Abstract
In this paper, we attempt to forecast which prison inmates are likely to engage in very serious misconduct while incarcerated. Such misconduct would usually be a major felony if committed outside of prison: drug trafficking, assault, rape, attempted murder and other crimes. The binary response variable is problematic because it is highly unbalanced. Using data from nearly 10,000 inmates held in facilities operated by the California Department of Corrections, we show that several popular classification procedures do no better than the marginal distribution unless the data are weighted in a fashion that compensates for the lack of balance. Then, random forests performs reasonably well, and better than CART or logistic regression. Although less than 3% of the inmates studied over 24 months were reported for very serious misconduct, we are able to correctly forecast such behavior about half the time.
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Notes
For both age variables, the categories represent how CDC records such data. We could not get other age breakdowns.
The upper bound of 50 represents how CDC records sentence length information. We could not distinguish between the several different kinds of sentences all labeled as “50”.
With no false positives, the cost ratio was infinite.
Without the oversampling, one risks getting a number of bootstrap samples with none of the rare cases. The response variable is then a constant.
For our software, there was no way to directly introduce costs into the algorithm. But there were fitted values one could interpret as estimates of the probability of serious misconduct. We set the threshold not at the usual 0.50, but at a value slightly below the observed proportion of cases for which serious misconduct was reported. This value was chosen to approximate the desired 10 to 1 balance of false positives to false negatives (implying that the costs of false negatives to false positives was 10 to 1). This is analogous to one of the methods for handling costs in random forest where the voting threshold would not be set at 50%, but at the marginal percentage for the response category that needed to be given more weight.
The small negative values represent sampling error and are properly interpreted as effectively zero.
The very small negative values again represent sampling error and are properly interpreted as effectively zero.
Had the partial response plot for no misconduct been shown, it would just have been the mirror image. For binary responses, only one of the two possible partial response plots need be shown. This is not true when there are more than two classification categories. Then, there needs to be one partial response plot for each response category.
The partial response plots are not very interesting for the two age variables and for gang activity because the age variables are measured in just a few ordinal categories and gang activity is a binary variable.
This is not caused by overfitting, which is measured by the decline of forecasting skill into a new random sample from the same population. Here the issue is a changing population.
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Acknowledgments
The research reported in this paper would have been impossible without the talents and efforts of our colleagues at the California Department of corrections: George Lehman, Maureen Tristan, Gloria Rea, Penny O’Daniel, Micki Mitchell, Mark Cook, Martha Pyog, and Terrence Newsome. Andy Liaw provided a number of useful suggestions on the random forests analysis. Support for work on this paper was provided by the National Science Foundation: (SES-0437169)“Ensemble Methods for Data Analysis in the Behavioral, Social and Economic Sciences.” The support is gratefully acknowledged.
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Berk, R., Kriegler, B. & Baek, JH. Forecasting Dangerous Inmate Misconduct: An Application of Ensemble Statistical Procedures. J Quant Criminol 22, 131–145 (2006). https://doi.org/10.1007/s10940-006-9005-z
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DOI: https://doi.org/10.1007/s10940-006-9005-z