The media are more likely to report on the murder when a bright, educated young person from a privileged background is killed, and we all think:
As you can see a low value of bandwidth produces a very detailed plot, while increasing this value creates a very smooth surface where the local details are lost.
This is basically an heat map of the crimes in London, therefore we need to be very careful in choosing the right bandwidth since these images if shown alone may have very different impact particularly on people not familiar with the matter.
The first image may create the illusion that the crimes are clustered in very small areas, while the last may provide the opposite feeling. Complete spatial randomness Assessing if a point pattern is random is a crucial step of the analysis.
If we determine that the pattern is random it means that each point is independent from each other and from any other factor. Complete spatial randomness implies that events from the point process are equally as likely to occur in every regions of the study window.
In other words, the location of one point does not affect the probability of another being observed nearby, each point is therefore completely independent from the others Bivand et al.
If a point pattern is not random it can be classified in two other ways: Clustered means that there are areas where the number of events is higher than average, regular means that basically each subarea has the same number of events. Below is an image that should better explain the differences between these distributions: Based on the curve generated by the G function we can determine the distribution of our data.
I will not explain here the details on how to compute the G function and its precise meaning, for that you need to look at the references. However, just by looking at the plots we can easily determine the distribution of our data.
These are the curves generated by the G function for each distribution. The blue line is the G function computed for a complete spatial random point pattern, so in the first case since the data more or less follow the blue line the process is random.
In the second case the line calculated from the data is above the blue line, this indicates a clustered distribution. On the contrary, if the line generated from the data is below the blue line the point pattern is regular. We can compute the plot this function for our data simply using the following lines:An Analysis of the Factors Determining Crime in England and Wales: A Quantile Regression Approach.
Crime and justice Figures on crime levels and trends for England and Wales based primarily on two sets of statistics: the Crime Survey for England and Wales (CSEW) and police recorded crime data. Serious and Organised Crime: Home Office research priorities April to March 1 November Research and analysis Exploring the role of the Financial Investigator.
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