Arrest - Table No. 01

\(\color{red}{\text{Table 01 - Version 1 and 2}}\)

NOTE For these tables the variable name definitions are the same as in the baseline regressions. I.e. in version 2 the demographics variable includes the same variables as in our baseline.

NOTE The only difference is in version 1 of table 01. The charge_features model contains only the charge features defined in our baseline. The charge_features_demographics model is the same combined model as in our baseline, with the addition of skin_tone as a demographic feature. This is just from the given structure of table 1 as there is no other place for the skin-tone information to go. Essentially this table pulls apart the combined demographics and arrest feature model (which is p_hat_covariates in our baseline).

Thus to summarize the above, in table 1 version 1:

1. charge_features contains:

• felony flag
• drug crime flag
• violent vs. non-violent crime flag
• property crime flag
• arrest year

2. change_features_demographics contains:

• All the above
• age (from MTurk)
• skin-tone (from MTurk)

Table 01 - Version 1

This version of the table is what was initially discussed as a benchmark for the project. This is split into (1) Singe-Variable Models and (2) Combined variables models:

1. Single Variable Model:

• Demographics on release outcome
• Arrest charge features on release outcome
• XgBoost Predicted risk on release outcome
• MTurk labels on release outcome
• p_hat_cnn on release outcome

2. Multiple Variable Model:

• Demographics + Charge Features in a combined model
• Demographics + Charge Features in a combined model + predicted risk
• Demographics + Charge Features + Risk + MTurk features
• Demographics + Charge Features + Risk + p_hat_cnn
• Demographics + Charge Features + Risk + p_hat_cnn + MTurk features

Table 01 - Arrest Regressions
Fit measured in adjusted R squared
Model Configuration	Adjusted R Squared
Single Variable Models
Demographics	0.0101
Charge Features	0.0906
Predicted Risk	0.0332
MTurk Labels	−0.0001
P-hat-CNN	0.0325
Combined Variable Models
Demographics and Charge Features	0.0973
Demographics and Charge Features and Predicted Risk	0.1123
Demographics and Charge Features and Predicted Risk and MTurk Featutures	0.1120
Demographics and Charge Features and Predicted Risk and P-hat-CNN	0.1216
Combined Model	0.1215

Table 01 - Version 2

This is the second version of Table 01. Here we run individual regressions and add p_hat_cnn separately. Note that the columns are (1) just a regression of the variable/s on the LHS on release and then (2-4) the same regressions with the addition on risk (predicted re-arrest), charge (charge feature model) and both combined.

Table 01 - Arrest Regressions - Configuration 2
Fit measured in adjusted R squared
Model Configurations	no added variables	adj-R2 with additional features
		risk	charge	risk + charge
p_hat_cnn	0.032454	0.056586	0.111614	0.125105
lower 95% C.I.	0.027027	0.048467	0.101016	0.113500
upper 95% C.I.	0.039009	0.065807	0.123645	0.137974
demographics	0.010105	0.038065	0.095901	0.111679
	0.007102	0.031559	0.085423	0.100809
	0.013802	0.045969	0.106881	0.123389
+p_hat_cnn	0.032969	0.056526	0.111661	0.125002
	0.027791	0.049057	0.101493	0.113577
	0.039980	0.065530	0.124350	0.137142
demographics+skin_tone	0.010008	0.038157	0.095914	0.112096
	0.010466	0.035639	0.088978	0.105110
	0.017974	0.049941	0.110837	0.127645
+p_hat_cnn	0.032668	0.056586	0.111642	0.125454
	0.030422	0.053075	0.104960	0.118627
	0.043870	0.070329	0.127465	0.141879
demographics+skin_tone+MTurk	0.009684	0.037883	0.095830	0.111870
	0.011210	0.035845	0.090059	0.105230
	0.018649	0.051033	0.111613	0.129229
+p_hat_cnn	0.032255	0.056323	0.111394	0.125157
	0.030917	0.053030	0.104523	0.118537
	0.044086	0.070171	0.127736	0.142515