Row Standardisation Questions

[ThomMackey]

Hello,
I've got a few questions about using Row Standardisation in the tools which request it in the Spatial Stats toolbox. I think I understand what it does (turns the absolute weight of the feature into a relative measure of how heavy a feature is compared to its neighbours) but I just want to make sure I'm clear of some things.

The help states "Row standardization is recommended whenever the distribution of your features is potentially biased due to sampling design or an imposed aggregation scheme." Why exactly is this the case? And does that mean it would apply every time you have aggregated your incident data, as recommended?

Further, it's mentioned that "Anytime you are working with polygon features representing administrative boundaries, you will likely want to choose the Row Standardization option." Is it possible to explain in more detail why this is the case?

Also, is there a reason not to use Row Standardisation all the time? What kind of distortion would you introduce if you used Row Standardisation on a pre-weighted points dataset, for example?

Overall, I get the impression that if using "fixed distance band" (which usually seems to be a good idea when dealing with point data and you have a reasonable idea of what scale you want your analysis to be good for) or "polygon continuity", it's a good idea to choose row standardisation - but
I'm not quite sure why this is the case 🙂

I'd appreciate any thoughts.

Cheers
-Thom

[LaurenScott]

Hi Thom,
Good questions 🙂
Let's think about this with points first... two examples involving variations in my point densities:
1) Suppose we have ALL crime incidents.  In some parts of our study area there are lots of points because those are places with lots of crime.  In other parts, there are few points, because those are low crime areas.  The density of the points is a very good reflection (is representative) of what I'm trying to understand: crime spatial patterns.
2) Suppose I've taken soil samples.  For some reason (the weather was nice or I happened to be in a location where I didn't have to climb fences, swim through swamps, hike to the top of a mountain, etc.), I have lots of samples in some parts of my study area, but fewer in others.  In other words, the density of my points is not strictly the result of a carefully planned random sample; some of my own biases may have been introduced.  Further, where I have more points is not necessarily a reflection of the underlying spatial distribution of the data I'm analyzing.

For case 1, whether a feature has more neighbors or not is a reflection of actual crime densities.  While it is fine to row standardize, in this case I'd rather have the density of my points play a role in my analysis, because they are reflective of what I'm studying.

For case 2, I want to minimize any bias that may have been introduced during sampling.  When you row standardize, the fact that one feature has 2 neighbors and another has 18 doesn't have a big impact on the results; all the weights sum to 1.

Make sense?

Okay, polygons... Whenever we aggregate our data we are imposing a structure on it.  If that structure is a good reflection of the data I'm studying, I might decide not to row standardize ... but to be honest, I can't think of a good example off the top of my head where that would be the case.  Some might argue that census polygons (like tracts) are designed around population, so if the data I'm analyzing has to do with people, I might not want to row standardize... but the way tracts appear in the census represent just one of many, many, many ways they could have been drawn.  So with polygon data, I always apply row standardization. 

I hope this helps!
Lauren


Lauren M. Scott, PhD
Esri
Geoprocessing and Analysis, Spatial Statistics

[ThomMackey]

Hi Lauren,

Thanks - you answered my questions exactly.

I'm really grateful for all the effort you & the SpatStat team have gone to, not only in implementing the tools, but your extensive documentation and ongoing support. Between the official documentation, the online seminars, and your regular contributions to this forum, nobody has an excuse not to understand and use these tools. It is honestly amazing!

Thanks again!

-Thom