W Function: A New Distance‐Based Measure of Spatial Distribution of Economic Activities

Abstract

Distance‐based methods are applied in various fields of research. In this paper, a new relative distance‐based method, the W function, is introduced. This method contributes to the assessment of spatial patterns of economic activities using the stochastic Monte Carlo simulation, and supplements the typology of distance‐based methods recently drawn up by Marcon and Puech. The capability of the W function is compared with results from the Kd and the recently defined m function methods, which are widely used for monitoring the spatial distribution of economic activities by considering several theoretical and empirical examples. The W function appears to provide more precise estimations of the density of economic activities compared to the m and Kd functions, particularly in cases of complex patterns such as double clustered distribution. It also appears to provide a more accurate evaluation of dispersion.

Spatial Patterns of Knowledge-Intensive Business Services in Cities of Various Sizes, Morphologies and Economies

“…Their concentration in the inner cities and also urban cores (rather than dispersion in the suburbs) can be explained by: (i) The image effect and prestige of the central locality (Praha, Brno); (ii) the connection to the global communication links (Praha) and regional links (Brno, Ostrava) and (iii) the combination of relatively weakly developed urban core industries (finance, insurance) and a relative decline of historical cores/inner cities as the result of commercial and residential sub-urbanization (Brno, Ostrava). In case of Ostrava (and advertising in Brno) the spatial patterns of companies are also clearly constrained by relatively weak urbanization and localization economies (nevertheless, some effects of localization economies, such as easier access to information and data for IT firms were recorded [14,30]), relatively high concentration of manufacturing firms [95], and industrial brownfields in the inner city [116,117], most of them not revitalized despite their central position [118]. Obviously, the urban contextual factors, such as the position in the urban hierarchy and inherited economic profile may significantly alter the theoretically expected localization patterns of advertising and IT.…”

“…Future research should be focused on possible application of other methods analyzing point pattern such as spatial autocorrelation, Duranton and Overman's Kd function [92] or W function [95]. Additionally, the multiscale assessment of the role of factors, mechanisms and actors that shape intra-urban hubs of KIBS companies should be studied.…”

“…An extension of the above-mentioned method is addressed in more recently developed approaches (G, F or K functions). The K-function [21,[93][94][95] that considers all events and provides the standardized average number of events to the distance d from any event is used to provide greater detail on how the companies are clustered in space. Standardization is done by the intensity:…”

Analysing and Predicting Micro-Location Patterns of Software Firms

“…Such an analysis could also investigate whether some location factors are more scale sensitive than others and whether the chosen operationalisation approach alters the estimated effect of the location factors (e.g. "proximity to universities" could be measured by a binary variable, a count variable, or a continuous distance variable; recent research indicates that distance-based methods may be scalerobust (Carlino et al 2017;Scholl & Brenner 2014;Kukuliač & Hor 2016)). …”

Analyzing and Predicting Micro-Location Patterns of Software Firms

“…However, for a thorough understanding of MAUP scaling effects on location factor-firm correlations, our encompassing regression specification should be applied to different levels of geographic aggregation. Such an analysis could also investigate whether some location factors are more scale sensitive than others and whether the chosen operationalization approach alters the estimated effect of the location factors (e.g., "proximity to universities" could be measured by a binary variable, a count variable, or a continuous distance variable; recent research indicates that distance-based methods may be scale-robust [89][90][91]). …”