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、估测单木存活概率是森林经营规划的核心基础任务。故此，本研究旨在基于广义线性模型（Generalized Linear Models, GLM），对火炬松（*Pinus taeda* L.）人工林的单木存活概率进行估测。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协变量（covariates）选择策略与伯努利广义线性模型中连接函数的多种设定形式。我们在样地水平上开展协变量选择，结合标准逐步回归法，同时考量了弹性网（elastic net）方法及其特例——套索（Lasso）与岭惩罚（Ridge Penalization）。分析结果表明，逐步回归法与补对数-对数连接函数相结合的模型拟合效果最优。对单木存活预测贡献最大的变量包括样地胸高断面积、林木株数、最大胸径、平均断面直径以及样地直径变异系数。该模型通过受试者工作特征曲线（Receiver Operating Characteristic curve, ROC）计算得到的准确率为81.5%。最后，我们通过半正态图与随机分位数残差对拟合模型进行评估，结果显示模型拟合效果良好。综上，我们建议在单木存活概率模型的协变量选择中采用逐步回归法，并搭配补对数-对数连接函数。