6.17 LR in R: Predicting Recidvism (1)

• Logistic regression (LR) models the probability that $Y$ belongs to a particular category (0 or 1)
  • Rather than modeling response $Y$ directly
• COMPAS data: Model probability to recidivate (reoffend)
  • Outcome $y$: Recidivism is_recid (0,1,0,0,1,1,...)
  • Predictors $x's$: age = age, prior offenses = priors_count
  • Predicted values $\hat{y}$: Pr(is_recid=Yes|age)
    • Values of Pr(is_recid=Yes|age) (abbr. p(age)) will range between 0 and 1
    • For given value of age (and other covariates in the model), a prediction can be made for outcome is_recid
• We can convert our predicted value (= a probability) to a 0/1 variable
  • e.g., individuals will recidivate (is_recid = Yes) if Pr(is_recid=Yes|age) > 0.5 (p(age) > 0.5)
  • More conservative: Use lower threshold, e.g., individuals will recidivate (is_recid = Yes) if Pr(is_recid=Yes|age) > 0.1
• Source: James et al. (2013 Chap. 4.3)

References

James, Gareth, Daniela Witten, Trevor Hastie, and Robert Tibshirani. 2013. An Introduction to Statistical Learning: With Applications in R. Springer Texts in Statistics. Springer.