The Mantel test versus Pearson's correlation analysis: Assessment of the differences for biological and environmental studies
The Mantel test versus Pearson's correlation analysis: Assessment of the differences for biological and environmental studies
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DOI：
10.2307/1400528
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发表时间：
2000-06-01
影响因子：
1.4
通讯作者：
Legendre, P
中科院分区：
文献类型：
--
作者：
Dutilleul, P;Stockwell, JD;Legendre, P
Mantel的时空聚类过程最初被设计为在广义回归方法中将空间距离度量矩阵和时间距离度量矩阵关联起来。该程序在生物和环境科学中被称为Mantel测试，包括与两个距离矩阵或更一般地两个邻近矩阵相关的任何分析。在本文中，我们讨论了当两种方法都适用时，两个邻近矩阵之间的Mantel类型分析与Pearson相关分析一致的程度（即，用于计算接近度的原始数据是可用的）。首先，我们证明了曼特尔检验和皮尔逊相关性分析应导致一个类似的决定，关于各自的零假设时，平方欧几里德距离被用于曼特尔检验和原始双变量数据呈正态分布。然后，我们使用鱼类和浮游动物的生物量数据，从伊利湖（北美五大湖）表明，皮尔逊的相关性统计可能是不显着的，而曼特尔统计计算非平方欧几里德距离是显着的。在小规模的人工例子后，我们尝试了七个二元分布模型来模拟数据重现分析之间的差异，其中三个模型确实重现了分析之间的差异，并对这些结果和一些推广进行了讨论。总之，当接近度之间建立的关系被反向转置到原始数据时，特别是当这些可能显示本文主体中描述的模式时，必须特别注意。
The space-time clustering procedure of Mantel was originally designed to relate a matrix of spatial distance measures and a matrix of temporal distance measures in a generalized regression approach. The procedure, known as the Mantel test in the biological and environmental sciences, includes any analysis relating two distance matrices or, more generally two proximity matrices. In this paper, we discuss the extent to which a Mantel type of analysis between two proximity matrices agrees with Pearson's correlation analysis when both methods are applicable (i.e., the raw data used to calculate proximities are available). First, we demonstrate that the Mantel test and Pearson's correlation analysis should lead to a similar decision regarding their respective null hypothesis when squared Euclidean distances are used in the Mantel test and the raw bivariate data are normally distributed. Then we use fish and zooplankton biomass data from Lake Erie (North American Great Lakes) to show that Pearson's correlation statistic may be nonsignificant while the Mantel statistic calculated on nonsquared Euclidean distances is significant. After small-size artificial examples, seven bivariate distributional models are tried to simulate data reproducing the difference between analyses, among which three do reproduce it. These results and some extensions are discussed. In conclusion, particular attention must be paid whenever relations established between proximities are backtransposed to raw data, especially when these may display patterns described in the body of this paper.