GEOG 566

         Advanced spatial statistics and GIScience

April 12, 2019

Exercise 1: The Spatial Patterns of Natural Resource Governance Perceptions


What are the spatial patterns of natural resource governance perceptions in the Puget Sound?

Tools and Approaches

  1. Moran’s I (with correlograms) and Semivariograms in R studio
  2. Kriging and IDW in ArcGIS Pro
  3. Hotspot Analysis in ArcGIS Pro


Analysis Steps

  1. To compute Moran’s I, I used the “ape” library in R which has a function called Moran.I(). This function takes the variable in question (governance perceptions), and a distance matrix to compute the observed and expected values of Moran’s I, as well as the standard deviation and a p-value. For this analysis, I also subset my data to examine spatial autocorrelation by demographics including area (urban, suburban, rural), political ideology, life satisfaction, income, and cluster (created by running a cluster analysis on the seven variables which comprise the governance index).  I created correlograms for the variables that were significant (urban, conservative, and liberal) using the “ncf” library and the correlog() function. These figures give a better picture of spatial autocorrelation at various distances.  To create semivariograms, I used the “gstat” and “lattice” libraries which contain a function called variogram. This function takes the variable of interest along with latitude and longitude locations. The object created can then be plotted. For this analysis I used the same subsets as in the Moran’s I analysis.
  2. To preform interpolation on my data, I loaded my point data into ArcGIS Pro. I then used the Spatial Analysis toolbox to preform Kriging  and IDW to compare the outputs of the two techniques. I used my indexed variable of governance perceptions. The values of the variable vary from 1 to 7. I then also uploaded a shapefile bounding the sample area, as well as a shapefile of shoreline, to delineate my study area better.
  3. To run a hotspot analysis I used my previously loaded point data inArcGIS Pro. I then used the Spatial Analysis toolbox to preform ‘hotspot analysis.’ I used my indexed variable of governance perceptions with values from 1 to 7. I used the shapefile of shoreline to delineate my study area better.


  1. The Moran’s I calculation was insignificant for rural, suburban, cluster groups, life satisfaction, and income, suggesting no spatial autocorrelation of governance perceptions by these subsets.


The Moran’s I calculation was significant for urban:

Observed value: -0.014

P-value: 0.0002


The Moran’s I calculation was also significant for ideology:


Observed value: -0.006

P-value: 0.002


Observed value: -0.002

P-value: 0.05


This suggests that in these subsets there is spatial autocorrelation between individual governance perceptions.

The semivariograms for the subsets that are significantly spatially autocorrelated are presented below.


None of these plots suggest high degrees of spatial autocorrelation. The urban plot does so more than the ideology plots, but the y axis scale is still very small.









The plot (top Urban, bottom left Liberal, bottom right Conservative) help to confirm the findings from above. The Moran’s I fluctuates around zero without much variation. The large spike in variation that the graphs do show are only for non significant points. Significant points are filled in, where non-significant points are open circles.

2. Interpolation

The kriging (bottom left) with individual points and IDW (bottom right), do not look incredibly different in terms of general trends. The kirging with shoreline (top) gives possibly the most interesting visual of spatial patterns. In general, perceptions are better (more green) in the center, where there is greater shoreline. There are also two sections that appear much more negative. To examine these locations further, I preformed a hotspot analysis.

3.  Hotspot Analysis

This image confirms the two bright red spots from the interpolation to be “cold spots” or spots that the value of perception is significantly lower at a 99% confidence. The orange dots are a 95% confidence. The green corridor appears to hold in the southern part of the Sound and is confirmed at a “hotspot” or a spot that the value of perception is significantly higher than the areas surrounding it at a 99% confidence level.

The three main areas of red or orange correspond to the cities of Shelton (bottom), Port Angeles (west), and Everett with a little of south Whidbey Island (east).

  1. Critique

I believe all methods are useful, but some are redundant. I think it would probably be sufficient to do only one of each type of method—spatial autocorrelation and interpolation—but it is interesting and more convincing to see the same type of analysis done in different ways. The p-values from the Moran’s I appear to agree with the shape of the curve’s in the semivariograms, where the smaller p-values have more defined shapes. The same goes for the interpolation methods, while they are interesting to see side-by-side, they essentially tell the same story. I think in this case, the hotspot analysis shows the most interesting interpretation of the data because it indicates areas of potential concern.

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