Height-diameter equations for larch plantations in northern and northeastern China: a comparison of the mixed-effects, quantile regression and generalized additive models

Alternative methods have been used for developing tree basic and generalized height-diameter models, including non-linear least-squares regression, non-linear mixed-effects method, quantile regression (QR) and a generalized additive model (GAM). However, these approaches have not been thoroughly compared. The purpose of this study was to compare these methods applied to tree height-diameter models for larch plantations in northern and northeastern China. The data were obtained from an extensive database curated by the China National Forest Inventory (NFI) that covers a wide distribution and range of stand conditions, including 5684 paired heights and diameters in 342 plots. Random effects at the Province, species and plot levels, and a combination of Province and species into the basic and generalized H-D models were incorporated. This study demonstrated that the mixed-effects basic model provided the best performance for model fitting and validation; QR could represent variable H-D relationships at different quantiles and the GAM was a suitable alternative for flexible modelling of the H-D relationship, especially for generalized H-D model. This finding indicates that the mixed-effects basic model does not require additional variables and is an adequate tool for generating missing height measurements for larch plantations in northern and northeastern China.