Improving Victimization Risk Estimation: A Geographically Weighted Regression Approach
Round 1
Reviewer 1 Report
I enjoyed this paper, and it is well written and articulated overall. I had a few questions, points of clarification and minor revisions I recommend prior to publication.
- Your title is ‘crime risk’ but you are quite explicit that this paper examines victimisation risk. I suggest changing the title.
- Your model has only been simulated and applied to one case study burglary areas. You may want to rephrase the title to reflect this (‘robust?). It is first proposal of GWRisk that needs others to test and replicate it.
- You specify victimization risk as ‘the likelihood of an individual within a reference population being victim of a crime’. You identify standardised crime rates as generally related to population but then discuss ‘noise’ – what do you mean here?
- You do not really discuss the performance of your two simulated models against each other (i.e with one reference population and two reference populations). Given you are examining burglary I would anticipate using households as my reference population rather than census population. On Line 32 you discuss the challenges of “(e.g., should we consider burglaries per residence, burglaries per resident, or maybe even burglaries per offender?” – but you do not come back to this point after your model. Your comparisons are with other tests.
- I would value further discussion about expanding this – to additional reference populations – can it be used for example with 3 or 4 reference populations when trying to identify appropriate crime denominators. Or are you arguing this approach rather than a standardised rate.
- I wonder about the impact of over-dispersion and small numbers, especially with crime data. Given crime is often associated with Poisson distributions, I have seen some non-crime papers using GWR with Negative binomial regression (GWNBR); GWPR (GWR Poisson Regression); and GWZIPR (GW zero inflated Poisson). Would this approach be valid to what you are developing? Is it something that could be explored in the future?
- I am also slightly unsure as to this statement - line 317 - when fitting the estimated risk to the true risk under an Ordinary Least-Squares Method. what do you mean by true risk. Is OLS valid here given crime data.
- One of the challenges in modelling concentration of crime (and risk) is the debate between highly micro level (street intersection) and area-based examinations of crime clustering. This model/technique is only applicable to the latter. I recommend you include some discussion as to how/where this might be of value for policy/practice/research might be beneficial and where/when this area-based approach is relevant.
- You rightly identify limitations of crime underreporting. But the currency of reference populations (2010) census is also an issue here, given they likely only occur every ten years.
- It would be interesting to see the performance of this model on other types of crime (e.g. outdoor violence, criminal damage) although reference populations here would be more difficult to ascertain. This is more pertinent considering Bloggs about need to use appropriate denominators. Is this an avenue for future research and why do you think your model would still work for this?
Author Response
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Author Response File: 
Author Response.pdf
Reviewer 2 Report
The introduction should not be repeated with the abstract.
Quality of figures could be improved to make them more understandable for readers.
Author Response
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Author Response File: Author Response.pdf
Reviewer 3 Report
I think the general idea makes quite a bit of sense. The simulation study using parameters derived from real data (and varied slightly) also is a straightforward way to validate the approach. Only have several minor comments I think the author can address without too much hassle.
- Confused about how you arrived at equation 8, and what f*eps refers too? Substituting in the stuff on the right hand side for r = C/P* I get r = (fV + eps_c )/(eps_p + P). Subsequently not sure about 9 ( the idea if P* > P and P* < P makes sense in general), but r is clearly bounded above 0 (can't have a negative number of crimes!), so 10 in the limit going to negative infinity is a bit strange assertation to make as well.
- pg 5 line 231 "issues of bias" -- instability is OK here in my opinion, I think bias is a bit too strong. It may be amendable in a simpler way to unbiased estimates (say instrumental variables GWR), but I don't see why these will be less biased offhand than other methods.
- Please describe how you estimated the bandwidth (and kernel chosen) for GWR. One concern I have is if you chose the bandwidth to correspond to your range estimates for the simulation, then that is a bit double dipping and will make GWR look better. This seems to me to be the crux of this method, determining how smooth to make the maps.
- Please spend a bit to describe the variogram parameters (what is range 50?) and what they mean (not familiar with how these are used to generate simulations, so the data conform to that particular function?)
- For all the maps you can turn off the axes to save space (since it is normalized to unit square they don't give any info anyway). For the simulated maps can just leave as is, but for the real data I think it would be good to have an outline for the city, scale bar, etc.
- Realize this is part of your point, but Figure 5/6 maps for naive and empirical Bayes, would like to see ones that have capped values, so they are a bit more comparable to the original risk map and can visualize the distribution more readily. For Figure 5 because of the outlier 4/2, the rest of the map is muted. [I imagine they will still make your point though, they will be spotty whereas GWR will be smoother.]
Andy Wheeler
Author Response
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Author Response File: Author Response.pdf
