Selective labels across judges ordered by leniency

With several judges whose release sets are nested from the strictest to the most lenient, a rule's identified interval shrinks with leniency (Research.P18.chain_width_antitone): the most lenient judge gives the sharpest interval, and the interval collapses to a point exactly when the rule releases nobody that judge detained (chain_width_zero_iff, chain_contraction). Judges need not be nested; then the function reports the sharpest interval among them and says the chain theorems do not apply.

Usage

morie_selective_labels_judges(y, released, rule_released, weights = NULL)

Arguments

y

Failure indicator (0/1) per defendant; only its values on released are used.

released

Logical matrix with one column per judge (rows are defendants), or a list of logical vectors, ordered from strictest to most lenient.

rule_released

Logical: released by the proposed rule.

weights

Optional non-negative weights.

Value

A list with judges (a data frame: release share, interval, width and whether the rule is identified, one row per judge), nested, best (the judge with the narrowest interval), identified, rule_rate (when identified), bounds, width and theorems.

Examples

set.seed(5)
n <- 400; risk <- runif(n); y <- rbinom(n, 1, risk)
judges <- cbind(strict = risk < 0.5, middle = risk < 0.7, lenient = risk < 0.85)
morie_selective_labels_judges(y, judges, rule_released = risk < 0.8)$judges
#>     judge release_share     lower     upper     width identified
#> 1  strict        0.5350 0.1688312 0.4740260 0.3051948      FALSE
#> 2  middle        0.6875 0.2857143 0.3928571 0.1071429      FALSE
#> 3 lenient        0.8475 0.3766234 0.3766234 0.0000000       TRUE