In jongbinjung/undi: Test for Unjustified Disparate Impact

knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>"
)

# Load necessary packages
library(tidyverse)
library(undi)

The purpose of undi is to analyze possibilities of (unjustified) disparate impact, within the context of a policy. The basic requirements of a policy are (1) an action taken upon each unit (e.g., requiring bail for defendants or deciding to frisk an individual) and (2) a clear outcome of interest (e.g., whether a defendant fails to appear for a future court date, or whether the individual is carrying an illegal weapon)[^binary].

[^binary]: For now, undi only deals with policies that have binary decisions and binary outcomes.

In addition to an action and outcome, analysis of disparate impact requires the definition of some group (e.g., race or gender) for which we would like to measure the possibility of disparate impact.

The setup

For illustration, we generate data from a (fictional) policy. The united nations of M&M's (yes, the candy) have recently enacted a "Nuts in my backyard" policy, which aims to reduce the population of potentially fatal peanut M&M's. As part of this effort, the M&M's police department (MMPD) were given the authority to stop, question, and slice pedestrian M&M's highly suspected of containing peanuts. Many attributes of M&M's, such as size or visible crack in coating, are indicitive of being of the peanut variety. And while certain colors are indeed more likely to be peanut M&M's, it is unclear whether the policy has unjustified disparate impact on certain colors of M&M's.

inv_logit <- stats::binomial()$linkinv
logit <- stats::binomial()$linkfun

N <- 3000

set.seed(1)
data <- tibble(id = rep(1:N)) %>%
  mutate(color = factor(sample(c("yellow", "blue", "red", "other"), 
                               N, replace = TRUE, prob = c(.15, .45, .35, .05))), 
    color = fct_relevel(color, "yellow"),
    size = rnorm(N, 0, 1),
    # yellow M&M's are systematically less-likely to have a crack
    p_crack = ifelse(color == "yellow", 0.1, 0.15),
    has_cracks = rbinom(N, 1, p_crack),
    # noise
    e_risk = rnorm(N, 0, .1),
    # risk of being peanut M&M's is a function of size/cracks/color
    risk = size + 2*has_cracks + 
      # blue and red colors are more likely to have peanuts 
      0.5 * (color == "blue") + 0.5 * (color == "red") + e_risk,  
    # MMPD actually slice blue M&M's at a higher rate 
    p_slice = inv_logit(risk + 0.2*(color == "blue")), 
    # MMPD slices 20% of the population, after adjusting for colorism
    slice = p_slice >= quantile(p_slice, .2) , 
    # slice = inv_logit(p_slice) > runif(n()), 
    # The actual outcome is only observed for sliced M&M's 
    has_peanut = ifelse(slice, inv_logit(risk) > runif(n()), FALSE))

Fitting the policy

In this setting, the unit of analysis is each inidividual candy. The treatment decision is weather or not to slice each candy, the outcome (response) is whether the candy contains peanuts, and color is the group of interest. Note that we only observe weather each M&M's contains peanuts if it is sliced, i.e., the response given control is always 0.

pol <- policy(slice ~ color + size + has_cracks,
              data,
              model = "glm",
              outcome = "has_peanut", 
              resp_ctl = 0)
plot(pol)

First, we can compute regular benchmark tests

compute_bm(pol, base_group = "yellow", minority_groups = c("blue", "red"))
compute_bm(pol, base_group = "yellow", minority_groups = c("blue", "red"), kitchen_sink = TRUE)

We can use the estimated risk scores to measure risk-adjusted disparate impact (rad)

compute_rad(pol, base_group = "yellow", minority_groups = c("blue", "red"))

jongbinjung/undi documentation built on May 8, 2019, 11:56 p.m.