Calibrate the minimum support by split-half reliability

Chooses the smallest support threshold at which the trend slope is reliable, measured by the agreement of slopes estimated on two random halves of the postings.

Usage

calibrate_min_support(
  incidence,
  id_col = "general_id",
  time_col = "mese_idx",
  skill_col = "skill_id",
  group_cols = NULL,
  window = 24L,
  grid = c(5, 10, 20, 30, 50, 100),
  target = 0.7,
  min_series = 10L,
  seed = 1L,
  weights = c("pooled", "observed")
)

Arguments

incidence

A data.frame/data.table with one row per posting and skill (duplicates are removed). Must contain id_col, time_col, skill_col and any group_cols. Each posting must belong to a single period and group.

id_col

Posting identifier column. Default "general_id".

time_col

Period column (typically an integer month index). Default "mese_idx".

skill_col

Skill identifier column. Default "skill_id".

group_cols

Optional character vector of grouping columns (e.g. "cp4"). Default NULL (global panel).

window

Number of trailing periods for the slope. Default 24.

grid

Numeric vector of candidate thresholds. Default c(5, 10, 20, 30, 50, 100).

target

Minimum split-half Spearman correlation. Default 0.7.

min_series

Minimum number of series for a valid correlation. Default 10.

seed

Integer seed for the split. Default 1.

weights

Trend weighting, "pooled" (default) or "observed"; see compute_share_trend().

Value

A list with tabella (data.table with n_min, n_serie, rho) and n_min (chosen threshold, NA with a warning when no value reaches target).

Details

Postings are split at random into two halves (by posting id, with a fixed seed; the global RNG state is restored). For each half the share panel is built and the slope of the last window periods is estimated as in compute_share_trend() (no breaks, no drift, the chosen weights). The support of a series is its average count per 3 periods in the full sample over the window, \(3 \sum_t x_t / window\), the same unit as the rolling count of detect_skill_onset(). For each value of grid, the Spearman correlation between the half-sample slopes of series with support at least that value is computed; the chosen threshold is the smallest one with correlation at least target and at least min_series series.

Examples

set.seed(4)
inc <- data.table::rbindlist(lapply(1:12, function(m) {
  ids <- (m * 1000):(m * 1000 + 299)
  data.table::rbindlist(lapply(letters[1:12], function(s) {
    p <- plogis(-2 + (match(s, letters) - 6) * 0.02 * m)
    data.table::data.table(general_id = ids[runif(300) < p],
      skill_id = s)
  }))[, mese_idx := m]
}))
calibrate_min_support(inc, window = 12, grid = c(5, 20), min_series = 5)
#> $tabella
#>    n_min n_serie       rho
#>    <num>   <int>     <num>
#> 1:     5      12 0.9440559
#> 2:    20      12 0.9440559
#> 
#> $n_min
#> [1] 5
#>