Estimating Sub-Pixel Soybean Fraction from Time-Series MODIS Data Using an Optimized Geographically Weighted Regression Model
Abstract
:1. Introduction
2. Study Area and Datasets
2.1. Study Area
2.2. Sample Data
2.3. Feature Set
2.4. Census Data
3. Methodology
3.1. An Optimized Geographically Weighted Regression Model
3.1.1. The Basic Framework of GWR Model
3.1.2. A Forward Stepwise Strategy for Selecting the Optimal Independent Variables
- Step 1: Start by calibrating all possible bivariate GW regressions by in turn regressing a single explanatory variable against the dependent variable. Calculate AICc in each case (31 runs in this study). Select the variable that produces the lowest AICc.
- Step 2: Sequentially introduce a variable from the remaining n − 1 features to construct new models with the permanently included independent variable in step 1. Calculate the change in AICc between step1 and step 2. Select variable yielding greatest reduction in AICc. Add this variable to the model.
- Step 3: Repeat step 2 until no independent variables among the candidate variables can be added into the model, and the model at this point is the final model.
3.1.3. F-Test Statistics
3.2. Accuracy Assessment
4. Results
4.1. Descriptive Statistics
4.2. The Optimal Independent Variables for Soybean Cultivation
4.3. GWR Results of Sub-Pixel Soybean Area Estimation
4.4. Sub-Pixel Soybean Map and Accuracy Assessment
5. Discussion
6. Conclusions
Acknowledgments
Author Contributions
Conflicts of Interest
References
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Model | AICc | RSS | R2 | Adjusted R2 |
---|---|---|---|---|
GWR | −3087.201 | 85.8289 | 0.5144 | 0.4377 |
OLS | −2220.059 | 132.1226 | 0.2524 | 0.2466 |
Variables | F-Value | NDF | DDF | p-Value (Significance) | |
---|---|---|---|---|---|
F1-test | / | 0.75 | 3606.49 | 3966 | <2.20 × 10−16 *** |
F3-test | Intercept | 6.85 | 348.37 | 3606.5 | <2.20×10−16 *** |
NDVI_65 | 1.81 | 523.21 | 3606.5 | <2.20 × 10−16 *** | |
NDVI_73 | 2.59 | 457.76 | 3606.5 | <2.20 × 10−16 *** | |
NDVI_81 | 1.78 | 445.29 | 3606.5 | <2.20 × 10−16 *** | |
NDVI_89 | 0.72 | 353.16 | 3606.5 | 0.999973 | |
NDVI_97 | 4.75 | 332.68 | 3606.5 | <2.20 × 10−16 *** | |
NDVI_105 | 2.08 | 258.34 | 3606.5 | <2.20 × 10−16 *** | |
NDVI_113 | 3.61 | 269.81 | 3606.5 | <2.20 × 10−16 *** | |
NDVI_121 | 1.15 | 484.77 | 3606.5 | 0.019104 * | |
NDVI_129 | 1.02 | 485.38 | 3606.5 | 0.354737 | |
NDVI_137 | 1.15 | 736.19 | 3606.5 | 0.006462 ** | |
NDVI_145 | 1.32 | 589.97 | 3606.5 | 2.18 × 10−6 *** | |
NDVI_153 | 0.53 | 666.26 | 3606.5 | 1 | |
NDVI_161 | 0.86 | 907.46 | 3606.5 | 0.998103 | |
NDVI_169 | 2.46 | 904.98 | 3606.5 | <2.20 × 10−16 *** | |
NDVI_177 | 1.25 | 610.68 | 3606.5 | 8.12 × 10−5 *** | |
NDVI_185 | 1.04 | 407.12 | 3606.5 | 0.296108 | |
NDVI_193 | 1.40 | 629.78 | 3606.5 | 6.44 × 10−9 *** | |
NDVI_201 | 0.85 | 292.13 | 3606.5 | 0.969006 | |
NDVI_209 | 0.77 | 226.61 | 3606.5 | 0.995028 | |
NDVI_217 | 1.64 | 252.09 | 3606.5 | 4.06 × 10−9 *** | |
NDVI_225 | 4.43 | 160.93 | 3606.5 | <2.20 × 10−16 *** | |
NDVI_233 | 7.19 | 227.22 | 3606.5 | <2.20 × 10−16 *** | |
NDVI_241 | 13.18 | 336.43 | 3606.5 | <2.20 × 10−16 *** | |
NDVI_249 | 2.70 | 632.45 | 3606.5 | <2.20 × 10−16 *** | |
NDVI_257 | 11.21 | 711.35 | 3606.5 | <2.20 × 10−16 *** | |
NDVI_265 | 2.93 | 772.44 | 3606.5 | <2.20 × 10−16 *** | |
NDVI_273 | 3.30 | 955.55 | 3606.5 | <2.20 × 10−16 *** | |
NDVI_281 | 2.40 | 737.06 | 3606.5 | <2.20 × 10−16 *** | |
NDVI_289 | 2.13 | 622.15 | 3606.5 | <2.20 × 10−16 *** | |
NDVI_297 | 1.80 | 418.44 | 3606.5 | <2.20 × 10−16 *** | |
NDVI_305 | 1.55 | 634.59 | 3606.5 | 1.28 × 10−14 *** |
Distance Calculation Ways | Bandwidth | AICc | RSS | R2 | Adjusted R2 |
---|---|---|---|---|---|
GCS/WGS84 (Great circle) | 736 | −3087.201 | 85.8289 | 0.5144 | 0.4377 |
Sinusoidal (Euclidean distance) | 687 | −2928.25 | 88.4218 | 0.4997 | 0.4177 |
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Hu, Q.; Ma, Y.; Xu, B.; Song, Q.; Tang, H.; Wu, W. Estimating Sub-Pixel Soybean Fraction from Time-Series MODIS Data Using an Optimized Geographically Weighted Regression Model. Remote Sens. 2018, 10, 491. https://doi.org/10.3390/rs10040491
Hu Q, Ma Y, Xu B, Song Q, Tang H, Wu W. Estimating Sub-Pixel Soybean Fraction from Time-Series MODIS Data Using an Optimized Geographically Weighted Regression Model. Remote Sensing. 2018; 10(4):491. https://doi.org/10.3390/rs10040491
Chicago/Turabian StyleHu, Qiong, Yaxiong Ma, Baodong Xu, Qian Song, Huajun Tang, and Wenbin Wu. 2018. "Estimating Sub-Pixel Soybean Fraction from Time-Series MODIS Data Using an Optimized Geographically Weighted Regression Model" Remote Sensing 10, no. 4: 491. https://doi.org/10.3390/rs10040491
APA StyleHu, Q., Ma, Y., Xu, B., Song, Q., Tang, H., & Wu, W. (2018). Estimating Sub-Pixel Soybean Fraction from Time-Series MODIS Data Using an Optimized Geographically Weighted Regression Model. Remote Sensing, 10(4), 491. https://doi.org/10.3390/rs10040491