Identifying and characterizing extrapolation in multivariate response data
Identifying and characterizing extrapolation in multivariate response data
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DOI：
10.1371/journal.pone.0225715
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发表时间：
2019-12-05
期刊：
影响因子：
3.7
通讯作者：
Wagner, Tyler
中科院分区：
文献类型：
--
作者：
Bartley, Meridith L.;Hanks, Ephraim M.;Wagner, Tyler
面对数据可获得性、资金和时间的限制，生态学家的任务往往是做出超出他们数据范围的预测。在生态学研究中，由于数据的多变量性质，在何时何地进行外推并不总是显而易见的。以前识别外推的工作主要集中在单变量响应数据上，但这些方法不能直接适用于多变量响应数据，而多变量响应数据在生态学调查中很常见。在这篇文章中，我们扩展了以前的工作，通过将预测方差从单变量设置应用到多变量情况来识别外推。我们建议使用预测方差矩阵的迹或行列式来获得标量值度量，当与选定的截止值配对时，该标量值度量允许在预测和外推之间进行划分。我们通过对来自美国东北部和中西部的7000多个内陆湖泊的联合建模湖泊营养物质以及藻类生物量和水透明度指标的分析来说明我们的方法。此外，我们概述了使用分类和回归树识别协变量空间中更可能发生外推的区域的新的探索性方法。在探索多变量统计模型预测的有效性时，使用我们的多变量预测方差(MVPV)测量和多个截止值可以帮助指导生态推断。
Faced with limitations in data availability, funding, and time constraints, ecologists are often tasked with making predictions beyond the range of their data. In ecological studies, it is not always obvious when and where extrapolation occurs because of the multivariate nature of the data. Previous work on identifying extrapolation has focused on univariate response data, but these methods are not directly applicable to multivariate response data, which are common in ecological investigations. In this paper, we extend previous work that identified extrapolation by applying the predictive variance from the univariate setting to the multivariate case. We propose using the trace or determinant of the predictive variance matrix to obtain a scalar value measure that, when paired with a selected cutoff value, allows for delineation between prediction and extrapolation. We illustrate our approach through an analysis of jointly modeled lake nutrients and indicators of algal biomass and water clarity in over 7000 inland lakes from across the Northeast and Mid-west US. In addition, we outline novel exploratory approaches for identifying regions of covariate space where extrapolation is more likely to occur using classification and regression trees. The use of our Multivariate Predictive Variance (MVPV) measures and multiple cutoff values when exploring the validity of predictions made from multivariate statistical models can help guide ecological inferences.