Modeling stem taper profile for Pinus sylvestris plantations using nonlinear quantile regression

ObjectiveThe aim of this study was to develop stem taper equation for Pinus sylvestris based on quantile regression, and the prediction accuracy of the nine quantiles (τ = 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9) and the traditional nonlinear regression stem taper equations was compared and analyzed.

MethodThe stem taper data of 154 Pinus sylvestris plantations in Jinsha Forest Farm of Qitaihe Forestry Bureau was taken as the research object. The single, segmented and variable form taper equations were selected, and the nonlinear quantile regression method was used to construct the stem taper equations of Pinus sylvestris. The performance of all constructed stem taper equations was compared and analyzed by these evaluation statistics: coefficient of determination (R²), mean absolute bias (MAB), root mean square error (RMSE), mean percentage of bias (MPB).

Result(1) The results showed that the stem taper equations could converge at 9 quantiles (τ = 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9), respectively. Quantile regression method can flexibly predict changes in taper curve of each quantile. (2) Compared with the nonlinear regression, the stem taper equations based on the median (τ = 0.5) perform best during the fitting process. The best performance was obtained for the variable exponential equation. (3) The validation results also showed that compared with the nonlinear regression equations, the MAB and MPB of the single taper equation based on the median (τ = 0.5) both decreased by 26.7% and the RMSE decreased by 19.9%. The segmented equation and the variable form equation based on the median (τ = 0.5) showed the better prediction ability. (4) The prediction equations of the median regression are better than the corresponding nonlinear equations for the most stem sections.

ConclusionQuantile regression method is a robust modeling method, the variable exponential equation based on the median (τ = 0.5) shows more prediction precision. It is suitable for the prediction of stem taper for Pinus sylvestris in this region.