Mugshots - Regression Tables

Regression Table No.1

• First column, just our p-hat face and constant term
• Second column, add gender, age, race

Table No.1 - ResNet 50

	Dependent variable:
	Release Outcome
	(1)	(2)
ML Face	0.693***	0.653***
	(0.626, 0.761)	(0.578, 0.729)
sexM		-0.031**
		(-0.052, -0.011)
age		0.001
		(-0.0003, 0.002)
raceB		-0.038
		(-0.123, 0.046)
Constant	0.245***	0.319***
	(0.194, 0.296)	(0.205, 0.433)
Observations	8,370	8,370
Adjusted R2	0.033	0.034
F Statistic	285.091*** (df = 1; 8368)	42.707*** (df = 7; 8362)
Note:	p<0.1; p<0.05; p<0.01

Regression Table No.2

• Collapsing age s.t. we get a long-table format

Table No.2 - ResNet 50

	Dependent variable:
	Release Outcome
	Age - Linear	Age - Non Parametric
	(1)	(2)
ML Face	0.653***	0.664***
	(0.578, 0.729)	(0.589, 0.740)
sexM	-0.031**	-0.028**
	(-0.052, -0.011)	(-0.049, -0.008)
raceB	-0.038	-0.036
	(-0.123, 0.046)	(-0.121, 0.049)
Constant	0.319***	0.133
	(0.205, 0.433)	(-0.135, 0.402)
Observations	8,370	8,370
Adjusted R2	0.034	0.035
F Statistic	42.707*** (df = 7; 8362)	17.676*** (df = 18; 8351)
Note:	p<0.1; p<0.05; p<0.01

Regression Table No.3

• Renaming the skin-tone row

Table No.3 - ResNet 50

	Dependent variable:
	Release Outcome
	(1)	(2)	(3)
ML Face	0.653***	0.648***	0.648***
	(0.578, 0.729)	(0.572, 0.724)	(0.572, 0.723)
sexM	-0.031**	-0.029**	-0.029**
	(-0.052, -0.011)	(-0.050, -0.008)	(-0.050, -0.009)
raceB	-0.038	-0.022	-0.021
	(-0.123, 0.046)	(-0.109, 0.064)	(-0.107, 0.066)
age	0.001	0.001	0.001
	(-0.0003, 0.002)	(-0.0002, 0.002)	(-0.0002, 0.002)
† skin-tone		0.020
		(-0.022, 0.061)
‡ skin-tone-cont			0.038*
			(0.004, 0.071)
Constant	0.319***	0.286***	0.290***
	(0.205, 0.433)	(0.167, 0.405)	(0.173, 0.407)
Observations	8,370	8,370	8,370
Adjusted R2	0.034	0.034	0.034
F Statistic	42.707*** (df = 7; 8362)	13.171*** (df = 24; 8345)	37.812*** (df = 8; 8361)
Note:	p<0.1; p<0.05; p<0.01
	† We collapse 18 skin-tone factors ‡ We encode skin-tone as a continuous variable increasing in brightness

Regresion Table No. 4

• First column, p-hat face, constant, gender, age (linear term), race, skin tone
• Second column, add current charge and risk

Table No.4 - ResNet 50

	Dependent variable:
	Release Outcome
	(1)	(2)
ML Face	0.648***	0.479***
	(0.572, 0.723)	(0.407, 0.552)
sexM	-0.029**	-0.002
	(-0.050, -0.009)	(-0.022, 0.017)
raceB	-0.021	0.043
	(-0.107, 0.066)	(-0.039, 0.125)
age	0.001	-0.001
	(-0.0002, 0.002)	(-0.002, 0.0003)
† skin-tone-cont	0.038*	0.043**
	(0.004, 0.071)	(0.012, 0.075)
Current Charge (p-hat)		1.073***
		(1.006, 1.141)
Recidivism Risk (p-hat)		-0.766***
		(-0.871, -0.660)
Constant	0.290***	-0.220***
	(0.173, 0.407)	(-0.347, -0.094)
Observations	8,370	8,370
Adjusted R2	0.034	0.130
F Statistic	37.812*** (df = 8; 8361)	125.574*** (df = 10; 8359)
Note:	p<0.1; p<0.05; p<0.01
	† We encode skin-tone as a continuous variable increasing in brightness

