The effects of base rate and cutoff point choice on commonly used measures of association and accuracy in recidivism research

Several measures of association and accuracy commonly used in the recidivism literature are examined for their sensitivity to variations in the proportion observed to recidivate (the base rate) and in the proportion selected for classification as recidivists (selection ratio). Logistic regression models are employed on a sample of 11,749 convicted offenders to generate predicted probabilities of four recidivism criteria varying in base rates from 0.06 to 0.48. Cutoff point selections from 0.1 to 0.9 show the effects of cutoff point changes on the following commonly used measures of association and accuracy: RIOC (relative improvement over chance), MCR (mean cost rating), Φ, γ, PRE (proportion reduction in error), and percentage correct. While all these statistics vary across base rate and cutoff points, some vary more than others: RIOC varies across cutoff points more than MCR, MCR more than Φ, and Φ more than γ. Researchers comparing such statistics across studies need be wary of the dangers of ignoring such variation.