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I'm writing a paper on the collapse of ancient agricultural terraces in the Mediterranean, and have come across a problem when trying to create a meaningful measure.

I have sampled with a GPS terrace failure points, and mapped them with GIS. I have assessed the damage in the field in a simplistic ordinal scale called "status", where "1" is partial damage, and "2" complete collapse to the bedrock. I have an hypothesis that the potential damage to terrace stone walls increases/decreases according to two factors:

  • Increasing: The number of other terrace failure points in the immediate higher catchment area of the sample point. (Hydrologically speaking, a terrace failure point creates a channel for surface runoff to pour on the lower terraces, increasing saturation, peak infiltration etc., which brings about a higher chance of failure.)
  • Decreasing: The number of other adjacent terrace failure points on the same terrace wall. (The reasoning this time being other likely preferred runoff channels that decrease the chance of higher damage in the sample point.)

I'm trying to find a way to use these opposing "vectors" together, but I hit a snag. The obvious way is to divide the former (Neighbours) with the latter (Brothers) (Neighbours/Brothers), thus increasing one or decreasing the other will give me a higher ratio that represents the potential damage.

The way in which I calculate the value of each is summing all the "status" values of the points which match my spatial query. However, this results in some points that have 0 value for Neighbours and/or 0 value for Brothers, so a simple division doesn't work well in all the cases.

So I'm asking if there are ways to make this more meaningful.

I have no pre-existing assessment on the possible outcomes of such a measure, and I don't know if I should be expecting a positive or negative (or any) correlation.

Nick Cox
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HDunn
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1 Answers1

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Your bottom line is important here, as is your observation that 0/0 as a ratio "doesn't work well". The latter is naturally an understatement.

A simple conclusion is that you don't have grounds for combining these measures in any way. A ratio will not work. A difference would be feasible, but there are not strong physical grounds for that. Keep them separate and then leave choices to data analysis stage. It might be that either variable would be better scored as binary (zero versus positive); it might be that the counts themselves are useful predictors; there are no grounds for definite decisions either way, so maximize the information you keep.

As a small personal note, I have a physical geography persona, including publications in hydrology, geomorphology, etc., but the advice here does not draw on that very much, just basic research strategy.

Nick Cox
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  • +1 - A good exploratory approach here might use two different types of spatial weights matrices, one for neighbors on the same wall, and another for neighbors within the catchment (but not on the same wall). – Andy W Aug 05 '13 at 23:30