Unveiling the Spatial Non-Stationarity Between Built Environment and External Relations in Small Towns Using MGWR and Mobile Phone Data: Evidence from the Yangtze River Delta
Abstract
1. Introduction
2. Literature Review
2.1. Theoretical Foundation of External Relations of Towns
2.2. Factors and Spatial Heterogeneity of External Relations of Towns
2.3. Spatial Autocorrelation and Non-Stationarity in Urban Networks
3. Methodology
3.1. Study Framework
| Category | Variable | Description | Unit | Data Sources |
|---|---|---|---|---|
| Economic development | X1 Enterprise | Number of enterprises per square kilometer. | count/km2 | Bureau of Industry and Commerce. |
| X2 Housing prices | Average housing price per square meter. | yuan/m2 | Anjuke Platform. (https://anjuke.com) | |
| Ecological environment | X3 PM2.5 | Concentration of PM2.5 in the air. | μg/m3 | The China High Air Pollutants (CHAP) dataset provided by the National Tibetan Plateau Science Data Center [59,60] (http://data.tpdc.ac.cn) |
| X4 Blue and Green Space | Percentage of water and vegetation spaces. | % | Sentinel-2 imagery from the Copernicus Data Space Ecosystem. (https://dataspace.copernicus.eu) | |
| Recreation and entertainment | X5 Commercial facility | Number of malls per square kilometer. | count/km2 | Amap. (https://www.amap.com/) |
| X6 Park | Number of parks per square kilometer. | count/km2 | ||
| Public service facilities | X7 Middle School | Number of middle schools per square kilometer. | count/km2 | |
| X8 Third-grade class-A hospital | Number of tertiary hospitals per square kilometer. | count/km2 | ||
| Transportation facilities | X9 Bus Stop | Number of bus stops per square kilometer. | count/km2 | |
| X10 Road Network | kilometers of roads per square kilometer. | km/km2 | ||
| Administrative factors | X11 Administrative System | Two-tier System of County Seats and Small Towns | - | - |
3.2. Study Area
3.3. Data and Methods
3.3.1. Mobile Phone Data to Identify People Flow
- Identification of home
- 2.
- Identification of workplace
- 3.
- Identification of recreational place

3.3.2. The Method for Defining the City-Ness and Town-Ness of People Flow Between County Towns and Small Towns
3.3.3. Spatial Environmental Data
3.3.4. The Regression Analysis Method for Spatial Influencing Factors
- Spatial autocorrelation and baseline diagnostics
- 2.
- Global spatial models (SAR and SEM)
- 3.
- Multiscale geographically weighted regression (MGWR)
4. Results
4.1. Spatial Patterns of External Relations of Towns
4.2. Results of OLS, SAR, SEM, GWR, and MGWR Models
4.2.1. Preliminary Selection of Influencing Factors

| Variable | VIF |
|---|---|
| X1 Enterprise | 1.37 |
| X2 Housing prices | 1.69 |
| X3 PM2.5 | 1.39 |
| X4 Blue and Green Spaces | 1.45 |
| X5 Commercial facility | 2.54 |
| X6 Park | 3.06 |
| X7 Middle School | 2.59 |
| X8 Tertiary Hospitals | 2.88 |
| X9 Bus Stop | 2.74 |
| X10 Road Network | 1.24 |
| X11 Administrative System | 2.26 |
4.2.2. Comparison of OLS, SAR, SEM, GWR, and MGWR Models
4.2.3. Scale Analysis of the MGWR Model
4.3. Unpacking Spatial Non-Stationarity of City-Ness and Town-Ness
4.3.1. Spatial Non-Stationarity of Commuting City-Ness
4.3.2. Spatial Non-Stationarity of Commuting Town-Ness


