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Distance-Based Measurement of Agglomeration, Concentration and Specialisation

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Measuring Regional Specialisation

Abstract

This chapter reviews the existing distance-based measures of agglomeration, which are based on the individual geo-references point data. It proves that they may be inefficient because of functional, non-index results and low sensitivity to extreme spatial patterns. Thus, the second part of the chapter develops the new measure of spatial agglomeration, SPAG. Its performance for different spatial patterns is being tested and simulated confidence interval developed. As shown, measure can compare the density of point location in given region with single number what is attractive result in terms of its further use in econometric analyses.

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Notes

  1. 1.

    Jensen and Michel (2011) give an analytical expression for variance of two-dimensional indices by Marcon and Puech (2009) and Duranton and Overman (2005).

  2. 2.

    The significance of spatial coefficients is usually obtained with Monte Carlo simulation. Jensen and Michel (2011) propose analytical expressions for the variance of several spatial coefficients to test the randomness of distributions.

  3. 3.

    With reference to point data, there exist technical conditions of index, which are based on mathematical properties of measures. Do and Campante (2009) for grid-based data give basic and refinement axioms of decomposability and monotonicity to be satisfied by the function being the index of spatial concentration. In those indicators, the main interest is in the density of economic activity and its spatial distribution over the territory.

  4. 4.

    Ripley’s K functions and their corrections are available in the dbmss package for R software (Marcon et al. 2015)

  5. 5.

    Distance-based measures react to issues that are invisible for cluster-based measures (see Chapter 2) mainly on the spatial distribution of economic activity. Assuming spatial patterns as in Fig. 3.1, cluster-based measures would aggregate the values (i.e. number of firms) over territory and independently of the spatial distribution of points, and the result would be the same. Distance-based measures look inside the region and track spatial allocation of points.

  6. 6.

    The SPAG measure was prepared as a part of works in scientific project financed by Polish National Center of Science (www.ncn.gov.pl) titled “Statistical models in identification of regional specialisation, including the component of spatial heterogeneity” (call OPUS 6, contract no UMO-2013/11/B/HS4/01098).

  7. 7.

    While characterising the location of points (xy) and their values (z), one of the popular methods is to represent point with a shape, which allows one to analyse patterns on the 2D surface. In the literature of the last 60 years, the shape measures were very well described. They are mostly based on combining the perimeter and area. For this combination, the shape matters a lot, as the shapes with the same perimeter may have various areas. If those two values are close, it proves the lower shape complexity and that the measures get much closer to simple Euclidean geometry (de Smith et al. 2015). It is possible to prove that the shape with the biggest area at given perimeter appears to be a circle. Because of this fact that circle has the smallest difference between values of area and perimeter and is the least complex shape. A circular shape is also provided with the border values of many shape measures (e.g. perimeter^2/area, compactness ratio, fractal dimension index), which is guaranteed dimensionless (independent of the size of the polygon). The main characteristics of the circle are that it is symmetric as every simple shape. It can be entered in or limited with other figures. It also solves the problem of isoperimetry (de Floriani and Spagnuolo 2008). As most exercises in shape geography and computational geometry rely on the simplification of shape, the mainstream of measures is dominated by the circles.

  8. 8.

    In spatial sampling theory, one can reach the even spatial overlay if adopting the rules of minimisation of the mean for the shortest distances (MMSD) in the Euclidean sense. This is viable in the case where territory is discretised into a grid (van Groenigen et al. 1999; Wang et al. 2012).

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Authors and Affiliations

  1. Chair of Statistics and Econometrics, Faculty of Economic Sciences, University of Warsaw, Warsaw, Poland

    Katarzyna Kopczewska

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  1. Katarzyna Kopczewska
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Kopczewska, K. (2017). Distance-Based Measurement of Agglomeration, Concentration and Specialisation. In: Measuring Regional Specialisation. Palgrave Macmillan, Cham. https://doi.org/10.1007/978-3-319-51505-2_3

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  • DOI: https://doi.org/10.1007/978-3-319-51505-2_3

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