Monotonicity of judges without outcomes: do the leniency rankings hold in every subgroup?

Judge designs need judges ordered by leniency: whoever a lenient judge detains, a stricter one detains too (nesting, the many-judge monotonicity). Nesting holds person by person, so it orders the judges' detention rates inside every subgroup of defendants (Research.P14Slope.subgroup_propensity_mono). For every pair of judges, the one with the higher detention rate overall should not have a lower one in any subgroup; a pair that does is nested in neither direction (crossing_refutes_both). With sampling noise a reversal is evidence only when it is significant, so each is tested (one-sided, difference of proportions) and the p-values are adjusted across every comparison made.

Usage

morie_judge_monotonicity(
  judge,
  d,
  group,
  min_n = 30,
  adjust = "holm",
  alpha = 0.05
)

Arguments

judge: Judge of each case.
d: 0/1 decision (1 = detained or incarcerated).
group: Subgroup of each case (an offence category, a year).
min_n: Smallest number of a judge's cases in a subgroup for that cell to be compared.
adjust: Multiple-comparison adjustment passed to p.adjust.
alpha: Level at which an adjusted reversal counts as significant.

Value

A list: judges (overall rate and cases per judge), comparisons (one row per pair and subgroup compared, stricter-overall judge first, with the subgroup rates, the z statistic for the reversal, raw and adjusted p-values), summary (comparisons, reversals, significant reversals, the pairs and judges involved), by_group (per subgroup: judges compared and the slope of the subgroup rate on the overall rate, the average-monotonicity check) and theorems.

Examples

set.seed(1)
judge <- sample(sprintf("J%02d", 1:8), 4000, replace = TRUE)
strict <- setNames(seq(0.2, 0.6, length.out = 8), sprintf("J%02d", 1:8))
group <- sample(c("drugs", "theft", "weapons"), 4000, replace = TRUE)
d <- rbinom(4000, 1, strict[judge])
r <- morie_judge_monotonicity(judge, d, group)
r$summary
#>   comparisons reversed share_reversed significant pairs_refuted judges_involved
#> 1          84        2     0.02380952           0             0               0