Additive decomposition of profile change by skill groups

Splits the squared distance d2 between base and target profiles of each profession into the contributions of skill groups.

Usage

decompose_profile_change(pair, skill_groups, group_cols)

Arguments

pair

Output of build_profile_pair().

skill_groups

A data.frame with the skill column of the pair and one or more group columns, one row per skill.

group_cols

Character vector of group columns (e.g. c("reusetype", "green", "digital")).

Value

A data.table with the profession column, tipo_gruppo (group column name), gruppo, d2_gruppo, d2 and quota (d2_gruppo / d2, 0 when d2 = 0).

Details

For any partition of the skills into groups \(G_1, \dots, G_M\), \(d^2 = \sum_m \sum_{k \in G_m} (a_k - b_k)^2\), so the group contributions add up exactly to d2 (the same property as compute_decomposed_distance()). Each column of group_cols defines one partition (group type). Skills without a group, or missing from skill_groups, go to the group "(mancante)".

Examples

panel <- data.table::data.table(
  cp4 = "p1", skill_id = rep(c("a", "b", "c"), 2),
  mese_idx = rep(1:2, each = 3), x = c(50, 50, 0, 50, 0, 50), n = 100
)
pair <- build_profile_pair(panel, "cp4", base = c(1, 1), target = c(2, 2))
groups <- data.table::data.table(skill_id = c("a", "b", "c"),
  green = c("no", "no", "si"))
decompose_profile_change(pair, groups, "green")
#>       cp4 tipo_gruppo gruppo d2_gruppo    d2 quota
#>    <char>      <char> <char>     <num> <num> <num>
#> 1:     p1       green     no      0.25   0.5   0.5
#> 2:     p1       green     si      0.25   0.5   0.5