Modeling variable exponential taper function for Cunninghamia lanceolata based on quantile regression

  Objective  In order to improve prediction accuracy of Chinese fir stem profile, we used nonlinear quantile regression to establish variable exponential taper equations at different quantile points, and compared their fitting and prediction accuracy with nonlinear regression model.

  Method  This study took 73 Chinese fir (Cunninghamia lanceolata) stem data from the Jiangle Forest Farm in Fujian Province of eastern China. Then we selected 4 variable exponential taper equations, and based on 5-fold cross-validation, used nonlinear quantile regression and nonlinear regression to establish taper equations, respectively. Five model evaluation indicators were selected, including the adjusted coefficient of determination (R²), root mean square error (RMSE), average error (ME), relative error (RE) and average absolute error (MAE), combined with graphs to evaluate the fitting and prediction results.

  Result  The research results showed: (1) the 4 variable exponential taper equations converged at all quantile points (t = 0.1, 0.3, 0.5, 0.7, 0.9), indicating that quantile regression can develop different models at different quantiles. So this method can describe the change of Chinese fir stem shape more comprehensively. (2) The accuracy of four taper equations at the quantile point of 0.5 was all higher than others, with R² about 0.97. For taper equations M1 and M3, the fitting and prediction accuracy based on the median regression (t = 0.5) were both higher than those of nonlinear regression. And the prediction values of the M1 equation were more concentrated. (3) At different quantile points, models had different prediction accuracies for varied stem positions. Models with quantile values of 0.9 and 0.3 had the highest prediction accuracy for the stem top part and the base part, respectively.

  Conclusion  The variable exponential taper equations developed by quantile regression can not only accurately predict stem diameters under average condition, but also predict the changing trend of stem shape under arbitrary quantile conditions. Quantile models have different prediction accuracies for varied stem positions. The multi-quantile regression model of M1 can further improve the prediction accuracy of the Chinese fir stem profile.