Hi Susanne,
Yes, you are correct... if you want to compare crime from one time period to another for the same location, it is important to use the same distance band. Please keep in mind that results from Hot Spot Analysis are correct for whatever distance band you use... When you don't have any criteria to help you select any particular distance band, you can use Incremental Spatial Autocorrelation, Calculate Distance Band from Neighbors and/or Optimized Hot Spot Analysis to find an appropriate distance band for your analysis. These are some of the strategies I would try if I had several years of crime data and wanted to compare the hot spot (and Global Moran's I) results:
1) I would use Optimized Hot Spot Analysis (OHSA) to find the optimal distance for each year and I would write down the result. Or for 10.1, I would use Incremental Spatial Autocorrelation (ISA). Suppose I see the following:
Year "Optimal" Distance from OHSA or ISA
----- ------------------------------------------
2004 2301.345
2005 4043.223
2006 2290.456
2007 2310.987
2008 2301.842
Because most years have distances around 2300, if that distance seems to fit the scale of the question I'm asking, I would use that as the distance band every year (even for 2005).
2) If the distances above are all over the place, I would create a single feature class with crimes from all years and run OHSA (or ISA) on all crimes and use whatever distance it returns consistently when I do my year by year analyses.
3) The best solution (not always possible) is to have a reason for selecting your distance band... if remediation/crime prevention will be neighborhood by neighborhood, for example, I might try to come up with a distance that best reflects neighborhood structure in my study area... or perhaps I could try to find theory or evidence to tell me the distances over which related crimes occur ???
Sensitivity Analysis: Your goal is to make sure your model isn't over fit and that it predicts well across data samples. When a model is over fit, you will get a very different result by removing just a few observations. Here one strategy (there certainly are others) to help you feel confident that you've found a trustworthy model:
1) Find a model for your full data set.
2) Randomly sample 50% of the data and make sure that when you apply the model in (1) to both 50% samples that you still have a properly specified model (a properly specified model is one that meets all of the assumptions of the OLS method).
I hope this helps!
Best wishes,
Lauren
Lauren M Scott, PhD
Esri
Geoprocessing, Spatial Statistics