Análise de dados composicionais

Abstract

Compositional Data (CoDa) are quantitative descriptions of the parts of a whole, which convey information relative to the total. The big difference, in this type of situation, is that the data components present a constant sum, 1 - for proportions and 100 - for percentages. Due to this restriction, compositional data has its own structure, called Simplex (natural space for such data), in which the operations performed may not have a clear correspondence with usual methods of real space. This fact culminates in the use of some transformations, which allow an equivalence between the Euclidean (real) space and the simplex space, making it possible to take advantage of the usual facilities of statistics and then return to the space with restrictions. The work addressed compositional transformations, exhibited the principles of compositional analysis, enunciated the operations in compositions, demonstrated the appropriate exploratory analysis and, finally, suggested alternatives for adapting models, in addition to explaining simulations and practical applications, which demonstrated analysis options of regression using the compositional methods in detriment to the usual methods.