Aoristic analysis
What is aoristic analysis?
Aoristic analysis addresses a temporal problem common with some types of recorded crime. In many cases, police know exactly when a crime occurred. Generally, the victim knows when they were robbed at gunpoint or when they were assaulted. Sometimes, however, this information is not known. For example, if a crime victim leaves their house at 8am and returns at 4pm to find their home broken into, the specific time of the crime is not known. It could have occurred any time in the eight hours between 8am and 4pm.
When victims of crime are unable to say when the event occurred, many police departments record a crime event as having a ‘start’ date and time, and an ‘end’ date and time. These dates/times can also be referred to as the ‘from’ and ‘to’ date and time. The start date-time usually references when the person left their house (or parked their car), and the end date-time records when they first discovered their property missing. The period between the start date-time and end date-time is referred to as the event’s time span. Incidents that have an undetermined event time are described as ‘aoristic’, defined by Merriam Webster as “denoting simple occurrence of an action without reference to its completeness, duration, or repetition”.
Rather than making an arbitrary choice of one particular time point along the time span, aoristic analysis evenly distributes the probability of a crime event across each hour of the time span. So for our example, the probability of the crime event would be distributed as 0.125 for each hour between 8am and 4pm. This crime event (labelled A) is the first of six in the picture here:
All figures are sourced from forthcoming book from Groff and Haberman. Please cite accordingly.
For each of the six crime events in this figure (A to F), you can see they have varying start and end times, and correspondingly longer or shorter time spans. Choosing to work with just the start time would skew the interpretation of 'when' the crimes occurred to the start of the day, as shown by the first column graph (a) below.
Alternatively, to use just the end time would skew the interpretation the other way (graph b). Using the mid-point, as shown in the third graph would favor one arbitrary time point, with no clear justification why (graph c). The only proportional probability distribution is the aoristic approach, which distributes the relative probability of the time event across each hour (graph d).
When I first proposed aoristic analysis (with Michael McCullagh) rounding up and down to the nearest hour made the approach analytically easier; however nowadays even with relatively large data sets it is possible to round to the nearest minute and then aggregate to hours for the purposes of display. That is what is happening in the last graph of the figure above (graph d).
Aoristic analysis package in R
To help with your analysis, I have created an 'aoristic' package in R.
For details of how to use the R package available for free from CRAN, please go to this dedicated page.
Aoristic analysis in other platforms
Andrew Wheeler has created a useful Excel spreadsheet that will do aoristic analysis and break the output across days of the week and hour of the day. It requires a little data manipulation to get your data into the required format. It does have some basic error checking and produces good graphs, if a little fiddly. Recommended. You can access Andrew's spreadsheet and accompanying blog entry here.
Andrew also has code to undertake aoristic analysis in SPSS. This code has not been tested by me, but if you want to take a look it is available here.
Relevant references
Ratcliffe, JH & McCullagh, MJ (1998) Aoristic crime analysis, International Journal of Geographical Information Science, 12 (7): 751-764.
- The original journal article that introduced aoristic analysis. It is available on my publications page if you scroll all the way down to number 2.
Ratcliffe, JH (2000) Aoristic analysis: the spatial interpretation of unspecific temporal events, International Journal of Geographical Information Science, 14 (7): 669-679.
- Greater articulation of the process as well as different ways to visualize the output from an aoristic analysis are shown in this article. It is available on my publications page as number 7.
Ratcliffe, JH (2002) Aoristic signatures and the temporal analysis of high volume crime patterns, Journal of Quantitative Criminology. 18 (1): 23-43.
- Correlation coefficients in this article demonstrate the necessity to use an aoristic approach for burglary (break and enter), vehicle crime, and stealing. This article also demonstrates how to generate 'aoristic signatures' for crime hot spots. It is available on my publications page as number 12.
Ashby, M. P. J., & Bowers, K. J. (2013). A comparison of methods for temporal analysis of aoristic crime. Crime Science, 2(1), 1-16.
- An excellent paper from Matt Ashby and Kate Bowers that statistically concludes start and end times should be avoided, and while a random point in the time line is as viable as the aoristic approach, it is more computationally challenging. They conclude that aoristic is appropriate in most circumstances, especially where software is available. It is available to download here.
Ratcliffe, JH (in press) Aoristic Crime Analysis.
- A chapter on aoristic crime analysis in the excellent book by Elizabeth Groff and Cory Haberman. The figures above comes from this chapter. Full citation is:
Ratcliffe, JH (in press) “Aoristic Analysis”. In; Groff, ER and Haberman, CP (Eds.) The Study of Crime and Place: A Methods Handbook. Temple University Press: Philadelphia, PA.