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.