Development of growth models for spruce based on mixed-effects models

The study of growth model is a basic research in forest growth and yield modeling. Most of growth models were developed using ordinary regression method. It is assumed that the observations were independent and obey Gauss distribution. Those models reflect the average growth across different plots, but neglect the correlation and variance between individuals and plots. However, mixed-effects models which include both fixed and random parameters could solve the problem very well. Our objective is to develop growth models for main tree species spruce in Changbai Mountains by using mixed-effects models. 14 clear cutting plots were investigated in Changbai Mountain area, China. Data of 619 individual trees including age, height, diameter, and volume were used in this study to calibrate the growth models. Richards model and its mixed-effects model were used to develop growth models by using PROC NLIN and PROC NLMIXED in SAS. Decision coefficient (R²), root mean square error (RMSE), and mean absolute difference (MAD) were used to evaluate the accuracy of the two models. Compared with the basic model, the R² of the mixed-effects model which included random-effect parameter increased 37%-82%, RMSE and MAD decreased 12%-30% and 13-28%, respectively. In conclusion, the mixed-effects model was suitable to calibrate growth models.