Objective This paper aims to construct a nonlinear mixed-effects model for the tree height-DBH relationship of Pinus koraiensis, compare the prediction accuracy of various sampling methods and sample sizes, and provide a theoretical basis for understanding the growth patterns of Pinus koraiensis.

Method This study used 4 441 sets of data from two sample plots in Jiaohe, Jilin Province, and Liangshui, Heilongjiang Province of northeastern China. The data were randomly divided into two parts, with 80% used for modeling and 20% for validation. Fifteen common tree height-DBH models were fitted, and the best-performing model was selected as the base model. Variables such as basal area, dominant height, and quadratic mean diameter were added to the base model to construct the optimal generalized model. Random effects at the plot level were also considered, resulting in the construction of a base mixed-effects model and a generalized mixed-effects model. The fitting ability and prediction accuracy of two fixed-effects models and two nonlinear mixed-effects models were evaluated. We validated the model prediction accuracy using validation data, compared three prediction types: fixed effects model average prediction (FPA), mixed model overall mean response prediction (MPA), and subject response prediction (MPS). Additionally, we analyzed the prediction accuracy and relationship between sample size and four sampling schemes for the mixed model: random sampling, the largest DBH sampling, the smallest DBH sampling, and average tree sampling (samples with DBH close to the average value).

Result (1)The optimal base model was the Prodan model (R², RMSE, MAE were 0.841, 3.335 m, 2.492 m, respectively). The generalized model incorporating quadratic mean , dominant height, and basal area had the highest prediction accuracy (R², RMSE, MAE were 0.914, 2.449 m, 1.816 m, respectively). Introducing plot-level random effects significantly improved model accuracy; the base mixed-effects model had R², RMSE, MAE of 0.961, 1.652 m, 1.231 m, respectively, and the generalized mixed-effects model had R², RMSE, MAE of 0.958, 1.719 m, 1.288 m, respectively. (2) Model accuracy tested with validation data showed MPA > FPA > MPS, and prediction accuracy of generalized model was better than base model. (3) Among four sampling schemes, the sampling method of average trees was the best, and the prediction ability was the best when eight trees were selected; in practical application, considering the labor cost and economic cost, the method of selecting five average trees to measure the tree height to estimate the random parameters was also reasonable and feasible.

Conclusion Incorporating stand factors and plot effects into the base model significantly improves the accuracy of tree height-DBH model for Pinus koraiensis. Additionally, the sampling method using average trees provides higher prediction accuracy. This study explores the relationship between tree height and DBH of Pinus koraiensis under a nonlinear mixed-effects model. It provides a theoretical foundation and practical reference for accurately predicting tree height of Pinus koraiensis, the main constructive species in northeastern China, as well as for subsequent field surveys and management practices.