Table 1.
Crime and property types analyzed in this study.
Fig 1.
Comparison of predictor and indicator metrics for the indicators total crime and total property transaction values.
The density metrics gave better correspondence to the scaling laws as indicated by Pearson correlation (ρ).
Table 2.
Comparison of metrics for prediction of crime and property transaction values.
All models included categorical variables describing the type of crime or property as: Predictor, Type, Predictor*Type. The model with the best R2 and PRESS statistics have been highlighted in bold.
Fig 2.
Comparison of Pearson correlations for different property and crime types.
Markedly improved correlations are observed using density metrics which were superior in all cases. Here the error bars stand for 99% confidence interval obtained via bootstrap and the asterisk marks indicate a significative difference between population density and day population density (via bootstrap two-sample mean test with 99% confidence).
Fig 3.
Comparison of the adjusted R2 obtained for the single power-law model (Eq 2) and the double power-law model (Eq 3).
Error bars stand for 99% bootstrap confidence intervals and the asterisk marks indicate a significant difference (via bootstrap two-sample mean test with 99% confidence). Notice that the double power-law model is a better fit in 19 out 24 metrics; however, for other crime, total crime and ASB, vehicle crime, and weapons the differences in the adjusted R2 are not statistically significant.
Fig 4.
Population density scaling behavior of all metrics.
The colorful dots are the empirical values and the black dots are the window average values (errors bars are 95% bootstrap confidence intervals). For metrics in which the double power-law is a better fit according to adjusted R2 (see also S4 Fig for AIC and BIC), the red dots show the low-density data (log d < log d*) and blue ones the high density data. The vertical line represents the position (log d*) of the transition to urban scaling. The numbers refer to the scaling law exponents and the threshold positions with uncertainty in parentheses. Total crime reports were 5,357,113. Total property transactions were £226,122,179,000.
Table 3.
Scaling parameters for police crime report density and property transaction value density with population density.
Fig 5.
Allometric exponents for crime metrics (upper panel) property transactions (bottom panel) using density metrics.
The error bars refer to the standard errors in the exponents.