Testing for Local Spatial Association Based on Geographically Weighted Interpolation of Geostatistical Data with Application to PM2.5 Concentration Analysis
Abstract
:1. Introduction
2. Methods and Data Sources for Evaluation of the Methods and Demonstration of Their Applicability
2.1. Local-Linear Geographically Weighted Interpolation and Interpolated-Value-Based Local Spatial Statistics with the Bootstrap Test for Significance of Local Spatial Association
2.1.1. Local-Linear Geographically Weighted Interpolation (LGWI)
2.1.2. Interpolated-Value-Based Local Spatial Statistics with the Bootstrap Test for Significance of Local Spatial Association
- (i)
- Based on the interpolated data and the spatial proximity matrix , compute the observed value of according to Equation (12), which we denote by .
- (ii)
- Draw a bootstrap sample with replacement from the interpolated data , on which the bootstrap value of , denoted by , is computed by
- (iii)
- Repeat Step (ii) times and obtain bootstrap values of , which we denote by
- (iv)
- The -value of testing for positive spatial autocorrelation is
2.2. Data Sources for Evaluating the Performance of LGWI and the Bootstrap Test with Interpolated-Value-Based Local Spatial Statistics
2.2.1. Synthetic Data for Evaluating Accuracy of LGWI and Power of the Test
- (i)
- Designed spatial region, sampling points and interpolation points.
- (a)
- Uniformly distributed sampling points on : 200 pairs of random numbers were independently drawn from the uniform distribution with each pair of the random numbers forming a sampling point on .
- (b)
- Unevenly distributed sampling points on : 100 pairs of random numbers were drawn from the normal distribution , where only the points in were retained and the others were discarded until 100 sampling points were obtained. With the same way, the other 100 pairs of random numbers were drawn from . Because of different means and variances of the two normal distributions, the sampling points form roughly two clusters around the means and respectively and are sparely distributed at the upper-left and lower-right corners.
- (ii)
- Model for generating data.
- (a)
- ;
- (b)
- ;
- (c)
- .
- (iii)
- Indices for measuring accuracy of the interpolation methods and power of the tests.
2.2.2. Real-Life Data for Demonstrating Applicability of LGWI and the Test Methods
- (i)
- Original data with preprocessing.
- (ii)
- Data sets formulated to explore seasonal local spatial association patterns of PM2.5 concentration.
3. Results with Comments
3.1. Simulation Results of Evaluating Accuracy of the LGWI Method and Power of the Test
3.1.1. Accuracy of LGWI
3.1.2. Power of the Bootstrap Test with the Interpolated-Value-Based Local Statistics in Identifying Local Spatial Association
3.2. Seasonal Local Spatial Association Patterns of PM2.5 Concentration in Guangdong Province
4. Conclusions and Discussion
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Interpolated Method | Spatial Process | Uniformly Sampling Scheme | Unevenly Sampling Scheme |
---|---|---|---|
LGWI | 0.0762 | 0.0997 | |
0.2018 | 0.2797 | ||
0.2302 | 0.2450 | ||
Kriging (spherical semi-variogram) | 0.1659 | 0.1830 | |
0.3162 | 0.3879 | ||
0.2074 | 0.2144 | ||
Kriging (exponential semi-variogram) | 0.1607 | 0.1757 | |
0.2891 | 0.3840 | ||
0.2089 | 0.2146 | ||
IDW (power parameter = 1) | 0.4824 | 0.4004 | |
0.9300 | 1.0080 | ||
0.4194 | 0.4067 | ||
IDW (power parameter = 2) | 0.2591 | 0.2186 | |
0.5029 | 0.7242 | ||
0.2803 | 0.3017 |
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Wang, F.-J.; Mei, C.-L.; Zhang, Z.; Xu, Q.-X. Testing for Local Spatial Association Based on Geographically Weighted Interpolation of Geostatistical Data with Application to PM2.5 Concentration Analysis. Sustainability 2022, 14, 14646. https://doi.org/10.3390/su142114646
Wang F-J, Mei C-L, Zhang Z, Xu Q-X. Testing for Local Spatial Association Based on Geographically Weighted Interpolation of Geostatistical Data with Application to PM2.5 Concentration Analysis. Sustainability. 2022; 14(21):14646. https://doi.org/10.3390/su142114646
Chicago/Turabian StyleWang, Fen-Jiao, Chang-Lin Mei, Zhi Zhang, and Qiu-Xia Xu. 2022. "Testing for Local Spatial Association Based on Geographically Weighted Interpolation of Geostatistical Data with Application to PM2.5 Concentration Analysis" Sustainability 14, no. 21: 14646. https://doi.org/10.3390/su142114646