Fig. 3.

Plots showing results of the NMDS and clustering process. (A) Plot of observed dissimilarities between the parcels (in the process of clustering parcels into regions), against the model-implied distance. A non-linear relationship indicates that the metric model is inadequate. The nonlinear relationship suggests that NMDS is a more appropriate procedure than linear methods in this case. (B) Z-scores of clustering quality relative to the clustering quality of permuted data (y-axis) plotted as a function of number of clusters in the solution (x-axis). A 21-cluster solution was associated with the greatest improvement over permuted data, and was therefore chosen as the best estimate. (C) Cluster quality for observed data (vertical line) compared with a histogram of clustering quality for permuted data for the 21-cluster solution. Figs. 3D–F show similar plots for the second iteration of the algorithm, clustering regions into large-scale groups. (D) NMDS is indicated by the non-linear relationship. (E) A six-cluster solution was associated with the highest improvement over permuted data, and was therefore chosen. (F) The quality of the selected six-cluster solution (compared with permuted solutions) is indicated by the vertical line.