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<article article-type="research-article" dtd-version="1.3" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xml:lang="ru"><front><journal-meta><journal-id journal-id-type="publisher-id">isplta</journal-id><journal-title-group><journal-title xml:lang="ru">Известия Санкт-Петербургской лесотехнической академии</journal-title><trans-title-group xml:lang="en"><trans-title>Izvestia Sankt-Peterburgskoj lesotehniceskoj akademii</trans-title></trans-title-group></journal-title-group><issn pub-type="ppub">2079-4304</issn><issn pub-type="epub">2658-5871</issn><publisher><publisher-name>СПбГЛТУ</publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="doi">10.21266/2079-4304.2025.256.38-60</article-id><article-id custom-type="elpub" pub-id-type="custom">isplta-640</article-id><article-categories><subj-group subj-group-type="heading"><subject>Research Article</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="ru"><subject>ЛЕСНОЕ ХОЗЯЙСТВО</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="en"><subject>FORESTRY</subject></subj-group></article-categories><title-group><article-title>Мультиколлинеарность переменных в евразийской базе данных о фитомассе деревьев и всеобщая аллометрия</article-title><trans-title-group xml:lang="en"><trans-title>Multicollinearity of variables in the Eurasian tree biomass database and generic allometry</trans-title></trans-title-group></title-group><contrib-group><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Усольцев</surname><given-names>В. А.</given-names></name><name name-style="western" xml:lang="en"><surname>Usoltsev</surname><given-names>V. A.</given-names></name></name-alternatives><bio xml:lang="ru"><p>УСОЛЬЦЕВ Владимир Андреевич – профессор кафедры лесной таксации и лесоустройства, доктор сельскохозяйственных наук; профессор кафедры информационных технологий и статистики </p><p>620100, ул. Сибирский тракт, д. 37, г. Екатеринбург</p><p>620144, ул. 8 Марта, д. 62/45, г. Екатеринбург</p></bio><bio xml:lang="en"><p>USOLTSEV Vladimir A. – DSc (Agricultural), Professor of the Department of Forest Taxation and Forest Management; professor of the Department of Information Technologies and Statistics </p><p>620100. Sibirskiy Trakt str. 37. Yekaterinburg</p><p>620144. 8 Marta str. 62/45. Yekaterinburg</p></bio><email xlink:type="simple">Usoltsev50@mail.ru</email><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Часовских</surname><given-names>В. П.</given-names></name><name name-style="western" xml:lang="en"><surname>Chasovskikh</surname><given-names>V. P.</given-names></name></name-alternatives><bio xml:lang="ru"><p>ЧАСОВСКИХ Виктор Петрович – профессор кафедры шахматного искусства и компьютерной математики , доктор технических наук, академик Российской академии военных наук</p><p>620144, ул. 8 Марта, д. 62/45, г. Екатеринбург</p></bio><bio xml:lang="en"><p>CHASOVSKIKH Viktor P. – DSc (Technical), Professor of the Department of Chess Art and Computer Mathematics, Academician of the Russian Academy of Military Sciences</p><p>620144. 8 Marta str. 62/45. Yekaterinburg</p></bio><email xlink:type="simple">u2007u@ya.ru</email><xref ref-type="aff" rid="aff-2"/></contrib></contrib-group><aff-alternatives id="aff-1"><aff xml:lang="ru">Уральский государственный лесотехнический университет; Уральский государственный экономический университет<country>Россия</country></aff><aff xml:lang="en">Ural State Forest Engineering University; Ural State University of Economics<country>Russian Federation</country></aff></aff-alternatives><aff-alternatives id="aff-2"><aff xml:lang="ru">Уральский государственный экономический университет<country>Россия</country></aff><aff xml:lang="en">Ural State University of Economics<country>Russian Federation</country></aff></aff-alternatives><pub-date pub-type="collection"><year>2025</year></pub-date><pub-date pub-type="epub"><day>12</day><month>03</month><year>2026</year></pub-date><volume>0</volume><issue>256</issue><elocation-id>38–60</elocation-id><permissions><copyright-statement>Copyright &amp;#x00A9; Усольцев В.А., Часовских В.П., 2026</copyright-statement><copyright-year>2026</copyright-year><copyright-holder xml:lang="ru">Усольцев В.А., Часовских В.П.</copyright-holder><copyright-holder xml:lang="en">Usoltsev V.A., Chasovskikh V.P.</copyright-holder><license license-type="creative-commons-attribution" xlink:href="https://creativecommons.org/licenses/by/4.0/" xlink:type="simple"><license-p>This work is licensed under a Creative Commons Attribution 4.0 License.