Abstract
Abstract Background: Hierarchical functional regions (FRs) can be calculated using data on interactions between basic spatial units (BSUs) and a hierarchical aggregation procedure. However, the results depend on the selected system of initial BSUs. In spatial sciences, this is known as the zonation effect, which is one of the effects of the Modifiable Areal Unit Problem (MAUP). Objectives: In this paper, we analyse the influence of the zonation effect on a system of hierarchical functional regions. Methods/Approach: We compared two systems of hierarchical functional regions of Slovenia modelled by the Intramax aggregation procedure using the inter-municipal labour commuting flows for the same year, but for two different initial sets of municipalities. Besides, we have introduced a new measure to compare systems of hierarchical FRs. Results: The results show that the zonation effect has an influence on hierarchical functional regions. The clustering comparison measure suggested here is a metric measure, which is appropriate for comparing hierarchical FRs. Conclusions: The zonation effect has influence on hierarchical FRs. The clustering comparison measure suggested in this paper is easy to interpret, but it should be adjusted for the number of clusterings
Highlights
In spatial sciences, the concept of functional regions (FRs) is one of the key concepts for analysing, modelling, monitoring, and predicting socio-economic structures. Brown and Hincks (2008) describe FRs as a combination of functionally complementing basic spatial units (BSUs), which have more economic interactions with each other than with outside units
To analyse the influence of the zonation effect on a system of hierarchical FRs, two systems of hierarchical FRs were calculated for Slovenia: one considering the actual state in 2011, i.e. 210 municipalities and labour commuting flows between them (SMARS, 2016; SORS, 2016), and another one considering the same data on intermunicipal flows for 2011, but considering an older zonation from 2000 when there were 192 municipalities in the country
Along the nine clustering comparison measures previously introduced in the literature, we suggested a new concept of comparing FRs based on an average maximum proportion of matched municipalities in FRs (Drobne et al, 2017)
Summary
The concept of functional regions (FRs) is one of the key concepts for analysing, modelling, monitoring, and predicting socio-economic structures. Brown and Hincks (2008) describe FRs as a combination of functionally complementing basic spatial units (BSUs), which have more economic interactions with each other than with outside units. The change of the number (and the size and the shape) of the BSUs brought about the effects of the Modifiable Areal Unit problem (MAUP). Hierarchical functional regions (FRs) can be calculated using data on interactions between basic spatial units (BSUs) and a hierarchical aggregation procedure. The results depend on the selected system of initial BSUs. the results depend on the selected system of initial BSUs In spatial sciences, this is known as the zonation effect, which is one of the effects of the Modifiable Areal Unit Problem (MAUP). We have introduced a new measure to compare systems of hierarchical FRs. Results: The results show that the zonation effect has an influence on hierarchical functional regions. The clustering comparison measure suggested in this paper is easy to interpret, but it should be adjusted for the number of clusterings
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