Analysis of similarities (ANOSIM) for 3-way designs,Austral Ecology

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Analysis of similarities (ANOSIM) for 3-way designs
Austral Ecology ( IF 1.6 ) Pub Date : 2021-07-28 , DOI: 10.1111/aec.13083
Paul J. Somerfield ₁ , K. Robert Clarke _{1,

2} , Ray N. Gorley ₂

Affiliation

Analysis of similarities (ANOSIM) is a robust non-parametric hypothesis-testing framework for differences in resemblances among groups of samples. To date, the generalisation and use of ANOSIM to analyse various 2-way nested and crossed designs with unordered or ordered factors has been described. This paper describes how the 2-way tests may be extended and modified for the analysis of 3-way designs, including the introduction of a different type of constrained permutation procedure for a design in which one factor is nested in another and crossed with a third. The construction of 3-way tests using the generalised statistic in various nested and crossed designs, with or without ordered factors, and with or without replication, is described. Applications of the new tests to ecological data are demonstrated using three marine examples. They are as follows: a study of changes in fish diet for fish of increasing size sampled in different locations at different times (a 3-way fully crossed design with ordered factors); a hierarchical spatial study of the fauna inhabiting kelp holdfasts (a 3-way fully nested design with unordered factors); and a study of infaunal macrobenthos in which sites within areas were resampled over a long time series (a design in which sites are nested in areas but crossed with years, both latter factors potentially being ordered). The magnitudes of the ANOSIM statistics provide information about relative effect sizes (accounting for other factors), which is often a focus for multifactorial designs. Though the described ANOSIM tests do not provide parallels for all the range of 3-way mixed-factor designs possible in ANOVA (and its multivariate semi-parametric counterpart PERMANOVA), it is seen that for nested factors these ANOSIM tests parallel the matching PERMANOVA random-effects models, and not their fixed-effects counterparts, thus allowing the same broader inference about the space from which these random factor levels are drawn.

中文翻译：

三路设计的相似性分析 (ANOSIM)

相似性分析 ( ANOSIM ) 是一个强大的非参数假设检验框架，用于分析样本组之间相似性的差异。迄今为止，ANOSIM的推广和使用已经描述了使用无序或有序因子分析各种 2 路嵌套和交叉设计。本文描述了如何扩展和修改 2-way 测试以分析 3-way 设计，包括为一个设计引入不同类型的约束置换过程，其中一个因素嵌套在另一个因素中并与第三个因素交叉. 描述了在各种嵌套和交叉设计中使用广义统计量构建 3 向检验，有或没有有序因素，有或没有复制。使用三个海洋示例演示了新测试对生态数据的应用。它们如下：研究在不同时间不同地点采样的大小增加的鱼类的鱼类饮食变化（具有有序因子的 3 路完全交叉设计）；对居住在海带中的动物群进行分层空间研究（具有无序因素的 3 向完全嵌套设计）；以及对大型底栖动物的研究，其中区域内的站点在长时间序列中重新采样（站点嵌套在区域中但与年份交叉的设计，后两个因素可能被排序）。的大小ANOSIM统计提供有关相对效应大小（考虑其他因素）的信息，这通常是多因素设计的重点。尽管所描述的ANOSIM测试并未为ANOVA（及其多元半参数对应PERMANOVA）中可能的所有 3 向混合因子设计范围提供相似性，但可以看出，对于嵌套因子，这些ANOSIM测试与匹配的PERMANOVA随机-效应模型，而不是它们的固定效应模型，因此允许对绘制这些随机因子水平的空间进行同样更广泛的推断。

更新日期：2021-08-25

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