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Summary
This summary is machine-generated.

This study introduces a general framework for analyzing k-factorial compositional data, extending previous methods. It enables orthogonal decomposition and coordinate representation for multi-factorial relative-valued data analysis.

Keywords:
Analysis of independenceCompositional dataCoordinate representationOrthogonal decomposition

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Area of Science:

  • Multivariate statistics
  • Data analysis
  • Geostatistics

Background:

  • Compositional data analysis (CoDa) traditionally focuses on vector or two-factorial data.
  • A gap exists in comprehensive methods for multi-factorial relative-valued data.
  • Existing literature lacks a unified framework for higher-order compositional structures.

Purpose of the Study:

  • To develop a general theoretical framework for k-factorial compositional data analysis.
  • To extend the orthogonal decomposition and coordinate representation concepts to multi-factorial structures.
  • To provide practical tools for analyzing complex compositional systems.

Main Methods:

  • Development of a general theoretical framework for k-factorial compositional data.
  • Orthogonal decomposition of multi-factorial structures into independent and interactive components.
  • Construction of a coordinate representation for separate analysis using standard methods.
  • Application to three-factorial compositions (compositional cubes) and generalization to k-factors.

Main Results:

  • A novel framework for analyzing k-factorial compositional data is established.
  • Multi-factorial compositional structures can be orthogonally decomposed.
  • A coordinate representation facilitates the analysis of independent and interactive parts.
  • The methodology is demonstrated with spatial and time-dependent compositional cubes.

Conclusions:

  • The proposed framework offers a comprehensive approach to multi-factorial compositional data.
  • Orthogonal decomposition and coordinate representation are key to analyzing complex relative-valued data.
  • The R package robCompositions implements the presented methodology for practical application.