Comparison of Parametric and Nonparametric Methods for Estimating Size–Density Relationships in Old-Growth Japanese Cedar (Cryptomeria japonica D. Don) Plantations
Abstract
:1. Introduction
2. Materials and Methods
2.1. Data
2.1.1. National Forest Resource Inventory Permanent Plots
2.1.2. Long-Term Experimental Plots
2.2. Parametric and Nonparametric Methods
2.2.1. Segmented Regression Models
2.2.2. Penalized Spline
2.2.3. Random Forest for Regression
2.3. Parameter Estimation and Method Evaluation
3. Results and Discussion
3.1. Size–Density Relationships Estimated by the Segmented Regression Models
3.2. Comparison of Parametric and Nonparametric Methods
4. Conclusions
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
References
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Sources | # of Plots | # of Obs. | Stand Variable | Average | Min. | Max. | Std. |
---|---|---|---|---|---|---|---|
Long-term experimental plots | 15 | 460 | Age | 36 | 2 | 105 | 24 |
DBH | 26.6 | 1.1 | 56.1 | 10.4 | |||
Dq | 27.4 | 1.1 | 58.8 | 10.6 | |||
TPH | 1269 | 190 | 3657 | 693 | |||
BA | 60.5 | 0.2 | 170.2 | 26.2 | |||
NFRI permanent plots | 222 | 515 | Age | 43 | 8 | 93 | 14 |
DBH | 25.9 | 11.9 | 55.6 | 8.2 | |||
Dq | 27.2 | 12.1 | 57.4 | 7.6 | |||
TPH | 1316 | 340 | 4400 | 604 | |||
BA | 79.5 | 13.3 | 197.6 | 35 |
Coefficient | Full Model | Reduced Model | ||
---|---|---|---|---|
Estimate | p-Value | Estimate | p-Value | |
β1 | 7.850 | <0.0001 * | 7.949 | <0.0001 * |
β2 | −1.267 | 0.079 | −0.445 | <0.0001 * |
β3 | −1.579 | 0.008 * | ||
β4 | −1.293 | <0.0001 * | ||
α1 | 2.389 | <0.0001 * | 1.833 | <0.0001 * |
α2 | 3.027 | 0.225 | ||
α3 | 3.211 | <0.0001 * |
Method | Fitting Data | Validation Data | ||
---|---|---|---|---|
MB | RMSE | MB | RMSE | |
Segmented Regression (Full) | 0.000 | 0.079 | 0.098 | 0.153 |
Segmented Regression (Reduced) | 0.000 | 0.083 | 0.083 | 0.151 |
Penalized Spline | 0.000 | 0.075 | 0.103 | 0.158 |
Random Forest for Regression | −0.001 | 0.040 | 0.110 | 0.190 |
Fitting Data | ||||||||
---|---|---|---|---|---|---|---|---|
Method | Stage I | Stage II | ||||||
Phase I | Phase II | Phase III | ||||||
MB | RMSE | MB | RMSE | MB | RMSE | MB | RMSE | |
Segmented Regression (Full) | −0.002 | 0.059 | 0.000 | 0.032 | −0.058 | 0.060 | 0.002 | 0.105 |
Segmented Regression (Reduced) | −0.061 | 0.073 | 0.080 | 0.039 | −0.032 | 0.062 | −0.016 | 0.106 |
Penalized Spline | −0.004 | 0.054 | 0.005 | 0.032 | −0.019 | 0.060 | 0.004 | 0.098 |
Random Forest for Regression | 0.010 | 0.021 | −0.003 | 0.018 | 0.002 | 0.032 | −0.002 | 0.052 |
Validation Data | ||||||||
Method | Stage I | Stage II | ||||||
Phase I | Phase II | Phase III | ||||||
MB | RMSE | MB | RMSE | MB | RMSE | MB | RMSE | |
Segmented Regression (Full) | - | - | −0.015 | 0.141 | −0.058 | 0.158 | 0.179 | 0.154 |
Segmented Regression (Reduced) | - | - | 0.049 | 0.144 | −0.033 | 0.158 | 0.143 | 0.150 |
Penalized Spline | - | - | −0.013 | 0.141 | −0.019 | 0.159 | 0.192 | 0.164 |
Random Forest for Regression | - | - | −0.003 | 0.140 | −0.021 | 0.175 | 0.202 | 0.212 |
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Chiou, C.-R.; Cheng, C.-P.; Yang, S.-I. Comparison of Parametric and Nonparametric Methods for Estimating Size–Density Relationships in Old-Growth Japanese Cedar (Cryptomeria japonica D. Don) Plantations. Forests 2020, 11, 625. https://doi.org/10.3390/f11060625
Chiou C-R, Cheng C-P, Yang S-I. Comparison of Parametric and Nonparametric Methods for Estimating Size–Density Relationships in Old-Growth Japanese Cedar (Cryptomeria japonica D. Don) Plantations. Forests. 2020; 11(6):625. https://doi.org/10.3390/f11060625
Chicago/Turabian StyleChiou, Chyi-Rong, Ching-Peng Cheng, and Sheng-I Yang. 2020. "Comparison of Parametric and Nonparametric Methods for Estimating Size–Density Relationships in Old-Growth Japanese Cedar (Cryptomeria japonica D. Don) Plantations" Forests 11, no. 6: 625. https://doi.org/10.3390/f11060625