</license-p></license></permissions><self-uri xlink:href="https://izvestiya-lta.spbftu.ru/jour/article/view/640">https://izvestiya-lta.spbftu.ru/jour/article/view/640</self-uri><abstract><p>В связи с изменением климата лесная фитомасса обретает исключительное экологическое значение планетарного уровня. Для ее оценки необходимы легко реализуемые методы, одним из которых является метод аллометрических моделей. Поскольку фитомасса связана с несколькими дендрометрическими показателями дерева, стали разрабатывать многофакторные аллометрические модели, однако проверка их на мультиколлинеарность обычно не проводилась, что приводило к их неустойчивости. В работе предпринята попытка на основе наиболее полной на сегодня авторской базы данных о фитомассе деревьев Евразии оптимизировать структуру многофакторной модели фитомассы по условию мультиколлинеарности независимых переменных. Для этого из базы данных для 12 лесообразующих родов отобраны 11170 модельных деревьев с измеренной надземной фитомассой, из которых только у 1514 деревьев была измерена фитомасса корней. Проанализирована мультиколлинеарность возраста дерева, его диаметра ствола и высоты. По результатам расчета коэффициента инфляции дисперсии (VIF) установлено, что при включении названных трех переменных в модель она не является корректной по условию мультиколлинеарности ни для одного из 12 родов. При анализе VIF по двум прогностическим переменным в разных сочетаниях наименьшие значения VIF (&lt; 5) оказались у переменных возраста и диаметра, но лишь для 6 родов, наиболее представленных по количеству измерений. Казалось бы, модель, включающая совокупность именно этих двух переменных с минимальным VIF, является оптимальной по структуре. Однако низкая мультиколлинеарность переменных еще не обеспечивает оптимальности структуры модели. Регрессионный анализ связи фитомассы с названными двумя переменными показал, что возраст в некоторых случаях статистически не значим, а его вклад в объяснение изменчивости фитомассы составил менее 7%. Это означает, что оптимальная структура модели может быть установлена в результате некого компромисса между низкой мультиколлинеарностью и высоким вкладом переменных в объяснение изменчивости фитомассы. В итоге для 12 родов рассчитаны всеобщие аллометрические модели для оценки надземной, подземной и общей фитомассы лишь по диаметру ствола, которые при локальном использовании могут давать смещения результатов. Вопрос оптимизации структуры модели фитомассы остается, таким образом, открытым, и исследователю в каждом случае приходится находить «золотую середину» между отбором независимых переменных с минимальной мультиколлинеарностью с одной стороны и включением в модель наибольшего количества статистически значимых независимых переменных с другой.</p></abstract><trans-abstract xml:lang="en"><p>Due to climate change, the forest biomass acquires exceptional ecological significance at the planetary level. To evaluate it, easy-to-implement methods are needed, one of which is the method of allometric models. Since biomass is related to some dendrometric indices of the tree, multifactorial allometric models began to be developed, however, their verification for multicollinearity was usually not carried out, and the models were often unstable. The paper attempts to optimize the structure of a multifactorial model of biomass under the condition of multicollinearity of independent variables based on the most comprehensive author's database of tree biomass to date. For this purpose, 11,170 model trees with measured aboveground biomass were selected from the database for 12 forest-forming genera, of which only 1,514 trees had their root biomass measured. The multicollinearity of the tree's age, DBH, and height is analyzed. Based on the calculation of the variance inflation coefficient (VIF), it was found that when these three variables being included in the model, give not correct result under the condition of multi-collinearity for 12 genera. When analyzing VIF for two prognostic variables in different combinations, the lowest VIF values (&lt; 5) were found for age and DBH, but only for 6 genera, the most represented by the number of measurements. It would seem that a model that includes a combination of these two variables with a minimum VIF is optimal in its structure. However, the low multicollinearity of variables does not ensure the optimality of the model structure. Regression analysis of the relationship of biomass with these two variables showed that age in some cases is not statistically significant, and its contribution to explaining the biomass variability was less than 7%. This means that the optimal model structure can be established as a result of some compromise between low multicollinearity and high contribution of variables to the explanation of biomass variability. After all, generic allometric models have been calculated to estimate the aboveground, underground, and total biomass by DBH for 12 genera, which, when used locally, can produce biased results. Thus, the issue of optimizing the structure of the biomass model remains open, and in each case the researcher has to find a “golden mean” between selecting independent variables with minimal multicollinearity, on the one hand, and between including the largest number of statistically significant independent variables in the model, on the other. </p></trans-abstract><kwd-group xml:lang="ru"><kwd>лесообразующие роды Евразии</kwd><kwd>база данных о фитомассе деревьев</kwd><kwd>мультиколлинеарность независимых переменных</kwd><kwd>всеобщие модели фитомассы</kwd><kwd>смещения оценок</kwd></kwd-group><kwd-group xml:lang="en"><kwd>forest-forming genera of Eurasia</kwd><kwd>database on biomass of trees</kwd><kwd>multicollinearity of independent variables</kwd><kwd>generic models of biomass</kwd><kwd>biases of estimates</kwd></kwd-group></article-meta></front><back><ref-list><title>References</title><ref id="cit1"><label>1</label><citation-alternatives><mixed-citation xml:lang="ru">Арманд Д.Л. 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