Weighted aggregation of source indices — aggregate

Combines per-source indices into one index per key and time with fixed source weights, renormalised over the sources present in each cell, with an optional cap on the weight of any source.

Usage

aggregate_index(
  idx,
  source_col,
  key_cols = NULL,
  time_col,
  index_col = "indice",
  weights,
  type = c("geometric", "arithmetic"),
  cap = NULL
)

Arguments

idx: A data.frame or data.table of per-source indices.
source_col: Name of the source column.
key_cols: Character vector of further key columns (e.g. skill), or NULL.
time_col: Name of the time column.
index_col: Name of the index column (default "indice").
weights: A data.frame with columns source_col and w (non-negative weights, e.g. base-period volumes).
type: "geometric" (default) or "arithmetic".
cap: NULL or a single number in (0, 1]: maximum weight of a source.

Value

A data.table with columns key_cols, time_col, index_col, n_sources, covered_weight and n_eff, one row per key x time of idx.

Details

In each key x time cell, the sources with a non-missing index and a positive weight are used, their weights w renormalised to sum to one. With cap, weights above cap are set to cap and the excess is redistributed proportionally over the other sources, repeating until no weight exceeds the cap (water-filling); when fewer than 1 / cap sources are present the cap is infeasible and equal weights are used. type = "geometric" returns exp(sum(w * log(I))), "arithmetic" returns sum(w * I). covered_weight is the share of the total weight of weights held by the sources present, before renormalisation, and n_eff = 1 / sum(w^2) is the effective number of sources (Kish) after renormalisation and cap. Sources of idx missing from weights are ignored with a warning.

Examples

weeks <- data.table::as.IDate("2024-01-01") + 7L * (0:3)
idx <- data.table::data.table(
  source = rep(c("a", "b"), each = 4), week = rep(weeks, 2),
  indice = c(100, 101, 102, 103, 100, 99, 98, 97)
)
w <- data.table::data.table(source = c("a", "b"), w = c(3, 1))
aggregate_index(idx, "source", time_col = "week", weights = w)
#>          week   indice n_sources covered_weight n_eff
#>        <IDat>    <num>     <int>          <num> <num>
#> 1: 2024-01-01 100.0000         2              1   1.6
#> 2: 2024-01-08 100.4962         2              1   1.6
#> 3: 2024-01-15 100.9849         2              1   1.6
#> 4: 2024-01-22 101.4661         2              1   1.6