Regression to predict CODIS database proportions
Hannah Van Wyk
2024-09-05 15:13:33
Last updated: 2024-09-05
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To estimate the number of people in CODIS by state and race, we need information on (1) the number of people in CODIS in each state, and (2) the racial composition of this number. We have several data sources, each of which provide different information for different states:
- Direct data on the number of Black and White people in CODIS, from a Freedom of Information Act (FOIA) request conducted by Muprhy and Tong (2020) for the following states: California, Florida, Indiana, Maine, Nevada, South Dakota, and Texas. [1]
- The number of people of each racial group in prison in each state. This data was pulled from a variety of sources and is available in Klein et al. (2023). [2]
- The number of people in the State DNA Indexing System (SDIS) and the National DNA Indexing System (NDIS). NDIS data is publicly available for all 50 states [3], whereas SDIS data is only available on a state-by-state basis and is obtained from internet searches. Within each DNA indexing system, both the number of offenders and the number of arrestees are recorded.
To leverage this data to make estimates on the number of people in CODIS by state, we separate states into three categories:
1. States who have data available in the Murphy & Tong dataset. For these states, no calculations are needed to estimate the number of people in CODIS.
2. States who have NDIS and SDIS data available but are not in the Murphy & Tong dataset.
3. States with only NDIS data available.
The plot below shows the data that is available for each state:
For states in categories (2) and (3), we need to generate an estimation of the racial composition of the SDIS profiles. To generate this estimation, we use the Murphy & Tong FOIA data to create a regression model of proportion of Black and White people in the data set with the following independent variables: the U.S. census proportion of each state for each rate, the percent of the state’s prison population that is each race, an indicator variable for Black/White race, and interaction variables for census proportion by race and prison racial population by race. We use the coefficients from the regression model to make predictions for the remaining states that do not have data available on the racial composition of the DNA databases.
\[Proportion_{race} = \beta_0 + \beta_1census_{proportion} + \beta_2prison_{proportion} + \beta_3race + \beta_4race*census_{proportion} + \beta_5race*prison_{proportion}\]
For states in category (3) we need both an estimation of the number of people in SDIS, and an estimation of the number of the racial composition of the datasets. To estimate the racial composition of the database, we use the regression model described above. To generate predictions of the number of people in SDIS for these states, we create an additional regression model with dependent variable the number of people in SDIS and independent variables for the U.S. census proportion of the population that is each race, the proportion of the state’s prison population that is each race, and the number of people in NDIS for that state. We create separate regression models for arrests and offenders to obtain more accurate predictions:
\[N_{arrestee} = \beta_0 + \beta_1census_{black} + \beta_2census_{white} + \beta_3prison_{black} + \beta_4prison_{white} + \beta_5NDIS_{arrestees} \] and
\[N_{offender} = \beta_0 + \beta_1census_{black} + \beta_2census_{white} + \beta_3prison_{black} + \beta_4prison_{white} + \beta_5NDIS_{offenders} \]
Part 1: regression to estimate the racial composition of each database.
The following plot shows the coefficient estimates for the regression model that estimates the racial composition of the CODIS dataset using the Murphy & Tong states.
| Version | Author | Date |
|---|---|---|
| 0cc6e3a | hcvw | 2024-08-14 |
While none of the coefficients were significant in the regression, our model had an \(R^2\) value of 0.93, demonstrating a good fit. The following plot showing the estimated racial composition using the regression model vs. the true values for the states with available data. We also plot a difference plot (also known as a Bland-Altman plot).
| Version | Author | Date |
|---|---|---|
| 1eb6d2c | hcvw | 2024-06-25 |
| Version | Author | Date |
|---|---|---|
| 1eb6d2c | hcvw | 2024-06-25 |
Part 2: SDIS regression
The following plots show the results of the SDIS regression for both arrestees (left) and offenders (right):
| Version | Author | Date |
|---|---|---|
| 0cc6e3a | hcvw | 2024-08-14 |
Part 3: final data
Using the above regression models, we make predictions of the number of Black and White people in CODIS by state. The plot below shows our estimates for each state, colored by the data source used for each state. The number of Black people in the database are indicated with circles and the number of White people is indicated by triangles.
| Version | Author | Date |
|---|---|---|
| 0cc6e3a | hcvw | 2024-08-14 |
We additionally generate a plot showing the difference in the percent of people in CODIS that are Black versus the U.S. census percent of the population that is Black in each state. 
