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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.


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

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

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



A data frame or matrix of BISG probabilities, with one row per individual. The output of bisg() can be used directly here.


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).


An optional data frame containing the variables named in formula.


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().


The number of bootstrap replicates to use to compute approximate standard errors for the estimator. 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.


An object of class est_weighted, inheriting from birdie, for which many methods are available. The model estimates may be accessed with coef().

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.


McCartan, C., Fisher, R., Goldin, J., Ho, D., & Imai, K. (2022). Estimating Racial Disparities when Race is Not Observed. Available at



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