Investigating Metropolitan Hierarchies through a Spatially Explicit (Local) Approach
Abstract
:1. Introduction
2. Methodology
2.1. Study Area
2.2. Data and Variables
2.3. Statistical Analysis
3. Results
3.1. Descriptive Statistics
3.2. Correlation Analysis
3.3. City-Size Distribution and the Metropolitan Hierarchy in Greece
3.4. Deriving a Spatially Explicit City–Size Relationship for Greece
Estimating Local Regression Parameters
4. Discussion
4.1. Exploring the Spatial Dimension of Metropolitan Hierarchies
4.2. From Global to Local Econometric Models
4.3. Local Econometrics and the Zipf’s Law
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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Variable | 1961 | 1971 | 1981 | 1991 | 2001 | 2011 |
---|---|---|---|---|---|---|
Mean | 374 | 486 | 612 | 650 | 693 | 695 |
Max | 19,809 | 24,650 | 36,781 | 34,431 | 34,106 | 29,976 |
Min | 0 | 0 | 0 | 1 | 1 | 1 |
Std. error | 52 | 67 | 84 | 84 | 85 | 82 |
Median | 42 | 37 | 37 | 38 | 40 | 35 |
25th pctile | 27 | 22 | 21 | 22 | 22 | 17 |
75th pctile | 76 | 70 | 75 | 80 | 91 | 93 |
Skewness | 7.2 | 6.7 | 6.9 | 6.4 | 6.0 | 5.5 |
Kurtosis | 59.5 | 51.4 | 59.9 | 49.7 | 44.8 | 36.2 |
Year | Total Population | Population Density | ||
---|---|---|---|---|
Linear | Log | Linear | Log | |
1961 | −0.909 | −0.843 | −0.842 | −0.962 |
1971 | −0.921 | −0.877 | −0.849 | −0.967 |
1981 | −0.922 | −0.887 | −0.859 | −0.971 |
1991 | −0.927 | −0.894 | −0.870 | −0.974 |
2001 | −0.934 | −0.904 | −0.879 | −0.978 |
2011 | −0.947 | −0.908 | −0.900 | −0.977 |
Parameter | OLS | RMA | MA |
---|---|---|---|
1961 | |||
Slope | −1.352 ± 0.012 | −1.405 ± 0.012 | −1.423 ± 0.012 |
Intercept | 5.227 ± 0.031 | 5.364 ± 0.001 | 5.411 ± 0.001 |
Adjusted-R2 | 0.926 | ||
Global R2 (GWR) | 0.934 | ||
1971 | |||
Slope | −1.500 ± 0.012 | −1.550 ± 0.012 | −1.572 ± 0.013 |
Intercept | 5.567 ± 0.032 | 5.698 ± 0.001 | 5.754 ± 0.001 |
Adjusted-R2 | 0.936 | ||
Global R2 (GWR) | 0.942 | ||
1981 | |||
Slope | −1.606 ± 0.012 | −1.655 ± 0.012 | −1.678 ± 0.013 |
Intercept | 5.857 ± 0.032 | 5.983 ± 0.001 | 6.043 ± 0.001 |
Adjusted-R2 | 0.942 | ||
Global R2 (GWR) | 0.946 | ||
1991 | |||
Slope | −1.650 ± 0.012 | −1.694 ± 0.012 | −1.715 ± 0.012 |
Intercept | 6.001 ± 0.031 | 6.113 ± 0.001 | 6.169 ± 0.001 |
Adjusted-R2 | 0.950 | ||
Global R2 (GWR) | 0.954 | ||
2001 | |||
Slope | −1.690 ± 0.011 | −1.729 ± 0.011 | −1.749 ± 0.012 |
Intercept | 6.135 ± 0.030 | 6.235 ± 0.001 | 6.286 ± 0.001 |
Adjusted-R2 | 0.956 | ||
Global R2 (GWR) | 0.959 | ||
2011 | |||
Slope | −1.806 ± 0.012 | −1.850 ± 0.012 | −1.874 ± 0.013 |
Intercept | 6.387 ± 0.033 | 6.500 ± 0.001 | 6.564 ± 0.001 |
Adjusted-R2 | 0.953 | ||
Global R2 (GWR) | 0.958 |
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Salvia, R.; Quaranta, G.; Rontos, K.; Cudlin, P.; Salvati, L. Investigating Metropolitan Hierarchies through a Spatially Explicit (Local) Approach. ISPRS Int. J. Geo-Inf. 2023, 12, 315. https://doi.org/10.3390/ijgi12080315
Salvia R, Quaranta G, Rontos K, Cudlin P, Salvati L. Investigating Metropolitan Hierarchies through a Spatially Explicit (Local) Approach. ISPRS International Journal of Geo-Information. 2023; 12(8):315. https://doi.org/10.3390/ijgi12080315
Chicago/Turabian StyleSalvia, Rosanna, Giovanni Quaranta, Kostas Rontos, Pavel Cudlin, and Luca Salvati. 2023. "Investigating Metropolitan Hierarchies through a Spatially Explicit (Local) Approach" ISPRS International Journal of Geo-Information 12, no. 8: 315. https://doi.org/10.3390/ijgi12080315
APA StyleSalvia, R., Quaranta, G., Rontos, K., Cudlin, P., & Salvati, L. (2023). Investigating Metropolitan Hierarchies through a Spatially Explicit (Local) Approach. ISPRS International Journal of Geo-Information, 12(8), 315. https://doi.org/10.3390/ijgi12080315