Multiple regression on distance matrices: a multivariate spatial analysis tool
Multiple regression on distance matrices: a multivariate spatial analysis tool
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DOI：
10.1007/s11258-006-9126-3
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发表时间：
2007-02-01
期刊：
影响因子：
1.7
通讯作者：
Lichstein, Jeremy W.
中科院分区：
文献类型：
--
作者：
Lichstein, Jeremy W.
探讨了距离矩阵多元回归(MRM)在生态数据空间分析中的应用，它是部分Mantel分析的扩展。MRM涉及对任意数量的解释矩阵的响应矩阵的多元回归，其中每个矩阵包含n个对象(样本单位)的所有成对组合之间的距离或相似性(就生态、空间或其他属性而言)；通过排列来执行统计显著性检验。该方法在可以分析的数据类型(计数、存在-不存在、连续、分类)和响应曲线的形状方面是灵活的。与传统的部分Mantel分析相比，MRM有几个优点：(1)将环境距离分成不同的距离矩阵，允许在单个变量的水平上进行推断；(2)可以使用非参数或非线性多元回归方法；(3)可以使用一系列滞后矩阵在不同的空间尺度上量化和测试空间自相关性，每个滞后矩阵代表一个地理距离类别。MRM滞后矩阵模型可以被参数化以产生关于空间自相关作为Mantel相关图的非常相似的推论。然而，与相关图不同的是，滞后矩阵模型还可以包括环境距离矩阵，从而可以在控制站点之间的环境相似性的同时量化物种丰度距离(群落相似性)的空间模式。文中给出了应用MRM进行空间分析的实例。
I explore the use of multiple regression on distance matrices (MRM), an extension of partial Mantel analysis, in spatial analysis of ecological data. MRM involves a multiple regression of a response matrix on any number of explanatory matrices, where each matrix contains distances or similarities (in terms of ecological, spatial, or other attributes) between all pair-wise combinations of n objects (sample units); tests of statistical significance are performed by permutation. The method is flexible in terms of the types of data that may be analyzed (counts, presence-absence, continuous, categorical) and the shapes of response curves. MRM offers several advantages over traditional partial Mantel analysis: (1) separating environmental distances into distinct distance matrices allows inferences to be made at the level of individual variables; (2) nonparametric or nonlinear multiple regression methods may be employed; and (3) spatial autocorrelation may be quantified and tested at different spatial scales using a series of lag matrices, each representing a geographic distance class. The MRM lag matrices model may be parameterized to yield very similar inferences regarding spatial autocorrelation as the Mantel correlogram. Unlike the correlogram, however, the lag matrices model may also include environmental distance matrices, so that spatial patterns in species abundance distances (community similarity) may be quantified while controlling for the environmental similarity between sites. Examples of spatial analyses with MRM are presented.