Spatial Differentiation in the Contribution of Innovation Influencing Factors: An Empirical Study in Nanjing from the Perspective of Nonlinear Relationships
Abstract
1. Introduction
2. Materials and Methods
2.1. Study Area
2.2. Materials
2.2.1. Innovation Space Agglomeration Measurement
2.2.2. Factor Selection
- Basic infrastructure (road accessibility, public transit networks, metro stations);
- Research resources (universities, patents);
- Industrial ecosystem (innovation platforms, top 100 enterprises);
- Human capital (population distribution);
- Cultural amenities (park-green spaces, art galleries, integrated commercial hubs).
2.3. Preprocessing
2.3.1. Normalization
- : Normalized value of the -th indicator
- : Original value of the -th indicator
- : Minimum observed value of the -th indicator
- : Maximum observed value of the -th indicator
- : Index enumerating the 12 explanatory variables in this study
2.3.2. Global Spatial Autocorrelation Analysis
- : Moran’s Index value (range: [−1, 1])
- : Total number of spatial observational units
- , : Observed values at spatial units and , respectively
- : Global mean of all observed values
- : Spatial weight between units and
- : Sample variance
- Statistical inference
- Z-score > 2.58 (equivalent to p < 0.01) indicates statistically significant spatial clustering at the 99% confidence level.
- Interpretation: Observed spatial clustering of innovation activities rejects the null hypothesis of complete spatial randomness (CSR).
2.4. Model Selection Framework
2.4.1. Multiple Linear Regression (MLR) Model
- : Measured value of innovation space agglomeration intensity within the -th spatial grid cell ( = 1, 2)
- : Global intercept term reflecting baseline agglomeration level
- : Partial regression coefficients quantifying the marginal effects of the 11 explanatory variables
- : Independently identically distributed (i.i.d.) error term capturing
2.4.2. Gradient Boosted Regression Tree (GBRT) Model
2.4.3. Multiscale Geographically Weighted Regression (MGWR) Model
2.4.4. Methodology Framework
- Stage 1: Collinearity Diagnostics:The MLR model was employed for collinearity diagnostics among influencing factors, establishing prerequisite conditions for subsequent analyses [53].
- Stage 2: Nonlinear Relationship Identification:The GBRT model was used to detect potential nonlinear associations between influencing factors and innovation space agglomeration intensity, while quantifying statistical significance and marginal effects.
- Stage 3: Spatial Heterogeneity Analysis:The MGWR model was constructed with the dataset to investigate spatial differentiations in contributions from distinct influencing factors to innovation space agglomeration across geographical units.
3. Results
3.1. Collinearity Diagnostics of Influencing Factors
3.2. Analysis of Influencing Factors, Contribution Significance, and Marginal Effects
- First item: Sustained growth pattern
- 2.
- Second item: Growth-stabilization pattern
- 3.
- Third item: Growth-decline pattern
- 4.
- Fourth item: Global stabilization pattern
- 5.
- Fifth item: Global fecline pattern
3.3. Spatial Differentiation Characteristics of Marginal Effects in Influencing Factors
3.3.1. Analysis of Model Computational Results
3.3.2. Spatial Differentiation in Contributions of Influencing Factors
- First item: Industrial ecosystem analysis
- 2.
- Second item: Research resources analysis
- 3.
- Third item: Cultural amenities analysis
4. Conclusions
- Sustained growth pattern (innovation platforms);
- Growth-stabilization pattern (patents; metro stations; road accessibility; art galleries);
- Growth-decline pattern (integrated commercial hubs; top 100 enterprises; universities);
- Global stabilization pattern (park-green spaces);
- Global decline pattern (public transit networks; population distribution).
5. Discussion
5.1. Further Discussion
- Saturation Effect Dominance:During the baseline period, the density levels of these factors had already reached elevated levels, resulting in minimal marginal innovation benefits from further density increases.
- Cost Pressure Trigger:High-density zones of these factors demonstrate strong spatial coupling with central districts, where consequential high land prices and rental costs compress operational space for innovation agents (particularly startups).
