Регрессионные модели смешанных эффектов зависимости высоты от диаметра ствола в сосновых древостоях европейской части России

Abstract

Evaluation of the relationship between tree heights and diameters in the course of logging sites can be done through the use of tables of height categories or regression models. Models of mixed effects make it possible to improve the accuracy of forest inventory to a large extent. The purpose of the study is to develop a mixed effects model for describing the dependence of heights on the diameters of pine trees in the European part of Russia. In the course of study we used the data from measurements of 3 571 model pine trees growing on 201 trial plots from 13 regions of the European part of Russia from Karelia to the Samara region and from the Tver region to the Komi Republic. The paper analyzes 28 simple regression models of the dependence of height on diameter, selected according to literary sources. The selection of the best models was based on quality metrics accepted in statistics, such as the square root of the root mean square error (RMSE), the average percentage of absolute error (MAPE), the average absolute error (MAE), bias (Bias), coefficient of determination (R2), information criteria Akaike (AIC) and Bayesian (BIC). The two-parameter Neslund equation is recognized as the most simple and universal among the fixed effects models. To increase the predictive power of the Neslund equation, a separate trial plot was added as a random effect, which made it possible to significantly improve the quality metrics. It has been established that the height curves predicted by the obtained model are flexible and have a significant response to the initial ratios of the height and diameter of individual trees. The resulting model of mixed effects is an alternative to the tables of height categories used in the practice of forest accounting, which show only conditional relationships between the heights and diameters of trees. The introduction of industry standards developed on the basis of the model will improve the efficiency of accounting for wood resources in pine forests in the European part of Russia.