4.3.3. Spatial Non-Stationarity of Recreational City-Ness
4.3.4. Spatial Non-Stationarity of Recreational Town-Ness

5. Discussion
5.1. Plausible Differentiated Mechanisms of the Built Environment Influencing City-Ness and Town-Ness
5.2. Spatial Heterogeneity and Plausible Mechanisms of Key Built Environment Factors
5.2.1. The Spatial Logic of the Jobs–Housing Separation: The Spatial Heterogeneity of Industrial and Housing Factors
5.2.2. Retention Mechanism of Social Anchors: The Spatial Heterogeneity of Education, Hospitals and Commercial Facilities
5.2.3. Hierarchical Lock-In of Connectivity: The Spatial Heterogeneity of Transportation Infrastructure and Administrative Ranks
5.3. Differentiated Territorial Spatial Planning Strategies for Small Towns Based on Spatial Non-Stationarity
5.4. Limitations
6. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
Abbreviations
| CFT | Central Flow Theory |
| MGWR | Multiscale Geographically Weighted Regression |
| CPT | Central Place Theory |
| APS | Advanced Producer Services |
| YRD | Yangtze River Delta |
| NEG | New Economic Geography |
| LISA | Local Indicators of Spatial Association |
| SAR | Spatial Autoregressive |
| SEM | Spatial Error Model |
| CHAP | The China High Air Pollutants |
| POI | Points of Interest |
| OLS | Ordinary Least Squares |
| GWR | Geographically Weighted Regression |
| VIF | Variance Inflation Factor |
| TOD | Transit-Oriented Development |
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| Dependent Variables | Model Goodness-of-Fit | ||||
|---|---|---|---|---|---|
| RSS | AICC | Adj. R2 | Pseudo-R2 | ||
| Commuting City-ness | OLS | 1898.921 | 6163.367 | 0.181 | - |
| SAR | 1877.609 | 6145.012 | - | 0.195 | |
| SEM | 1899.700 | 6136.043 | - | 0.185 | |
| GWR | 432.840 | 3747.789 | 0.814 | - | |
| MGWR | 355.433 | 3028.962 | 0.822 | - | |
| Commuting Town-ness | OLS | 1231.038 | 5153.046 | 0.469 | - |
| SAR | 887.214 | 4485.857 | - | 0.620 | |
| SEM | 1309.388 | 4475.731 | - | 0.450 | |
| GWR | 424.052 | 3760.900 | 0.775 | - | |
| MGWR | 375.769 | 3217.014 | 0.809 | - | |
| Recreational City-ness | OLS | 1458.038 | 5547.530 | 0.372 | - |
| SAR | 1328.452 | 5375.768 | - | 0.431 | |
| SEM | 1390.388 | 4475.731 | - | 0.371 | |
| GWR | 516.015 | 4028.115 | 0.735 | - | |
| MGWR | 405.631 | 3310.615 | 0.797 | - | |
| Recreational Town-ness | OLS | 888.722 | 4393.540 | 0.617 | - |
| SAR | 603.969 | 3586.957 | - | 0.741 | |
| SEM | 962.390 | 3538.477 | - | 0.600 | |
| GWR | 327.960 | 3031.812 | 0.830 | - | |
| MGWR | 279.786 | 2502.412 | 0.859 | - | |
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Li, Y.; Wang, Y.; Han, M.; Xia, Y.; Ma, Y. Unveiling the Spatial Non-Stationarity Between Built Environment and External Relations in Small Towns Using MGWR and Mobile Phone Data: Evidence from the Yangtze River Delta. Land 2026, 15, 659. https://doi.org/10.3390/land15040659
Li Y, Wang Y, Han M, Xia Y, Ma Y. Unveiling the Spatial Non-Stationarity Between Built Environment and External Relations in Small Towns Using MGWR and Mobile Phone Data: Evidence from the Yangtze River Delta. Land. 2026; 15(4):659. https://doi.org/10.3390/land15040659
Chicago/Turabian StyleLi, Yang, Yao Wang, Min Han, Yuli Xia, and Yan Ma. 2026. "Unveiling the Spatial Non-Stationarity Between Built Environment and External Relations in Small Towns Using MGWR and Mobile Phone Data: Evidence from the Yangtze River Delta" Land 15, no. 4: 659. https://doi.org/10.3390/land15040659
APA StyleLi, Y., Wang, Y., Han, M., Xia, Y., & Ma, Y. (2026). Unveiling the Spatial Non-Stationarity Between Built Environment and External Relations in Small Towns Using MGWR and Mobile Phone Data: Evidence from the Yangtze River Delta. Land, 15(4), 659. https://doi.org/10.3390/land15040659

