Calculate Weighted Estimate of (Discrete) Outcomes By Race

Calculates the "standard" weighted estimator of conditional distributions of an outcome variable $Y$ by race $R$, using BISG probabilities. This estimator, while commonly used, is only appropriate if $Y \perp R \mid X, S$, where $S$ and $X$ are the last names and covariates (possibly including geography) used in making the BISG probabilities. In most cases this assumption is not plausible and birdie() should be used instead. See the references below for more discussion as to selecting the right estimator.

Up to Monte Carlo error, the weighted estimate is equivalent to performing multiple imputations of the race vector from the BISG probabilities and then using them inside a weighted average or linear regression.

Usage

est_weighted(
  r_probs,
  formula,
  data = NULL,
  weights = NULL,
  prefix = "pr_",
  se_boot = 0
)

# S3 method for est_weighted
print(x, ...)

# S3 method for est_weighted
summary(object, ...)

Arguments

r_probs: A data frame or matrix of BISG probabilities, with one row per individual. The output of bisg() can be used directly here.
formula: A two-sided formula object describing the estimator structure. The left-hand side is the outcome variable, which must be discrete. Subgroups for which to calculate estimates may be specified by adding covariates on the right-hand side. Subgroup estimates are available with coef(..., subgroup=TRUE) and tidy(..., subgroup=TRUE).
data: An optional data frame containing the variables named in formula.
weights: An optional numeric vector specifying weights.
prefix: If r_probs is a data frame, the columns containing racial probabilities will be selected as those with names starting with prefix. The default will work with the output of bisg().
se_boot: The number of bootstrap replicates to use to compute an approximate covariance matrix for the estimator. If no bootstrapping is used, an analytical estimate of standard errors will be returned as $se. For bootstrapping, when there are fewer than 1,000 individuals or 100 or fewer replicates, a Bayesian bootstrap is used instead (i.e., weights are drawn from a $\text{Dirichlet}(1, 1, ..., 1)$ distribution, which produces more reliable estimates.
...: Additional arguments to generic methods (ignored).
object, x: An object of class est_weighted.

Value

An object of class est_weighted, inheriting from birdie, for which many methods are available. The model estimates may be accessed with coef(). Uncertainty estimates, if available, can be accessed with $se and vcov.birdie().

Methods (by generic)

print(est_weighted): Print a summary of the model fit.
summary(est_weighted): Print a more detailed summary of the model fit.

References

McCartan, C., Fisher, R., Goldin, J., Ho, D., & Imai, K. (2022). Estimating Racial Disparities when Race is Not Observed. Available at https://arxiv.org/abs/2303.02580.

Examples

data(pseudo_vf)

r_probs = bisg(~ nm(last_name) + zip(zip), data=pseudo_vf)

# Process zip codes to remove missing values
pseudo_vf$zip = proc_zip(pseudo_vf$zip)

est_weighted(r_probs, turnout ~ 1, data=pseudo_vf)
#> Weighted estimator
#> Formula: turnout ~ 1
#>    Data: pseudo_vf
#> Number of obs: 5,000; groups: 1
#> Estimated distribution:
#>     white black  hisp asian aian other
#> no  0.315 0.335 0.357 0.468 0.53 0.329
#> yes 0.685 0.665 0.643 0.532 0.47 0.671

est = est_weighted(r_probs, turnout ~ zip, data=pseudo_vf)
tidy(est, subgroup=TRUE)
#> # A tibble: 7,416 × 4
#>    zip   turnout race  estimate
#>    <chr> <chr>   <chr>    <dbl>
#>  1 28748 no      white    0.276
#>  2 28748 yes     white    0.724
#>  3 28748 no      black    0.340
#>  4 28748 yes     black    0.660
#>  5 28748 no      hisp     0.147
#>  6 28748 yes     hisp     0.853
#>  7 28748 no      asian    0.284
#>  8 28748 yes     asian    0.716
#>  9 28748 no      aian     0.211
#> 10 28748 yes     aian     0.789
#> # ℹ 7,406 more rows