Derivative measures: How to create new indicators
Chapter 4: Mapping Crime and Geographic Information Systems

Derivative measures are new variables created by manipulating information in one or more databases. The rate calculations discussed in the section "Using GIS to measure from maps" are a simple form of derivative measures that divide a crime count by a population measurement to produce a population-based rate. Generally, if you can express a sought-after relationship using ordinary mathematical logic, then it can be calculated in a GIS. There you will typically find an array of operators (+, -, =, *, "like," "contains," "and," "or," "not," and so forth), aggregates (average, count, minimum, maximum, sum, and so forth), and functions (area, centroid, distance, perimeter, day, year, and so forth). These provide substantial versatility in general analysis or in creating derived measures.

Getting a bit more fancy

The complexity of potential derivative measures is unlimited. For example, you might want to create a quality-of-life measure for community areas that goes beyond mapping income or real estate values. This index could include such variables as crime rate, education levels, dropout rate, drug addiction measures, and incivility reports. Provided the underlying data can be geocoded, or joined to a geocoded table, they can be mapped. Then most, if not all, mathematical manipulations can be done in the GIS.

Apples and oranges

How do you combine variables measured in different units, such as dollars, years, or population? The quickest approach is to combine data in the GIS using overlays and then to use "logical operators" such as "greater than" or "less than" to reselect groups using your criteria. A more indepth process, but one that leads to greater familiarity with the data, involves converting the data values into ranks (ordinal scale measurement) before making any calculations. Although you will lose the ratio level measurement this way, you gain the overwhelming advantage of being able to work with any units of measurement. Another advantage of this process is that conversion to ranks smooths the effects of poorly measured data by intentionally making them less precise. The conversion eliminates some of the "phony" precision of data that are inherently subject to error.

A problem that can generally be overcome is that GIS software is typically weak in statistical (as compared with purely mathematical) tools and may not be able to convert data to an ordinal scale.2 This could be done by using a statistical software package such as S+, SAS, or SPSS. Or if the number of measures and areas is not too large, the work could be done manually. Then ranks are summed to generate the index, after taking care to organize ranks so the lower numbers always represent either the best or the worst, but not a mix of both. The resulting numbers will indicate a cumulative rank, or relative status, that can be mapped (figure 4.14). Crime data can then be overlaid on the index map to show a possible relationship with, for example, social dysfunction. For additional explanation, see Harries and Powell (1994).

Figure 4.14

Chapter 4: Mapping Crime and Geographic Information Systems
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Mapping Crime: Principle and Practice, by Keith Harries, Ph.D., December 1999