topic Generation of Spatial Weights Matrix - How it works for Lines? in Spatial Statistics Questions

Generation of Spatial Weights Matrix - How it works for Lines?

BerkA_ — Thu, 18 Aug 2011 15:54:25 GMT

Hi,

I am trying to understand how the spatial weights matrix is generated for a polyline shape file? I have tried the fixed distance option with Euclidean distance and left the distance threshold empty. After this, it detected a threshold value so that each feauture would have at least 1 neighbour. However, I could not understand the physical meaning of this calculated distance (note that, as far as I did the right things, it is not the euclidean distance between the start-end points of the polylines, nor the distance between their mid-points)!

Could someone please explain how it works for line objects, as the source is not sufficient.

Kind Regards,
Berk

Re: Generation of Spatial Weights Matrix - How it works for Lines?

LaurenRosenshein — Thu, 18 Aug 2011 22:20:08 GMT

Hi Berk,

That's a great question! For line and polygon features, feature centroids are used in distance computations. For multipoints, polylines, or polygons with multiple parts, the centroid is computed using the weighted mean center of all feature parts. The weighting for point features is 1, for line features is length, and for polygon features is area.

Re: Generation of Spatial Weights Matrix - How it works for Lines?

JeffreyEvans — Fri, 19 Aug 2011 15:20:31 GMT

Lauren,
Having you spell this out is making me a bit twitchy. In autocorrelation statistics that operate on discrete random fields the spatial weights matrix (Wij) should be based on Nth order neighbor contingency. This is because areas/lengths tend to not be standard making spatial process a function of the represented areas/lengths and not distance. How have these methods been modified to allow for the specification of a distance based matrix? How exactly are areas/lengths standardized to normalize the spatial structure within a given statistic? Can weighting the distance based on area/length really provide the same measure of spatial structure as contingency? I am not aware of this in the literature and would like to be pointed to some papers that justify this.