Bayesian Improved Surname Geocoding (BISG) is a simple model that predicts individual race based off last names and addresses. While predictive, it is not perfect, and measurement error in these predictions can cause problems in downstream analyses.
Bayesian Instrumental Regression for Disparity Estimation (BIRDiE) is a class of Bayesian models for accurately estimating conditional distributions by race, using BISG probabilities as inputs. This package implements BIRDiE as described in McCartan, Fisher, Goldin, Ho, and Imai (2025). It also implements standard BISG and an improved measurement-error BISG model as described in Imai, Olivella, and Rosenman (2022).
Do I need BIRDiE?
BIRDiE is a statistical model to let you estimate the average value of a variable in different racial groups. To take an example from our research paper, if your data are tax records and you want to estimate the rate at which different racial groups take a certain tax credit, BIRDiE can help you do that.
BIRDiE is applied on top of individual-level imputations/predictions of race from methods like BISG. If your only goal is to estimate individual race probabilities, then BIRDiE is not helpful—BISG alone suffices. The graphic below gives an overview of the problem BIRDiE solves and how it fits together with existing methods.
What is the difference between BIRDiE and BISG?
BISG is a simple model that estimates the probability of each individual belonging to diferent racial groups, based on their last name and/or residence location.
BIRDiE is a statistical model that takes race probabilities (like BISG) as inputs to estimate the average value of an outcome variable in different racial groups. If your research question involves both race and another (outcome) variable, then you likely need to apply BIRDiE on top of BISG to avoid biases caused by measurement error in BISG predictions.
Is BIRDiE better than BISG, fBISG, etc?
There are many methods for imputing or predicting individual race, including BISG, fBISG, and others. Mainly, these methods use different data sources or slightly different models.
BIRDiE is not a replacement for these methods, but rather a complementary tool that uses the outputs of these methods to properly estimate disparities in other variables. When BIRDiE is applied on top of these methods, it generally produces far more accurate estimates than directly thresholding or weighting by the outputs of the prediction methods alone.
Do I have to use the birdie software to do BISG?
The birdie software includes, for convenience, an implementation of basic BISG.
More complicated BISG models that use more data are possible using birdie, but may be easier with other software packages, such as wru.
The BIRDiE method, found in the birdie() function here, can take race predictions from any software package as inputs.
You can install the latest version of the package from CRAN with:
install.packages("birdie")You can also install the development version with:
# install.packages("remotes")
remotes::install_github("CoryMcCartan/birdie")A basic analysis has two steps. First, you compute BISG probability
estimates with the bisg() or bisg_me() functions (or using any other
probabilistic race prediction tool). Then, you estimate the distribution
of an outcome variable by race using the birdie() function.
library(birdie)
data(pseudo_vf)
head(pseudo_vf)
#> # A tibble: 6 × 4
#> last_name zip race turnout
#> <fct> <fct> <fct> <fct>
#> 1 BEAVER 28748 white yes
#> 2 WILLIAMS 28144 black no
#> 3 ROSEN 28270 white yes
#> 4 SMITH 28677 black yes
#> 5 FAY 28748 white no
#> 6 CHURCH 28215 white yesTo compute BISG probabilities, you provide the last name and (optionally) geography variables as part of a formula.
r_probs = bisg(~ nm(last_name) + zip(zip), data=pseudo_vf)
head(r_probs)
#> # A tibble: 6 × 6
#> pr_white pr_black pr_hisp pr_asian pr_aian pr_other
#> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
#> 1 0.956 0.00371 0.0103 0.000674 0.00886 0.0202
#> 2 0.162 0.795 0.0122 0.00102 0.000873 0.0292
#> 3 0.943 0.00378 0.0218 0.0107 0.000386 0.0202
#> 4 0.569 0.365 0.0302 0.00114 0.00108 0.0339
#> 5 0.971 0.00118 0.0131 0.00149 0.00118 0.0125
#> 6 0.524 0.315 0.0909 0.00598 0.00255 0.0610Computing regression estimates requires specifying a model structure. Here, we’ll use a Categorical-Dirichlet regression model that lets the relationship between turnout and race vary by ZIP code. This is the “no-pooling” model from McCartan et al. We’ll use Gibbs sampling for inference, which will also let us capture the uncertainty in our estimates.
fit = birdie(r_probs, turnout ~ proc_zip(zip), data=pseudo_vf,
family=cat_dir(), algorithm="gibbs")
#> Using weakly informative empirical Bayes prior for Pr(Y | R)
#> This message is displayed once every 8 hours.
print(fit)
#> Categorical-Dirichlet BIRDiE model
#> Formula: turnout ~ proc_zip(zip)
#> Data: pseudo_vf
#> Number of obs: 5,000
#> Estimated distribution:
#> white black hisp asian aian other
#> no 0.293 0.34 0.372 0.569 0.685 0.499
#> yes 0.707 0.66 0.628 0.431 0.315 0.501The proc_zip() function fills in missing ZIP codes, among other
things. We can extract the estimated conditional distributions with
coef(). We can also get updated BISG probabilities that additionally
condition on turnout using fitted(). Additional functions allow us to
extract a tidy version of our estimates (tidy()) and visualize the
estimated distributions (plot()).
coef(fit)
#> white black hisp asian aian other
#> no 0.2934753 0.3403649 0.3720582 0.5687325 0.6847874 0.4994076
#> yes 0.7065247 0.6596351 0.6279418 0.4312675 0.3152126 0.5005924
head(fitted(fit))
#> # A tibble: 6 × 6
#> pr_white pr_black pr_hisp pr_asian pr_aian pr_other
#> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
#> 1 0.961 0.00349 0.0101 0.000523 0.00577 0.0195
#> 2 0.0765 0.893 0.00814 0.00102 0.00106 0.0207
#> 3 0.932 0.00542 0.0287 0.00538 0.000384 0.0286
#> 4 0.587 0.352 0.0260 0.000833 0.000783 0.0335
#> 5 0.945 0.00224 0.0219 0.00368 0.00334 0.0238
#> 6 0.528 0.324 0.0895 0.00379 0.00143 0.0538
tidy(fit)
#> # A tibble: 12 × 3
#> turnout race estimate
#> <chr> <chr> <dbl>
#> 1 no white 0.293
#> 2 yes white 0.707
#> 3 no black 0.340
#> 4 yes black 0.660
#> 5 no hisp 0.372
#> 6 yes hisp 0.628
#> 7 no asian 0.569
#> 8 yes asian 0.431
#> 9 no aian 0.685
#> 10 yes aian 0.315
#> 11 no other 0.499
#> 12 yes other 0.501
plot(fit)
A more detailed introduction to the method and software package can be found on the Get Started page.