Death Penalty Sentencing Data

Data on 674 homicide cases examining the relationship between death penalty sentencing, defendant race, and victim race. This dataset is a classic example in categorical data analysis used to illustrate logistic regression goodness-of-fit testing, the effects of confounding variables, and Simpson's paradox in the context of criminal justice. The data show that the victim's race is a stronger predictor of death penalty sentencing than the defendant's race.

Usage

penalty

Format

A tibble with 674 rows and 3 columns:

def_bl

Defendant race indicator. Type: numeric. Binary (0/1) where 1 = Black defendant, 0 = White defendant.

vic_bl

Victim race indicator. Type: numeric. Binary (0/1) where 1 = Black victim, 0 = White victim.

death_pe

Death penalty sentencing outcome. Type: numeric. Binary (0/1) where 1 = death penalty imposed, 0 = no death penalty.

Source

Agresti, A. (2002). Categorical Data Analysis (2nd ed.). Wiley. Based on data from Radelet, M. L. (1981). Racial characteristics and the imposition of the death penalty. American Sociological Review, 46(6), 918-927. Original data file: penalty.dta

Details

This dataset is used in Chapter 11 (Multiple Logistic Regression: Model Fit and Diagnostics) to illustrate goodness-of-fit tests for logistic regression models, including the Pearson chi-squared test and the likelihood ratio test (deviance). The main-effects model with defendant and victim race is tested against the saturated model. Key analyses include: logistic regression with two binary predictors, Pearson and deviance goodness-of-fit statistics, cross-tabulation of observed versus expected frequencies, and assessment of whether the main-effects model is adequate (it fits well, with Pearson X-squared = 0.20, p = 0.66).

Examples

data(penalty)
head(penalty)
#> # A tibble: 6 × 3
#>   def_bl vic_bl death_pe
#>    <int>  <int>    <int>
#> 1      0      0        0
#> 2      0      1        0
#> 3      0      0        0
#> 4      0      0        0
#> 5      0      0        0
#> 6      0      0        0
# Logistic regression: death penalty ~ defendant race + victim race
glm(death_pe ~ def_bl + vic_bl, family = binomial, data = penalty)
#> 
#> Call:  glm(formula = death_pe ~ def_bl + vic_bl, family = binomial, 
#>     data = penalty)
#> 
#> Coefficients:
#> (Intercept)       def_bl       vic_bl  
#>     -2.0595       0.8678      -2.4044  
#> 
#> Degrees of Freedom: 673 Total (i.e. Null);  671 Residual
#> Null Deviance:	    440.8 
#> Residual Deviance: 419 	AIC: 425