Distributional Equivalence and Subcompositional Coherence in the Analysis of Compositional Data, Contingency Tables and Ratio-Scale Measurements

2009 ◽  
Vol 26 (1) ◽  
pp. 29-54 ◽  
Author(s):  
Michael Greenacre ◽  
Paul Lewi
Keyword(s):  
Compositional Data ◽  
Contingency Tables ◽  
Ratio Scale ◽  
Subcompositional Coherence

scholarly journals The Mathematics of Compositional Analysis

2016 ◽  
Vol 45 (4) ◽  
pp. 57-71 ◽  
Author(s):  
Carles Barcelo-Vidal ◽  
Josep-Antoni Martín-Fernández
Keyword(s):  
Scale Invariance ◽  
Compositional Data ◽  
Quotient Space ◽  
Compositional Analysis ◽  
Space Structure ◽  
Compositional Data Analysis ◽  
New Developments ◽  
Quotient Spaces ◽  
Subcompositional Coherence ◽  
Logratio Transformations

The term compositional data analysis is historically associated to the approach based on the logratio transformations introduced in the eighties. Two main principles of this methodology are scale invariance and subcompositional coherence. New developments and concepts emerged in the last decade revealed the need to clarify the concepts of compositions, compositional sample space and subcomposition. In this work the mathematics of compositional analysis based on equivalence relation is presented. The two principles are essential attributes of the corresponding quotient space. A logarithmic isomorphism between quotient spaces induces a metric space structure for compositions. Using this structure, the statistical analysis of compositions consists of analysing logratio coordinates.

An Introduction to the Analysis of Contingency Tables

1993 ◽  
Vol 38 (8) ◽  
pp. 797-798
Author(s):  
Stephen E. Fienberg
Keyword(s):  
Contingency Tables
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