Regression Table No. 5

• First column, M-turk features and constant,
• Second column, add gender, age (linear), race, skin tone, current charge, risk [NO P-HAT CNN]

Table No.5 - ResNet 50

	Dependent variable:
	Release Outcome
	(1)	(2)
attractiveness	-0.013	-0.014
	(-0.047, 0.020)	(-0.046, 0.018)
competence	0.013	0.010
	(-0.021, 0.047)	(-0.022, 0.042)
dominance	-0.022	-0.002
	(-0.050, 0.005)	(-0.029, 0.024)
trustworthiness	0.051**	0.035*
	(0.018, 0.085)	(0.003, 0.067)
sexM		-0.054***
		(-0.072, -0.036)
raceB		0.041
		(-0.042, 0.123)
age		-0.001**
		(-0.002, -0.0003)
† skin-tone-cont		0.056***
		(0.024, 0.088)
Current Charge (p-hat)		1.114***
		(1.046, 1.182)
Recidivism Risk (p-hat)		-0.817***
		(-0.923, -0.711)
Constant	0.748***	0.168**
	(0.729, 0.766)	(0.055, 0.281)
Observations	8,370	8,370
Adjusted R2	0.001	0.117
F Statistic	2.767** (df = 4; 8365)	86.705*** (df = 13; 8356)
Note:	p<0.1; p<0.05; p<0.01
	† We encode skin-tone as a continuous variable increasing in brightness.

Regression Table No. 6

• First column, constant, gender, age (linear), race, skin tone ,current charge, risk
• Second column, add M-turk to first column
• Third column, add p-hat CNN to first column
• Fourth column, add both M-turk and p-hat CNN to first column

Table No.6 - ResNet 50

	Dependent variable:
	Release Outcome
	(1)	(2)	(3)	(4)
sexM	-0.055***	-0.054***	-0.002	-0.003
	(-0.073, -0.037)	(-0.072, -0.036)	(-0.022, 0.017)	(-0.022, 0.017)
raceB	0.041	0.041	0.043	0.043
	(-0.042, 0.123)	(-0.042, 0.123)	(-0.039, 0.125)	(-0.039, 0.125)
age	-0.001**	-0.001**	-0.001	-0.001
	(-0.002, -0.0003)	(-0.002, -0.0003)	(-0.002, 0.0003)	(-0.002, 0.0003)
† skin-tone-cont	0.057***	0.056***	0.043**	0.043**
	(0.025, 0.089)	(0.024, 0.088)	(0.012, 0.075)	(0.011, 0.075)
Current Charge (p-hat)	1.114***	1.114***	1.073***	1.073***
	(1.046, 1.182)	(1.046, 1.182)	(1.006, 1.141)	(1.005, 1.141)
Recidivism Risk (p-hat)	-0.821***	-0.817***	-0.766***	-0.763***
	(-0.927, -0.715)	(-0.923, -0.711)	(-0.871, -0.660)	(-0.869, -0.657)
attractiveness		-0.014		-0.016
		(-0.046, 0.018)		(-0.048, 0.016)
competence		0.010		0.005
		(-0.022, 0.042)		(-0.026, 0.037)
dominance		-0.002		0.002
		(-0.029, 0.024)		(-0.024, 0.028)
trustworthiness		0.035*		0.032*
		(0.003, 0.067)		(0.0003, 0.063)
ML Face			0.479***	0.477***
			(0.407, 0.552)	(0.404, 0.549)
Constant	0.184***	0.168**	-0.220***	-0.230***
	(0.073, 0.295)	(0.055, 0.281)	(-0.347, -0.094)	(-0.357, -0.103)
Observations	8,370	8,370	8,370	8,370
Adjusted R2	0.117	0.117	0.130	0.130
F Statistic	124.625*** (df = 9; 8360)	86.705*** (df = 13; 8356)	125.574*** (df = 10; 8359)	89.973*** (df = 14; 8355)
Note:	p<0.1; p<0.05; p<0.01
	† We encode skin-tone as a continuous variable increasing in brightness