, 47(2), 321–347.

Examples

set.seed(2026)
frame <- data.frame(
  region = rep(c("north", "east", "south", "west"), each = 25),
  pupils = rlnorm(100, 4), staff = rlnorm(100, 2)
)
s <- chromy_sample(frame,
  n = 20, variables = c("pupils", "staff"),
  order_by = c("region", "chromy_size")
)
s
#> <chromy_sample> 20 units, 20 hits, from a frame of 100
#> Head all at list position 79; without replacement.
#> Size: maximal measure over pupils, staff.
#> # A tibble: 20 × 11
#>     unit position expected_hits  hits weight fixed_hits random_hits region
#>    <int>    <int>         <dbl> <int>  <dbl>      <dbl>       <dbl> <chr> 
#>  1    96        3        0.358      1   2.80          0           1 west  
#>  2    87        5        0.294      1   3.40          0           1 west  
#>  3    89        6        0.285      1   3.50          0           1 west  
#>  4    95       21        0.0312     1  32.1           0           1 west  
#>  5    33       31        0.125      1   8.01          0           1 east  
#>  6    39       37        0.179      1   5.59          0           1 east  
#>  7    45       41        0.221      1   4.53          0           1 east  
#>  8    46       43        0.364      1   2.75          0           1 east  
#>  9    26       46        0.594      1   1.68          0           1 east  
#> 10    32       47        0.970      1   1.03          0           1 east  
#> 11    19       48        0.683      1   1.46          0           1 north 
#> 12    22       49        0.584      1   1.71          0           1 north 
#> 13     1       54        0.234      1   4.28          0           1 north 
#> 14    25       63        0.0924     1  10.8           0           1 north 
#> 15    15       72        0.0340     1  29.4           0           1 north 
#> 16    54       90        0.138      1   7.24          0           1 south 
#> 17    56       94        0.217      1   4.60          0           1 south 
#> 18    90       98        0.985      1   1.02          0           1 west  
#> 19    77       99        0.737      1   1.36          0           1 west  
#> 20    93      100        0.613      1   1.63          0           1 west  
#> # ℹ 3 more variables: pupils <dbl>, staff <dbl>, chromy_size <dbl>
estimate_total(s, c("pupils", "staff"))
#> # A tibble: 2 × 5
#>   variable total    se cv_pct random_draws
#>   <chr>    <dbl> <dbl>  <dbl>        <int>
#> 1 pupils   6868. 1130.   16.5           20
#> 2 staff    1560.  187.   12.0           20

# The frame is the first argument, so a design reads as a pipeline:
frame |>
  chromy_sample(n = 20, size = "pupils") |>
  estimate_total("staff")
#> # A tibble: 1 × 5
#>   variable total    se cv_pct random_draws
#>   <chr>    <dbl> <dbl>  <dbl>        <int>
#> 1 staff    1309.  573.   43.8           18