Tree Height Prediction Using a Double Hidden-Layer Neural Network and a Mixed-Effects Model

The double hidden-layer neural network has increasingly been applied in tree height modeling due to its superior performance. To improve the precision of tree height estimation, this study compared the performance of a double hidden-layer neural network with that of a nonlinear mixed-effects model, aiming to provide a new method for tree height prediction. Taking the Larix olgensis forest plantation in Jilin Province as the research object, a double hidden-layer back propagation (BP) neural network was established for tree height prediction by adopting trial and error, k-fold cross-validation, and near-domain optimization strategies. In constructing the nonlinear mixed-effects model, the overall and local differences in forest growth data, as well as the autocorrelation among the various levels of data, were considered. Accordingly, after determining the base model, random effects were introduced, the correlation variance-covariance matrix was calculated, and random parameters were estimated to compare the predictive performance of the two aforementioned models. For the mixed-effects model, the coefficient of determination R² was 0.8590, the root mean square error (RMSE) was 1.6230, and the mean absolute error (MAE) was 2.2658. For the double hidden-layer BP neural network, the R² reached 0.9068 (an increase of 5.56%), the RMSE was 1.3197 (a decrease of 18.69%), and the MAE was 1.2736 (a decrease of 43.79%). The results demonstrate that the double hidden-layer BP neural network is superior to the nonlinear mixed-effects model for tree height prediction. Therefore, the results provide a more accurate method for tree height prediction.