Table 1 Tests of power-law model for the street-network evolution of the city of Dundee. The symbols are as follows. Number of street segments for each time period (n), scaling exponent based on MLE (α) (± shows the standard error on α), the number of observations in the power law range, ntail (± shows the standard error of the ntai)l, lower bound of power law (xmin) at which the power law model no longer applies (± shows the standard error of xmin), power law fits and the corresponding p-values and each of the subsequent rows shows the log likelihood ratios (LR) for the alternative models (fits) and the associated p-values. Positive values for LR indicate that the power law model is favoured over the alternative models if the p-value < 0.1. However, if the p-value is large than 0.1, the sign is not a reliable indicator as to which model provides the better fit to the data
Tests of power law behaviour in street data sets | |||||||
|---|---|---|---|---|---|---|---|
Dundee evolution | 1600 | 1776–77 | 1821 | 1846 | 1912 | 2007 | |
n | 70 | 209 | 376 | 1360 | 2184 | 9616 | |
α | 3.46 ± 0.39 | 2.79 ± 0.42 | 2.71 ± 0.43 | 3.33 ± 0.14 | 2.93 ± 0.27 | 3.27 ± 0.09 | |
ntail | 32 ± 11 | 93 ± 30 | 185 ± 71 | 440 ± 110 | 615 ± 358 | 961 ± 241 | |
x min | 101 ± 23 | 108 ± 37 | 103 ± 50 | 100 ± 15 | 164 ± 57 | 165 ± 26 | |
Power law | p | 0.99 | 0.00 | 0.40 | 0.32 | 0.21 | 0.34 |
Log normal | LR | 0.000 | −3.388 | −8.461 | −1.198 | −4.181 | −0.402 |
p | 0.57 | 0.22 | 0.00 | 0.17 | 0.04 | 0.29 | |
Exponential | LR | 3.048 | −5.044 | −9.436 | 19.214 | 24.124 | 90.124 |
p | 0.89 | 0.11 | 0.00 | 0.98 | 0.96 | 0.99 | |
Stretched | LR | 0.048 | −5.080 | −9.520 | −1.279 | −4.169 | −0.359 |
exponential | p | 0.63 | 0.11 | 0.00 | 0.17 | 0.04 | 0.36 |