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Scaling of variability measures in hierarchical demographic data

Aleksejus Kononovicius, Justas Kvedaravicius

Abstract

Demographic heterogeneity is often studied through the geographical lens. Therefore it is considered at a predetermined spatial resolution, which is a suitable choice to understand scalefull phenomena. Spatial autocorrelation indices are well established for this purpose. Yet complex systems are often scale-free, and thus studying the scaling behavior of demographic heterogeneity may provide valuable insights. Furthermore, migration processes are not necessarily influenced by the physical landscape, which is accounted for by the spatial autocorrelation indices. The migration process may be more influenced by the socio-economic landscape, which is better reflected by the hierarchical demographic data. Here we explore the scaling behavior of variability measures in the United Kingdom 2011 census data set. As expected, all of the considered variability measures decrease as the hierarchical scale becomes coarser. Though the non-monotonicity is observed, it can be explained by accounting for the imperfect hierarchical relationships. We show that the scaling behavior of variability measures can be qualitatively understood in terms of Schelling's segregation model and Kawasaki-Ising

Scaling of variability measures in hierarchical demographic data

Abstract

Demographic heterogeneity is often studied through the geographical lens. Therefore it is considered at a predetermined spatial resolution, which is a suitable choice to understand scalefull phenomena. Spatial autocorrelation indices are well established for this purpose. Yet complex systems are often scale-free, and thus studying the scaling behavior of demographic heterogeneity may provide valuable insights. Furthermore, migration processes are not necessarily influenced by the physical landscape, which is accounted for by the spatial autocorrelation indices. The migration process may be more influenced by the socio-economic landscape, which is better reflected by the hierarchical demographic data. Here we explore the scaling behavior of variability measures in the United Kingdom 2011 census data set. As expected, all of the considered variability measures decrease as the hierarchical scale becomes coarser. Though the non-monotonicity is observed, it can be explained by accounting for the imperfect hierarchical relationships. We show that the scaling behavior of variability measures can be qualitatively understood in terms of Schelling's segregation model and Kawasaki-Ising
Paper Structure (6 sections, 4 equations, 6 figures)

This paper contains 6 sections, 4 equations, 6 figures.

Table of Contents

  1. Introduction
  2. Scaling behavior in the UK 2011 census data
  3. Baseline null model
  4. Non--monotonicity of variability
  5. Modeling (anti--)segregation
  6. Conclusions

Figures (6)

  • Figure 1: Normalized variability (colored curves) of four different demographic categorizations across different hierarchical scales.
  • Figure 2: Normalized standard deviation of the two different demographic categorizations across the different scales: empirical data (red curve) compared against the null model (median is shown as solid black curve, while $95\%$ confidence interval is limited by the thin dashed black curves).
  • Figure 3: Random grid (left) and normalized standard deviation curve (right) measured across the consistent (red curve) and inconsistent hierarchical scales (green curve). Thin black dashed curve shows Eq. \ref{['eq:scaling-rel']}.
  • Figure 4: Segregated random grid (left) and normalized standard deviation curve (right) measured across the consistent scales (red curve). Thin black dashed curve shows Eq. \ref{['eq:scaling-rel']}.
  • Figure 5: Normalized standard deviation curves obtained for the Schelling's model with different happiness thresholds: $0$ (red curve), $25\%$ (green), $37.5\%$ (blue), and $50\%$ (cyan). All of the obtained curves are above or overlap the thin black dashed curve, which corresponds to the random grid model.
  • ...and 1 more figures