Table 1.
Ranked Swiss metropolitan areas based on SAMI and related statistics (GRC hierarchy, Population size, Median and Mean income (CHF)).
Fig 1.
(a) Sixteen metropolitan areas in Switzerland as detected by the modularity maximisation method. Different colours are used to differentiate metropolitan areas. (b) The settlement network of the Sion metropolitan area. (c) The settlement network of the Zurich metropolitan area.
Fig 2.
The relation between mean income and the population size of the metropolitan areas in Switzerland where β = 1.04 and Y0 = 27447.
The grey area indicates the 95% confidence interval. SAMI is the deviation from scaling law, which is used for ranking urban areas.
Table 2.
Statistical analysis of different models using main explanatory variables.
Fig 3.
The relationship between hierarchy of settlement network and SAMIs.
The red line is the ordinary least squares fit to data points and the green line shows the reference line (SAMI = 0). Metropolitan areas above the green line are associated with a higher economic outcome than expected from urban scaling, while metropolitan areas below the green line have a lower than expected outcome. The grey area indicates the 95% confidence interval.
Fig 4.
(a) Scatter plot showing the relationship between mean personal income and metropolitan hierarchy (GRC). SAMIs are shown with a colour gradient. (b) Scatter plot showing the interdependence of two explanatory variables. The isoclines represent different mean income levels (i.e. 40’000, 45’000 and 50’000 CHF). The colour gradient shows the mean income of metropolitan areas.
Fig 5.
Comparison of modelled median income and observed median income.
Table 3.
The scale of ΔBIC in the model comparison as suggested by Kass and Raftery [96].
Fig 6.
An illustration model to show different connection patterns in settlement network and relative changes in Global Reaching Centrality (GRC): (a) GRC = 0.42, (b) GRC = 0.25, (c) GRC = 0.07.