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I have a point feature class that I used the Average Nearest Neighbor from the ArcGIS software to calculate the pattern.

ArcGIS produces output chart that says whether the data is dispersed, random or clustered. But what if it's uniformed? what if it's regular?

Why are these patterns not in the ArcGIS result and what can I do to tell if my point feature class is uniformed or regular using ArcGIS and the "Average Nearest Neighbor tool"?

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  • It does to some extent.. a regular pattern is over-dispersed, when compared to CSR. – user5219763 Apr 14 '16 at 16:58
  • so does that mean that a z value higher than 1.96 is regular? – Rudolf O Apr 14 '16 at 17:00
  • it really depends how you define "regular". It means the points are more evenly spaced (larger on average) than you would expect if you placed the points at random. similarly if its 'clustered' it means the interpoint distances are smaller than would be expected if the points had been placed randomly and and independent of each other. There are lots of ways you can form a 'regular' pattern which might have very different interpoint distances. – user5219763 Apr 14 '16 at 17:05
  • I took the term regular from wikipedia, which I now see does not have the term uniform at all. Isn't there a fixed definition to what is regular like there is for random, clustered and dispersed? Do you have any example that you have used this ArcGIS tool and concluded from the result it is regular? that could be a good starting point for me – Rudolf O Apr 14 '16 at 17:11
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    I use an r package called spatstat personally, but the ideas are the same and the authors of that package have lots of good info on spatial point processes that might help you out umaine.edu/computingcoursesonline/files/2011/07/… or any text on spatial point process models. I don't know of any fixed definition of a regular pattern in point processes. – user5219763 Apr 14 '16 at 17:18
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You should look at the output. In the toolbox window click on the results tab at the bottom (and if necessary, uncollapse the Average Nearest Neighbor entry).

The NNI ratio, p value, expected and observed are all reported. You need to interpret the actual statistic and not rely in ESRI's GUI interpretation. A random or uniform distribution would be near zero and as the value increases the process becomes more clustered.

Normally, I loath the ESRI spatial statistics tools but, I have the NNI statistic available in one of my R library and ESRI's results are identical. The z value has nothing to do with the clustering, but rather is a measure of significance. To derive the p-value from the z score you can take a two sided approach and use the cumulative density function (eg., 2 * pnorm(-abs(z)) ). With a z score of 1.96 the p value would be 0.049 which is sitting right at a 0.05 significance level and can be accepted as a significant result.

In the case of the NNI regular, uniform and independent are interchangeable. This statistic does not indicate if there is a dispersal process and you cannot interpret it in the context of a statistic like Moran's-I which is two tailed thus, indication two types of spatial process with zero being random. The NNI indicates randomly dispersed, as tested against a CSR Poisson process, to clustered. The f-hat and g-hat statistics are similar in nature.

Not to be harsh here but, you need to state an actual hypothesis of the spatial process and then select an appropriate statistic and not go on a fishing expedition based on available ESRI tools, which is becoming all to common. An exploratory spatial analysis is also quite warranted as well. For example, as a starting point, have you looked at the open space characteristics of the data. Also, check whether your data is homogeneous or following an intensity process. These are critical questions to address before trying to fit a point process model.

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  • just to clarify one point- when you say that regular, uniform and independent are interchangeable as far as NNI is concerned - what exactly do you mean? are they all random? – Rudolf O Apr 14 '16 at 20:50

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