**Please see screenshot of prompt for equations.**
In March 2024 the Massachusetts Department of Correction (MDOC) issued a press release https://www.mass.gov/news/massachusetts-department-of-correction-recidivism-study-demonstrates-programming-impact-on-lasting-rehabilitation announcing the results of a study “Demonstrat[ing] Programming Impact on Lasting Rehabilitation.” The studyLinks to an external site., linked in the press release, “illustrate[s] the positive impact of substance abuse and educational programming on recidivism.” Recidivism, as defined in the studyLinks to an external site., is a binary outcome indicating whether an individual released from a correctional facility is convicted for an offense occurring within one year.
While there are sound reasons to believe that substance abuse treatment and educational opportunities improve incarcerated individuals’ life trajectories after they are released, a review of the study reveals that the statistical methods used were fairly primitive. The “impact” of the educational and substance use programming was inferred by comparing the recidivism of those who completed the programming with a group of individuals who were assigned to the same programming but did not complete it. The statistics in the study consist of two-sample proportion tests only, there are no analyses attempting to assess whether the differences in recidivism between completers and non-completers might be explained, at least in part, by other factors. Any factor that might help explain why some incarcerated individuals recidivate and others do not is thus a potential omitted variable.
To put a finer point on that, you can think of this analysis as presenting the results of regression models of the form
where is a binary indicator for recidivism, is a binary indicator for whether an incarcerated individual completed substance abuse programming, and is a binary indicator for whether an incarcerated individual completed educational programming, in a sample where all individuals were assigned to complete both. The study also examines samples of incarcerated individuals assigned to only the first program, or only the second.
For this memo, suppose that Dr. Rhiana Kohl, MDOC Executive Director of Strategic Planning and Research, has asked for your advice about how to expand this analysis. In 1-2 pages, address the following topics:
Do you have reason to worry about omitted variable bias? (HINT: there is a LOT of relevant evidence for this question in the Appendix tables to the studyLinks to an external site.)
What statistical technique(s) would you recommend to MDOC to more thoroughly study whether the two programs do indeed reduce recidivism? Be very specific, listing all the control variables you think appropriate and recommending a specific model or models (i.e., linear probability model, logit, probit).
