Interesting contribution to the Crimemap listserv below related to hot spot
analysis.
-jtj

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J. T. Johnson
Institute for Analytic Journalism
505.577.6482(c) 415.775.2530(h)
http://www.jtjohnson.com tom@...

"He who refuses to do arithmetic is doomed to talk nonsense."
-John McCarthy, Stanford University mathematician
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-----Original Message-----
From: Lauren Scott [mailto:lscott@...]
Sent: Thursday, November 04, 2004 10:04 PM
To: J T Johnson @ncjrs.org
Subject: RE: [crimemap] Minimum number of incidents required for hotspot
a nalysis


Hi all,
Am I too late to add my 2 cents?

Specifically, I'd like to address two points raised in the discussion:
1) relative vs. absolute crime counts
2) how to lie with density maps

As was mentioned, we cannot define a hot spot by a fixed number of crimes...
or even by a fixed crime density. Five crimes in a downtown Los Angeles
neighborhood might be very low, while 5 crimes in a small town neighborhood
might be unusually high. What we want to know is, given the overall pattern
of crimes in our study area, where are we seeing unexpected clustering of
crime events?

Someone also noted that constructing density maps with different parameters
can result in very different results... Sure enough. Even different
rendering methods (the colors and symbols we choose) can impact what and how
our maps communicate.

I'd like to recommend a spatial statistic called the Getis-Ord Gi*
statistic. It is a relative measure of spatial clustering. --- Sorry, but
here comes the plug: the Hot Spot Gi* tool is available in all versions of
ArcGIS 9 -- ArcView, ArcEditor, and ArcInfo; oh, and I wrote it using the
Python scripting language, so you get the tool AND the source code (core
functionality in ArcToolbox). --- The Hot Spot Analysis tool works by
comparing a local mean (a particular census block and all of its nearby
neighboring census blocks, for example) to the global mean (all census
blocks in your study area) to determine where you are getting either MORE
crimes than you would expect or FEWER crimes (cold spots) than you would
expect if the overall pattern were a random one. The result of this
analysis is that every feature in the study area is assigned a Z Score (a
standard deviation), so interpretation is a bit more straightforward. Z
Scores above 1.96, for example, are statistically significant at the 0.05
level. (So we can render those features RED, because they are HOT spots...
and we can render scores of -1.96 or less with BLUE to represent cold
spots...).

Of course there are some parameters to consider with this tool too... how
you define "local" can yield different results. I like to use a distance
band which reflects maximum spatial autocorrelation, unless I have a very
good feel for the spatial scale of the events I'm analyzing... I can direct
you to a sample python script that will calculate this distance if you are
interested.

And of course how you structure you analysis depends on the questions you
want to answer:
1) Where in my study area do I have the most crime? (Maybe I want to verify
that I'm allocating police resources effectively). For this analysis I can
run Gi* on all crime events. I'm guessing, however, that the police
officers working in the study area already KNOW where the heavy crime areas
are. They are not going to get excited about your hot spot map.
2) We expect more crime where we have more people. In addition, we know
that some neighborhoods have higher crime rates than others... Normalizing
different sets of crimes by ALL CRIME EVENTS can answer more interesting
questions. (Using ALL crime events, as a "control", takes into account
population patterns AND crime rate variations).
a) Suppose we want to know where to implement a vandalism prevention
program. If we just run Gi* on the raw vandalism counts we find our hot
spots are just where we expect: downtown where we have lots of people and
lots of crime. Instead divide vandalism by ALL CRIMEs for each feature
(census block) and run Gi* on the normalized ratios... This tells you where
vandalism is a larger component of crime events. We find that, in fact,
vandalism is a suburban issue... it is a larger proportion of crime in the
suburbs.
b) A similar approach can be adapted to looking for temporal patterns of
crime (do crime events peak during certain hours of the day or certain days
of the week?).
c) We can normalize crimes in relation to officers on duty to see how
changes in patrol patterns impact crime patterns...

... ooops, I think I've given more than my 2 cents. I hope the information
is helpful.

Lauren Scott, Ph.D.
ESRI Geoprocessing
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