Risk-Adjusted Regression.

rar

Quantitative studies of disparate impact face two key challenges:

1. Omitted-variable bias occurs when an analyst omits relevant variables, like a job applicant’s work history, in their regression model.
2. Included-variable bias occurs when a researcher includes variables in their regression model that are not relevant to the outcome of interest, like a job applicant’s height. These variables can mask the relevance of gender, race, or other protected attributes.

The rar package supports risk-adjusted regression, a framework for mitigating included-variable bias. It computes risk-adjusted disparities and performs an interpretable sensitivity analysis that can be used to assess the robustness of regression results to omitted-variable bias. See “Mitigating Included- and Omitted-Variable Bias in Estimates of Disparate” for more details.

Installation

You can install the latest stable release of rar from CRAN with:

install.packages("rar")

You can install the development version of rar from GitHub with:

# install.packages("devtools")
devtools::install_github("jgaeb/rar")

Example

To perform risk-adjusted regression, use the sens() function.

library(rar)

# Generate some data
set.seed(1)
df <- tibble::tibble(
  group = factor(
    sample(c("a", "b"), 1000, replace = TRUE),
    levels = c("a", "b")
  ),
  p = runif(1000)^2,
  frisked = runif(1000) < p + 0.1 * (group != "a")
)

# Compute risk-adjusted regression coefficients and perform sensitivity analysis
sens(df, group, frisked, p, "a", 0.1, eta = 0.001, m = 10)
#> # A tibble: 10 × 3
#>    epsilon beta_min_b beta_max_b
#>      <dbl>      <dbl>      <dbl>
#>  1  0          0.102       0.102
#>  2  0.0111     0.0752      0.125
#>  3  0.0222     0.0472      0.151
#>  4  0.0333     0.0185      0.178
#>  5  0.0444    -0.0106      0.207
#>  6  0.0556    -0.0394      0.236
#>  7  0.0667    -0.0677      0.265
#>  8  0.0778    -0.0950      0.295
#>  9  0.0889    -0.123       0.324
#> 10  0.1       -0.151       0.354