After I completed my master’s thesis, I was very curious about why we didn’t seem to be able to measure change after the second assessment. According to theory, prediction should improve if offenders changed. The prediction was not improving. Was no change occurring? The data did not seem to support that. Offender risk scores were changing. However, the changes in risk score weren’t leading to improvements in prediction accuracy. Why?
I finished my master’s thesis in May of 2007 and tried to find some answers to this conundrum. Later in 2007, I met Ross Macmillan, a professor at the University of Minnesota. I told Dr. Macmillan about the problems I was having with the risk score data and he agreed to tutor me for a semester. He set up a doctoral research class where we met twice a week for one on one instruction. I also started taking classes in Life Course Sociology at the University of Minnesota.
This was an amazing learning opportunity. I learned many different statistical skills, and I might have invented a few that people had never heard of before. This was where I started doing “data pattern analysis,” which is a technique I developed for comparing data between cohorts. I wrote the following paper describing my work over the year in 2008.
The Nonlinear Dynamics of Criminal Behavior
Upon examining the offender risk score data, it became clear that risk scores were changing. The plot shown below provides a sample of plots from the 12 offenders who had 8 risk assessments. With the exception of some plots that were completely constant with zero change, the plots were all different. No two plots were the same. There was no discernable pattern that I could uncover.
I found myself thinking about change again. First, I had noticed a zig-zap pattern in my attempts to improve. Then, I had noticed a zig-zag pattern in the inmates path to recovery. Now, I was seeing zig-zag patterns in offender risk scores. This seemed like some sort of repeating pattern.
One of the most startling findings from this work was that the changes in offender risk scores at the group level seem to be constantly occurring at exactly the same rate every six months. The change frequencies for assessment pairs done at six month intervals are plotted below. I grouped offenders into 3 point change buckets (-2 to -4, -1 to 1, 2 to 4 point changes, etc.) for each assessment pair. The plot LSI-R 2-3 indicates the changes in scores from LSI-R #2 to LSI-R #3. Similarly, LSI 3-4 and LSI-R 4-5 indicated the change scores from the third to fourth and fourth to fifth assessments respectively.
Notice that the frequencies of the changes in scores between assessments are almost identical. Each 6 months, about the same number of offenders have changes in score in the -4 to -2 range, the -1 to 1 range, and the 2 to 4 range, etc. The changes in the risk scores of the individual offenders in each group were different each time, but the group change was constant! How could this be?