5.2. Policy Recommendations
5.2.1. Innovation Resource Integration Optimization
5.2.2. Regional Spatial Quality Enhancement
5.3. Future Outlook
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
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Innovation Entity Types | Innovation Entity | Source | POI Count (2023) |
---|---|---|---|
Research-oriented | Research Institutions | AutoNavi | 914 |
Research Centers | AutoNavi | ||
Multi-tier Laboratories | AutoNavi | ||
Production-oriented | High-Tech Enterprises | www.innocom.gov.cn | 6658 |
Incubation-oriented | National Makerspaces | www.qcc.com | 35 |
National Technology Incubators | www.qcc.com | 60 | |
Provincial Technology Incubators | www.qcc.com | 62 | |
Total | 7729 |
Types | Influencing Factors | Statistical Description | Note |
---|---|---|---|
Basic Infrastructure | road accessibility | Road accessibility within the grid | Vector road network processed via AutoNavi Route Planning API, accessibility computed with OD cost matrix. |
public transit networks | Kernel density of public transit network within the grid | Average kernel density of public transit networks within the grid across the study area. | |
metro stations | Kernel density of metro stations within the grid | Average kernel density of metro stations within the grid across the study area. | |
Research Resources | universities | Weighted kernel density of universities within the grid | Kernel density of universities weighted by institutional ranking (assigned scores: 5 for top-tier, 4, 3, 2, 1 for lower tiers). |
patents | Kernel density of patents within the grid | Invention and utility model patents with a value score >80 over the past decade (as of 31 December 2023). | |
Industrial Ecosystem | innovation platforms | Kernel density of innovation platforms within the grid | Represents regional innovation planning layout; independent of the dependent variable (incubation-type innovation entities). |
top 100 enterprises | Kernel density of top 100 enterprises within the grid | Top 100 enterprises act as industrial anchors, attracting upstream and downstream innovation firms. Note: Partial overlap with dependent variable indicators, but impact on regression results is negligible due to limited sample size (<100 entries in the study area). | |
Human Capital | population distribution | Population density within the grid | |
Cultural Amenities | park-green spaces | Scored proximity to parks from grid centroids | Scoring based on shortest distance from grid centroid to park green spaces: Parks with area > 100,000 m2: Score 5 if distance < 1500 m; score 3 if 1500–4000 m; score 1 if 4000–6000 m. Parks with area 10,000–100,000 m2: Score 3 if distance < 1500 m; score 1 if 1500–3000 m. Parks with area < 10,000 m2: Score 3 if distance < 750 m. |
art galleries | Kernel density of art galleries within the grid | Average kernel density of art galleries within the grid across the study area. | |
integrated commercial hubs | Kernel density of integrated commercial hubs within the grid | Average kernel density of integrated commercial hubs within the grid across the study area. |
Influencing Factors | Coefficient | Robust_Pr (p) | VIF |
---|---|---|---|
road accessibility | 4.357366 | 0.001298 * | 1.896368 |
public transit networks | −17.774658 | 0.000000 * | 4.40435 |
metro stations | 6.134481 | 0.001901 * | 3.966856 |
universities | 3.526029 | 0.469566 | 4.714737 |
innovation platforms | 35.145364 | 0.000000 * | 1.704641 |
top 100 enterprises | 10.480851 | 0.017388 * | 3.059993 |
patents | 10.573542 | 0.005728 * | 3.843127 |
population distribution | −3.798563 | 0.513066 | 2.32027 |
park-green spaces | 0.017923 | 0.988579 | 1.239891 |
art galleries | −1.278176 | 0.761103 | 2.630183 |
integrated commercial hubs | 14.923316 | 0.001573 * | 3.15158 |
AdjR2 | AICc | Koenker (BP) (p) | Joint Wald Statistic (p) |
0.568 | 6412.166 | 0.000000 * | 0.000000 * |
Influencing Factors | MCT (p) | Bandwidth | STD |
---|---|---|---|
road accessibility | 0.740 | 916.000 | 0.004 |
public transit networks | 0.794 | 916.000 | 0.004 |
metro stations | 0.582 | 916.000 | 0.005 |
universities | 0.000 | 50.000 | 0.463 |
innovation platforms | 0.000 | 43.000 | 0.295 |
top 100 enterprises | 0.997 | 916.000 | 0.001 |
patents | 0.000 | 45.000 | 0.452 |
population distribution | 1.000 | 916.000 | 0.001 |
park-green spaces | 0.976 | 916.000 | 0.002 |
art galleries | 0.000 | 52.000 | 0.639 |
integrated commercial hubs | 0.000 | 52.000 | 0.274 |
AdjR2 | AICc | Residual sum of squares | Log-likelihood |
0.874 | 897.981 | 96.759 | −270.052 |
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Wang, C.; Luo, R.; Zhou, L. Spatial Differentiation in the Contribution of Innovation Influencing Factors: An Empirical Study in Nanjing from the Perspective of Nonlinear Relationships. Buildings 2025, 15, 2565. https://doi.org/10.3390/buildings15142565
Wang C, Luo R, Zhou L. Spatial Differentiation in the Contribution of Innovation Influencing Factors: An Empirical Study in Nanjing from the Perspective of Nonlinear Relationships. Buildings. 2025; 15(14):2565. https://doi.org/10.3390/buildings15142565
Chicago/Turabian StyleWang, Chengyu, Renchao Luo, and Lingchao Zhou. 2025. "Spatial Differentiation in the Contribution of Innovation Influencing Factors: An Empirical Study in Nanjing from the Perspective of Nonlinear Relationships" Buildings 15, no. 14: 2565. https://doi.org/10.3390/buildings15142565
APA StyleWang, C., Luo, R., & Zhou, L. (2025). Spatial Differentiation in the Contribution of Innovation Influencing Factors: An Empirical Study in Nanjing from the Perspective of Nonlinear Relationships. Buildings, 15(14), 2565. https://doi.org/10.3390/buildings15142565