使用线性混合效应方法开发单树基数增量模型
Summary
混合效应模型是分析林业中分层随机结构数据的灵活而有用的工具，也可用于显著提高森林生长模型的性能。在这里，提出了一个协议，合成与线性混合效应模型相关的信息。
Abstract
在这里，我们根据一个数据集开发了一个5年基底面积增量的单树模型，其中包括来自中国西北部新疆省779个样本地块的21898 棵皮卡阿斯佩拉塔 树。为了防止来自同一采样单元的观测结果之间的高相关性，我们使用具有随机绘图效果的线性混合效应方法开发了该模型，以考虑随机变异性。各种树和立级变量，如树的大小、竞争和场地条件的指数，都作为固定效应包括在内，以解释残余变异性。此外，通过引入方差函数和自动相关结构来描述异构性和自动相关性。最佳线性混合效应模型由几个合适的统计数据决定：Akaike 的信息标准、贝叶斯信息标准、对数可能性和可能性比率测试。结果表明，单树基底面积增量的重要变量为胸高直径的反向转化、大于主体树的树木基底面积、每公顷树木数量和海拔高度。此外，方差结构中的错误最成功地通过指数函数建模，并且通过一阶自动反向结构 （AR（1）显著纠正了自动反差。与使用普通最小正方形回归的模型相比，线性混合效应模型的性能显著提高。
Introduction
与均匀的单一栽培、不均匀年龄的混合种林管理相比，具有多重目标的混合物种森林管理最近受到越来越多的关注。预测不同的管理备选方案是制定强有力的森林管理战略的必要条件，特别是对于复杂的不均匀年龄的混合物种森林4。森林生长和产量模型已被广泛使用，以预测树木或站在发展和收获下的各种管理计划5，6，7。森林生长和产量模型分为个体树模型、大小级模型和全站生长模型6、7、8。不幸的是，大小类模型和全站模型不适合年龄不均匀的混合物种森林，这需要更详细的描述来支持森林管理决策过程。因此，单树生长和产量模型在过去几十年中受到越来越多的关注，因为它们能够预测森林站与各种物种组成，结构和管理策略9，10，11。
普通最小正方形 （OLS） 回归是开发单树生长模型 12、13、14、15 的最常用方法。在同一采样单元（即样本图或树）上，在同一采样单元（即样本图或树）上反复收集的单树生长模型数据集具有层次结构，在观测点 10、16之间缺乏独立性和高空间和时间相关性。分层随机结构违反了 OLS 回归的基本假设：即独立残余和通常分布的数据具有相等的方差。因此，OLS回归的使用不可避免地会产生对这些数据13、14参数估计标准误差的偏颇估计。
混合效应模型为分析结构复杂的数据提供了强大的工具，例如重复测量数据、纵向数据和多级数据。混合效应模型由固定组件和随机组件组成，这些组件是每个采样水平所特有的。此外，混合效应模型通过定义非对角方差-共变结构矩阵17、18、19来考虑空间和时间的异构性和自动校际性。为此，混合效应模型已广泛应用于林业，如直径高度模型20，21，冠模型22，23，自瘦模型24，25，生长模型26，27。
在这里，主要目标是使用线性混合效应方法开发单树基底区域增量模型。我们希望混合效应方法能够得到广泛应用。
Protocol
1. 数据准备 准备建模数据，包括单树信息（1.3米乳房高度的物种和直径）和绘图信息（坡度、侧面和海拔）。在这项研究中，数据取自中国西北新疆省第8次（2009年）和第9次（2014年）中国国家森林清查，其中包括对779个样本地块的21，898次观测。这些样本地块为方形，面积为1亩（面积相当于0.067公顷），系统地排列在4公里×8公里的网格上。注：建模（基础区域）增量的数据至少需要一…
Representative Results
P. asperata的基本基底区域增量模型表示为方程 （7）。参数估计值、相应的标准误差和不合适的统计数据显示在表 2中。残余情节显示在图 1中。观察到残留物的明显异构性。(7) 估计 标准错误 t 测试</st…
Discussion
发展混合效应模型的一个关键问题是确定哪些参数可以被视为随机效应，哪些参数应被视为固定效应34，35。提出了两种方法。最常见的方法是将所有参数视为随机效应，然后由 AIC、BIC、Loglik 和 LRT 选择最佳模型。这是我们研究35所采用的方法。另一种选择是为 OLS 回归的每个示例图安装基底区域增量模型。在这些模型的样本图中具有?…
Declarações
The authors have nothing to disclose.
Acknowledgements
这项研究由中央大学基础研究基金资助，资助编号为2019GJZL04。我们感谢中国国家林业和草原管理局森林盘点与规划学院的曾伟生教授提供数据。
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Citar este artigo
Wang, W., Bai, Y., Jiang, C., Meng, J. Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach. J. Vis. Exp. (161), e60827, doi:10.3791/60827 (2020).