Share series at fixed source weights — fixed_weight

Computes for every key and period the average of the source shares with weights fixed over the whole period, renormalised over the sources present in each period, next to the observed share.

Usage

fixed_weight_share(
  counts,
  key_cols,
  source_col = "source",
  time_col,
  weights = NULL,
  x_col = "x",
  n_col = "n",
  source_totals = NULL
)

Arguments

counts: data.frame or data.table with one row per key, source and period, holding the count x_col and, when source_totals is NULL, the source denominator n_col.
key_cols: Character vector of key columns.
source_col: Name of the source column (default "source").
time_col: Name of the period column.
weights: Optional named numeric vector of non-negative source weights (names = sources). By default the weight of a source is its share of the postings over all the periods of source_totals (or of counts).
x_col, n_col: Names of the count and denominator columns (defaults "x", "n").
source_totals: Optional data.frame with one row per source and period and columns source_col, time_col, n_col (postings of the source in the period, also where the key has no posting). Without it the denominators are read from counts and must be the same for all keys of a source and period.

Value

A data.table with one row per key and period (all keys of counts crossed with all periods with at least one source) and columns key_cols, time_col, quota_fissa, quota_osservata, n_fonti (sources with a positive denominator in the period).

Details

With source shares p_kst = x_kst / n_st and fixed weights w_s,

quota_fissa_kt = sum_{s in S_t} w_s p_kst / sum_{s in S_t} w_s

where S_t is the set of sources with n_st > 0. The observed share is sum_s x_kst / sum_s n_st. With fixed weights the reallocation of postings among continuing sources does not move the series, so the difference between the two series measures the composition effect (see decompose_share_change()). Entry and exit of sources still change S_t. When all the sources of a period have weight 0, quota_fissa is NA.

Examples

counts <- data.frame(
  code = "a",
  source = c("s1", "s2", "s1", "s2"),
  mese = c(1, 1, 2, 2),
  x = c(10, 5, 10, 20)
)
totals <- data.frame(
  source = c("s1", "s2", "s1", "s2"),
  mese = c(1, 1, 2, 2),
  n = c(100, 100, 100, 400)
)
fixed_weight_share(counts, "code", time_col = "mese",
                   source_totals = totals)
#>      code  mese quota_fissa quota_osservata n_fonti
#>    <char> <num>       <num>           <num>   <int>
#> 1:      a     1  0.06428571           0.075       2
#> 2:      a     2  0.06428571           0.060       2