The table containing the estimates for the number of people of each race in CODIS by state, along with the source of the data is below:
State Black Profiles White Profiles Source
1 Alabama 181118.5149 217600.769 SDIS+regression
2 Alaska 5596.7385 39630.160 Regression only
3 Arizona 58937.7928 257171.363 Regression only
4 Arkansas 4031.2855 8680.932 SDIS+regression
5 California 473373.9990 819407.624 Murphy
6 Colorado 57866.4208 262106.908 SDIS+regression
7 Delaware 4936.0840 5883.454 Regression only
8 Florida 475434.7840 829309.538 Murphy
9 Georgia 206442.0982 181496.282 SDIS+regression
10 Hawaii 1242.7095 11370.778 Regression only
11 Idaho 963.4824 34101.874 SDIS+regression
12 Illinois 253303.7558 305785.832 SDIS+regression
13 Indiana 80005.6400 215399.800 Murphy
14 Iowa 21894.1213 120329.347 Regression only
15 Kansas 44290.8194 211390.025 Regression only
16 Kentucky 41636.3797 216467.194 Regression only
17 Louisiana 432013.8926 338844.041 SDIS+regression
18 Maine 1281.0330 30482.016 Murphy
19 Maryland 78186.4500 46816.131 Regression only
20 Massachusetts 33450.8754 94768.533 Regression only
21 Michigan 230924.1616 377879.691 Regression only
22 Minnesota 37914.2174 115906.979 SDIS+regression
23 Mississippi 77616.9619 62226.769 SDIS+regression
24 Missouri 103504.8306 309407.963 SDIS+regression
25 Montana 641.1110 28312.414 SDIS+regression
26 Nebraska 8812.8921 34470.431 Regression only
27 Nevada 42937.8560 116401.844 Murphy
28 New Hampshire 688.2462 14974.579 Regression only
29 New Jersey 12389.6261 11436.627 SDIS+regression
30 New Mexico 8751.9992 138557.311 Regression only
31 New York 249297.7042 253243.373 Regression only
32 North Carolina 151156.0304 193565.650 SDIS+regression
33 North Dakota 3538.4080 28698.008 Regression only
34 Ohio 314004.1958 655065.396 Regression only
35 Oklahoma 45010.2059 150326.416 Regression only
36 Oregon 13670.4923 202025.158 Regression only
37 Pennsylvania 157187.6331 289547.031 Regression only
38 Rhode Island 5961.4416 8911.275 SDIS+regression
39 South Carolina 91029.7856 91493.358 SDIS+regression
40 South Dakota 4056.0000 45156.800 Murphy
41 Tennessee 156566.7349 321730.195 Regression only
42 Texas 279646.6350 358447.405 Murphy
43 Utah 6684.4747 107006.651 Regression only
44 Vermont 680.5597 12917.961 Regression only
45 Virginia 218711.3900 275687.781 SDIS+regression
46 Washington 31472.5629 235805.829 SDIS+regression
47 West Virginia 4234.0180 47855.252 SDIS+regression
48 Wisconsin 96085.5115 280247.231 Regression only
49 Wyoming 668.1218 18897.896 Regression onlyFinally, we generate side-by-side pie charts for each state showing the racial composition according to the census (left) versus the estimated racial composition of CODIS (right) for each state. Note that groups not identifying as Black or White are omitted for easy comparison.
References
[1] Murphy, Erin, and Jun H. Tong. “The racial composition of forensic DNA databases.” Calif. L. Rev. 108 (2020): 1847.
[2] Klein, Brennan, et al. “COVID-19 amplified racial disparities in the US criminal legal system.” Nature 617.7960 (2023): 344-350.
[3] https://le.fbi.gov/science-and-lab/biometrics-and-fingerprints/codis/codis-ndis-statistics
sessionInfo()R version 4.4.1 (2024-06-14)
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