ON CRITERIA FOR MEASURES OF COMPOSITIONAL DIFFERENCE
ON CRITERIA FOR MEASURES OF COMPOSITIONAL DIFFERENCE
复制标题
DOI：
10.1007/bf00891269
复制
发表时间：
1992-05-01
期刊：
影响因子：
--
通讯作者：
AITCHISON, J
中科院分区：
文献类型：
--
作者：
AITCHISON, J
对成分性质的简单认识通过逻辑必然性导致对成分数据的某些形式的分析。在本文中的后果的基本要求的规模，扰动和排列不变性，连同子成分的优势，适用于问题的特征变化和措施之间的差异两个组成。它将被证明，一个强烈主张的标量测量的差异失败这些测试的逻辑必要性，和一个特定形式的标量测量的差异（总和的平方所有可能的对数比差异的两个组成部分），虽然不是唯一的，出现作为最简单和最听话的满足标准。
Simple perceptions about the nature of compositions lead through logical necessity to certain forms of analysis of compositional data. In this paper the consequences of essential requirements of scale, perturbation and permutation invariance, together with that of subcompositional dominance, are applied to the problem of characterizing change and measures of difference between two compositions. It will be shown that one strongly advocated scalar measure of difference fails these tests of logical necessity, and that one particular form of scalar measure of difference (the sum of the squares of all possible log ratio differences in the components of the two compositions), although not unique, emerges as the simplest and most tractable satisfying the criteria.