“Multiple response” analysis of arrest records

Question

Background:

I'm a junior researcher at an institute dealing with regional issues, particularly involving drug policy. Almost two years ago, one of our senior researchers began collecting arrest data about a nearby large city. He had been transcribing newspaper police blotter by hand until I joined a year and change ago and convinced him to switch to automated data collection.

We're now ready to start analyzing this dataset. It contains about 20k arrest records with virtually no missing or invalid values (I'd estimate that there are less than 100 such records, and some of those are just parser errors). These records include full name and home address of the arrested person, arresting officers, exact charges, etc. (we've even found SSNs in the data). At this point, we're just exploring the data, but we expect to find differences in number and severity of charges according to race, arrest location, and home location.

Question

The dataset has two variables that, to my understanding, are categorical multiple-response questions. "Arresting Officer" is two columns, one of which always has a value and one of which may have an a value (for the second officer present at the arrest). "Charges" is five columns, each containing a single charge and in no particular order. To complicate the structure further, a person arrested on more than five charges will be issued multiple records.

We messed around with the above dataset for a few hours so far and have gotten as far as being able to obtain useful counts and percentages in SPSS by using the Multiple Response Set feature and plugging that into Custom Tables. This is a fine start, but we'd like to move on to more detailed analysis at some point. Unfortunately, neither of us are aware of the recommended (or anti-recommended) methods for analyzing a categorical multiple-response question. This also applies to our desire to eventually group specific charges (e.g., "possession of controlled substances < 4 oz.") into broader categories such as 'violent crimes' or 'drug crimes'.

Note that I'm not looking for just a snap answer here, as we don't have a deadline. I would be glad to do readings, so feel free to point me in the direction of tutorials, textbooks, and so on. I'm also not particularly attached to SPSS - it's just what my coworker is used to. If there are clear disadvantages to using it for this type of problem, I don't mind learning something new.

Answer 1

I can't particularly comment on how to handle multiple response categories, but you need to further refine your question for people on this forum to be able to give useful advice.

You mention various interests, such as some sort of drug policy intervention, and differential charges according to race, arrest location, and home location. For the differential charges their is a huge body of criminological literature assessing various aspects of this. Are you interested in discretionary behavior of particular officers (or racially prejudiced treatment)? Are you interested in aspects of disproportionate minority contact with the criminal justice system? There is such a wide variety of potential questions I can not give any advice. Of what nature is the drug policy intervention? Are you interested in criminal histories and the effect of some policy?

The nature of your data is pretty typical. Some recent arrest data I worked with had an average of around 3 charges per arrest (I remember 1 case having 20 charges in a single arrest). You will typically have some charges that tend to come together (and some times functionally redundant charges). Often times drug possession charges are not alone because the offender did something else to attract an officers attention (most often another crime), and upon arrest they were searched and drugs were found. You will undoubtedly have a core of prolific offenders in your data, and for any analysis you will want to know their histories, and likely take them into account for your analysis (do you have unique identifiers for individuals or do you have to match based on names, DOBs, and/or SSN's?) You may also have co-offending behavior that may be of interest.

Most projects I have been involved in (including my own work) have dealt with the multiple charges in two ways. One is only include the "top" charge according to some ranking criteria, the other is to only analyze a particular subset of charges. This is hardly universal advice though, and without knowing the question you are addressing it is probably not advisable to do either of these at the onset. If you clump any charges together (e.g. treat possession of weed the same as possession of cocaine) I would suggest you do it on theoretical grounds as opposed to using some sort of statistical methods (although again depending on the question some type of stat clustering method may be useful).

The more specific questions you have the better this community will be able to give advice. The nature of your data may seem complicated but many people on this forum will have had experience with similar data structures (at least in various aspects).

Answer 2

It is not clear what you questions you are trying to answer but here are are several ways to deal with the multiple-response data:

1. Arresting Officer

   Convert the two columns into a single count variable (1 or 2) which indicates the no of arresting officers. You will lose the arresting officer's identities but perhaps that is not of interest to you per se?

2. Charges

   Again convert to a count variable or perhaps a weighted count with the weights being the severity of the crime. The count variable represents the number of charges against the defendant.

The above strategies to deal with multiple-response variables has drawbacks as you lose information (e.g., identity of officers, details of specific crimes charged etc) but perhaps that is acceptable to you given the research questions you want to pursue.

A better answer can potentially be given but that will require some knowledge of what you are trying to accomplish with the data.

Answer 3

I've examined associations between multiple response catgeogrical variables in the past basically following the log-linear approach for marginal data outlined in the following:

• Strategies for Modeling Two Categorical Variables with Multiple Category Choices (Bilder, Loughlin, 2003)

Your case may be more complicated since you're looking at more than just Officer by Charges. But the Bilder paper and references within may be a good start for exploring your modeling choices. The nice thing is that I was able to fit this in R without much trouble.

The problem you're likely to run into is ending up with a sparse contingency table which can lead to convergence problems when fitting your log-linear model. In this respect, I think Andy's and Srikant's advice will serve you well -- you'll have to make some assumptions or simplifications suitable for your domain. Figure out what question you're interested in and see if you can reduce the dimensions in some way.