GENERALIZED LINEAR MODELS FOR TREE SURVIVAL IN LOBLOLLY PINE PLANTATIONS

ABSTRACT To quantify the surviving trees in a forest stand and estimate the probability of an individual tree to survival are a fundamental task in forest management planning. Therefore, the main goal of this paper was to estimate the tree survival probability in loblolly pine (Pinus taeda L.) plantations based on generalized linear models (GLM). The data set was obtained from forest inventories carried out in the Midwest of Santa Catarina State, Brazil. The data analysis combined strategies for selecting covariates and different specifications of link functions in a Bernoulli GLM. We performed strategies for covariate selection at plot-level along with the standard stepwise procedure, where we considered the elastic net approach, as well as its special cases the lasso and ridge penalization. Our analyses showed that the stepwise procedure combined with the complementary log-log link function provide the best fit. The variables that most contributed to assess tree survival were basal area, number of individuals, maximum diameter, diameter of the average cross-sectional area and the diameter coefficient of variation per plots. This model presents 81.5% of accuracy given by ROC curve. Finally, we evaluated the fitted model by means of the half-Normal plots and randomized quantile residuals, whose results showed evidence of a suitable fit. We suggest the stepwise procedure for selecting covariates for a tree survival probability model, besides a complementary log-log link function.

摘要：量化林分中存活林木数量、估算单木存活概率是森林经营规划的核心基础任务。为此，本研究旨在基于广义线性模型（Generalized Linear Models, GLM）估算火炬松（Pinus taeda L.）人工林的单木存活概率。本数据集源自巴西圣卡塔琳娜州中西部开展的森林资源清查工作。本次数据分析结合了伯努利广义线性模型中的协变量选择策略与多种连接函数设定方案：在样地尺度下采用协变量选择策略，结合标准逐步回归法，同时纳入弹性网（Elastic Net）方法及其特例——套索（Lasso）与岭（Ridge）惩罚回归。分析结果表明，结合互补双对数（complementary log-log）连接函数的逐步回归法可获得最优拟合效果。对单木存活概率评估贡献最大的变量依次为胸高断面积、样地株数、最大直径、平均断面积直径以及样地直径变异系数。经受试者工作特征（Receiver Operating Characteristic, ROC）曲线验证，该模型的预测准确率可达81.5%。最后，本研究通过半正态图与随机化分位数残差对拟合模型进行检验，结果证实模型拟合效果良好。综上，本研究建议在构建单木存活概率模型时，采用逐步回归法进行协变量选择，并搭配互补双对数连接函数。