Objective The aim of this study was to construct tree height equation for quantile regression and mixed-effects based on nonlinear regression and generalized models. And fitting effect and prediction accuracy of nonlinear models, different quntile models (τ = 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9), generalized models and nonlinear mixed-effects models were compared and analyzed, so as to provide theoretical basis for further study of stand growth and harvest.

Method Based on 21.12 ha sample plot data, taking the main tree species (Pinus koraiensis, Acer mono, Tilia amurensis and Fraxinus mandshurica) from coniferous and broadleaved mixed forest of Jiaohe, Jilin Province of northeastern China as the research object. And the base model was first selected from 11 widely-used tree height equations, then we explored the influence of stand variables on tree height and constructed generalized model containing stand variables. Finally, on the basis of basic model and the generalized model, the quantile model was constructed, and the mixed-effect model was established considering the impact of sample effect on tree height.

Result (1) Richards was selected as base model for all tree species because of its higher fitting accuracy and biological significance. And considering the correlation between stand variables and tree height and the convergence of models, the generalized model established by adding dominant tree height can significantly improve the fitting effect. (2) All models based on the median (τ = 0.5) performed best, and the prediction accuracy was close to the nonlinear regression. The highest R² values of Pinus koraiensis, Acer mono, Tilia amurensis and Fraxinus mandshurica were 0.811, 0.809, 0.724 and 0.617, respectively. The generalized median regression prediction ability was further improved, and R² values were 0.891, 0.874, 0.858 and 0.627, respectively. (3) Mixed-effect models can significantly improve the prediction accuracy compared with other models, among which base mixed model was slightly better than generalized mixed model, and the R² values of four tree species reached 0.937, 0.919, 0.906 and 0.643, respectively, indicating that mixed models including sample effect can improve the more accurate and stable prediction results.

Conclusion Compared with base model, generalized model and median regression model established by traditional methods, the height-diameter model based on nonlinear mixed-effects has higher prediction accuracy, and base mixed-effects model has superiority and stability for height-DBH model construction of mixed forests in Jiaohe, Jilin Province of northeastern China.