Turnover of profession skill profiles — compute_profile

Measures how much the skill profile of each profession changed between the base and the target window, net of sampling noise.

Usage

compute_profile_turnover(pair)

Arguments

pair: Output of build_profile_pair().

Value

A data.table with one row per profession: the profession column, n_base, n_target, n_skill, turnover_coseno, d2, d2_atteso, turnover_netto.

Details

With \(a\) and \(b\) the base and target profiles of a profession:

turnover_coseno \(= 1 - a \cdot b / (\|a\| \|b\|)\);
d2 \(= \sum_k (a_k - b_k)^2\);
d2_atteso \(= \sum_k s_k (1 - s_k) (1/n_a + 1/n_b)\), the expected value of d2 when both windows share the pooled profile \(s = (n_a a + n_b b)/(n_a + n_b)\) (binomial sampling noise);
turnover_netto \(= \max(0, d2 - E[d2]) / \sum_k \bar s_k^2\), with \(\bar s = (a + b)/2\), a scale-free change net of noise.

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))
compute_profile_turnover(pair)
#>       cp4 n_base n_target n_skill turnover_coseno    d2 d2_atteso
#>    <char>  <num>    <num>   <int>           <num> <num>     <num>
#> 1:     p1    100      100       3             0.5   0.5    0.0125
#>    turnover_netto
#>             <num>
#> 1:            1.3