Calculates individual probabilities of belonging to racial groups given last
name, location, and other covariates (optional). The standard function
`bisg()`

treats the input tables as fixed. An alternative function
`bisg_me()`

, assumes that the input tables are subject to measurement error,
and uses a Gibbs sampler to impute the individual race probabilities, using
the model of Imai et al. (2022).

## Usage

```
bisg(
formula,
data = NULL,
p_r = p_r_natl(),
p_rgx = NULL,
p_rs = NULL,
save_rgx = TRUE
)
bisg_me(
formula,
data = NULL,
p_r = p_r_natl(),
p_rgx = NULL,
p_rs = NULL,
iter = 1000,
warmup = 100,
cores = 1L
)
# S3 method for bisg
summary(object, p_r = NULL, ...)
# S3 method for bisg
predict(object, adj = NULL, ...)
```

## Arguments

- formula
A formula specifying the BISG model. Must include the special term

`nm()`

to identify the surname variable. Certain geographic variables can be identified similarly:`zip()`

for ZIP codes, and`state()`

for states. If no other predictor variables are provided, then`bisg()`

will automatically be able to build a table of census data to use in inference. If other predictor variables are included, or if other geographic identifiers are used, then the user must specify the`p_rgx`

argument below. The left-hand side of the formula is ignored. See the examples section below for sample formulas.- data
The data frame containing the variables in

`formula`

.- p_r
The prior distribution of race in the sample, as a numeric vector. Defaults to U.S. demographics as provided by

`p_r_natl()`

. Can also set`p_r="est"`

or`"estimate"`

to estimate this from the geographic distribution. Since the prior distribution on race strongly affects the calibration of the BISG probabilities and thus the accuracy of downstream estimates, users are encouraged to think carefully about an appropriate value for`p_r`

. If no prior information on the racial makeup of the sample is available, and yet the sample is very different from the overall U.S. population, then`p_r="estimate"`

will likely produce superior results.- p_rgx
The distribution of race given location (G) and other covariates (X) specified in

`formula`

. Should be provided as a data frame, with columns matching the predictors in`formula`

, and additional columns for each racial group containing the conditional probability for that racial group given the predictors. For example, if Census tracts are the only predictors,`p_rgx`

should be a data frame with a tract column and columns`white`

,`black`

, etc. containing the racial distribution of each tract. If`formula`

contains only labeled terms (like`zip()`

), then by default`p_rgx`

will be constructed automatically from the most recent Census data. This table will be normalized by row, so it can be provided as population counts as well. Counts are required for`bisg_me()`

. The`census_race_geo_table()`

function can be helpful to prepare tables, as can be the`build_dec()`

and`build_acs()`

functions in the`censable`

package.- p_rs
The distribution of race given last name. As with

`p_rgx`

, should be provided as a data frame, with a column of names and additional columns for each racial group. Users should not have to specify this argument in most cases, as the table will be built from published Census surname tables automatically. Counts are required for`bisg_me()`

.- save_rgx
If

`TRUE`

, save the`p_rgx`

table (matched to each individual) as the`"p_rgx"`

and`"gx"`

attributes of the output. Necessary for some sensitivity analyses.- iter
How many sampling iterations in the Gibbs sampler

- warmup
How many burn-in iterations in the Gibbs sampler

- cores
How many parallel cores to use in computation. Around 4 seems to be optimal, even if more are available.

- object
An object of class

`bisg`

, the result of running`bisg()`

.- ...
Additional arguments to generic methods (ignored).

- adj
A point in the simplex that describes how BISG probabilities will be thresholded to produce point predictions. The probabilities are divided by

`adj`

, then the racial category with the highest probability is predicted. Can be used to trade off types of prediction error. Must be nonnegative but will be normalized to sum to 1. The default is to make no adjustment.

## Value

An object of class `bisg`

, which is just a data frame with some
additional attributes. The data frame has rows matching the input data and
columns for the race probabilities.

## Methods (by generic)

`summary(bisg)`

: Summarize predicted race probabilities. Returns vector of individual entropies.`predict(bisg)`

: Create point predictions of individual race. Returns factor vector of individual race labels. Strongly not recommended for any kind of inferential purpose, as biases may be extreme and in unpredictable directions.

## References

Elliott, M. N., Fremont, A., Morrison, P. A., Pantoja, P., and Lurie, N.
(2008). A new method for estimating race/ethnicity and associated disparities
where administrative records lack self-reported race/ethnicity. *Health
Services Research*, 43(5p1):1722–1736.

Fiscella, K. and Fremont, A. M. (2006). Use of geocoding and surname analysis
to estimate race and ethnicity. *Health Services Research*,
41(4p1):1482–1500.

Imai, K., Olivella, S., & Rosenman, E. T. (2022). Addressing census data
problems in race imputation via fully Bayesian Improved Surname Geocoding and
name supplements. *Science Advances*, 8(49), eadc9824.

## Examples

```
data(pseudo_vf)
bisg(~ nm(last_name), data=pseudo_vf)
#> # A tibble: 5,000 × 6
#> pr_white pr_black pr_hisp pr_asian pr_aian pr_other
#> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
#> 1 0.826 0.0701 0.0305 0.00353 0.0208 0.0491
#> 2 0.362 0.547 0.0298 0.00315 0.00454 0.0533
#> 3 0.918 0.00887 0.0397 0.00697 0.00223 0.0240
#> 4 0.620 0.293 0.0317 0.00379 0.00545 0.0460
#> 5 0.892 0.0237 0.0413 0.00831 0.00295 0.0322
#> 6 0.844 0.0790 0.0309 0.00384 0.00542 0.0370
#> 7 0.491 0.419 0.0297 0.00390 0.00548 0.0512
#> 8 0.982 0.00574 0.0120 0 0 0
#> 9 0.713 0.194 0.0319 0.00422 0.00695 0.0497
#> 10 0.593 0.337 0.0262 0.00278 0.00406 0.0368
#> # ℹ 4,990 more rows
r_probs = bisg(~ nm(last_name) + zip(zip), data=pseudo_vf)
summary(r_probs)
#> BISG individual race probabilities
#>
#> Implied marginal race distribution:
#> pr_white pr_black pr_hisp pr_asian pr_aian pr_other
#> 0.641 0.215 0.074 0.020 0.007 0.043
#>
#> Entropy decrease from marginal distribution:
#> Min. 1st Qu. Median Mean 3rd Qu. Max.
#> -0.5137 0.1193 0.3315 0.3665 0.6386 1.0563
head(predict(r_probs))
#> [1] white black white white white white
#> Levels: white black hisp asian aian other
data(pseudo_vf)
bisg_me(~ nm(last_name) + zip(zip), data=pseudo_vf)
#> # A tibble: 5,000 × 6
#> pr_white pr_black pr_hisp pr_asian pr_aian pr_other
#> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
#> 1 0.969 0.003 0.002 0 0.016 0.01
#> 2 0.196 0.783 0.009 0.003 0 0.009
#> 3 0.982 0 0.006 0.009 0 0.003
#> 4 0.647 0.317 0.0180 0.001 0.003 0.014
#> 5 0.985 0.001 0.005 0 0.002 0.007
#> 6 0.660 0.247 0.0510 0.006 0.008 0.0280
#> 7 0.181 0.758 0.0320 0.003 0.005 0.0210
#> 8 0.985 0.007 0.008 0 0 0
#> 9 0.817 0.166 0.003 0 0.001 0.013
#> 10 0.907 0.0750 0.006 0.003 0.002 0.007
#> # ℹ 4,990 more rows
```