Justice-pipeline rates with a lag between stages

The rate at which one stage of the justice process follows another (charges per reported offence, settlements per charge, convictions per trial), summing each over a window and setting the outcome's window after the input's, because cases take time to move through.

Usage

piperate(num, den, win = 12L, lag = 0L, grp = NULL)

Arguments

num, den

The outcome and input counts, in period order.

win

The number of periods summed (default 12).

lag

The number of periods the input's window precedes the outcome's (default 0).

grp

Optional grouping (for example a court or municipality), the counts in period order within it.

Value

A data frame of class rmbl_pipeline_rate: group, index (the period's position within its group), numerator, denominator (the window sums), rate.

Details

For period \(t\), a window of \(W\) periods and a lag of \(L\), $$R_t = \frac{\sum_{s = t - W + 1}^{t} O_s}{\sum_{s = t - L - W + 1}^{t - L} I_s},$$ with \(O\) the outcome stage and \(I\) the input stage. With \(W = 1, L = 0\) it is the same-period ratio (cases with detention over cases charged; acquittals over acquittals and convictions). Rates are NA until the windows are filled, and when the denominator is zero. These are administrative counts of every case, so no sampling interval is given.

References

Council of Europe, European Commission for the Efficiency of Justice (CEPEJ) (2014). European judicial systems: efficiency and quality of justice. CEPEJ Studies 20.

Applied to the stages of a Colombian criminal-procedure reform: Acosta, Mejia and Zorro Medina (2023), see plndid.

See also

caseflow for clearance rates and inventories.

Examples

set.seed(2)
reports <- rpois(36, 400)
charges <- rpois(36, 90)
piperate(charges, reports, win = 12, lag = 3)[30:36, ]
#> ╭── Lagged pipeline rate ────────────────────────────────────────────────╮
#> │   Groups          1                                                    │
#> │   Periods         36                                                   │
#> │   Rates computed  7                                                    │
#> │                                                                        │
#> │   group  index  numerator  denominator    rate                         │
#> │   -----  -----  ---------  -----------  ------                         │
#> │   all       30      1,091        4,882  0.2235                         │
#> │   all       31      1,093        4,810  0.2272                         │
#> │   all       32      1,088        4,799  0.2267                         │
#> │   all       33      1,109        4,796  0.2312                         │
#> │   all       34      1,106        4,826  0.2292                         │
#> │   all       35      1,095        4,879  0.2244                         │
#> │   all       36      1,088        4,858  0.2240                         │
#> │                                                                        │
#> │   Each rate is the numerator summed over the window over the           │
#> │   denominator summed over the same window moved back by the lag (cases │
#> │   out over cases in earlier); it is missing until a full window is in. │
#> ╰────────────────────────────────────────────────────────────────────────╯