Construction of taper equation for Larix olgensis based on two-level nonlinear mixed effects model

NIE Luyi, DONG Lihu, LI Fengri, MIAO Zheng, XIE Longfei

JOURNAL OF NANJING FORESTRY UNIVERSITY ›› 2022, Vol. 46 ›› Issue (3) : 194-202.

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JOURNAL OF NANJING FORESTRY UNIVERSITY ›› 2022, Vol. 46 ›› Issue (3) : 194-202. DOI: 10.12302/j.issn.1000-2006.202108050

Construction of taper equation for Larix olgensis based on two-level nonlinear mixed effects model

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Abstract

【Objective】 Based on the stem taper data of 177 artificial Larix olgensis trees from 31 permanent sample plots in Heilongjiang Province, a non-linear mixed effect model was used to construct a taper equation for L. olgensis. This will provide a theoretical basis for the precise prediction of the stem shape and tree volume. 【Method】 Among the different types of taper equations, the Kozak equation with the best fitting effect was selected as the basic model, and then the crown characteristic variables were introduced using reparameterization to analyze the influence of the crown size on the stem shape. Based on the model with the crown variables, the two-level mixed-effect model considering the impact of the sample plot effect and the sample tree effect on the stem shape was used to develop the taper equations for Larix olgensis trees. Prediction precision of the mixed-effect models was tested using two different sampling strategies. Strategy Ⅰ: the global optimal plan that does not limit the sampling position. Strategy Ⅱ: the plan with a relatively high limit of less than 0.1. 【Result】 Among the tree crown variables, the crown length rate has the closest relationship with the stem shape. Introducing the crown length rate into the taper equation, the fitting accuracy of the model was improved, and the model parameters were all significant at the 5% significance level. The results of the likelihood ratio test showed that the sample plot effect and the sample tree effect significantly (P < 0.01) improved the model accuracy. The exponential function and CAR (1) structure were used to solve the common heteroscedasticity and autocorrelation problems in the taper equation. The goodness-of-fit for the mixed-effect models for R a 2 was 0.994 1, RMSE was 0.623 1 which was better than the basic model ( R a 2 increased by 0.4%, RMSE decreased by 24.6%). When using a different sampling strategy for model prediction, Strategy Ⅰ had the best results (RMSE was 0.470 0, MAPE was 4.62%), when the sampling number was 5. For Strategy Ⅱ, there were little differences in predicting accuracy with different sampling numbers (the range of MAE was 0.520 3-0.536 6, the range of MAPE was 5.14%-5.22%), but still better than the basic model. 【Conclusion】 The two-level mixed-effects model, including plot effect and tree effect, was better than the basic model for the fitting effect and prediction accuracy, and it will be suitable for effectively predicting stem shape changes in L. olgensis. The results will provide a foundation for precisely predicting the timber volume and total tree volume of L. olgensis.

Key words

Larix olgensis / stem shape / nonlinear mixed-effect model / mixed model calibration / taper equation

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NIE Luyi , DONG Lihu , LI Fengri , et al . Construction of taper equation for Larix olgensis based on two-level nonlinear mixed effects model[J]. JOURNAL OF NANJING FORESTRY UNIVERSITY. 2022, 46(3): 194-202 https://doi.org/10.12302/j.issn.1000-2006.202108050

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