Resumen de Subcompositional coherence and and a novel proportionality index of parts

Juan José Egozcue Rubí , Vera Pawlowsky Glahn

• Research in compositional data analysis was motivated by spurious (Pearson) corre- lation. Spurious results are due to semantic incoherence, but the question of ways to relate parts in a statistically consistent way remains open. To solve this problem we frst defne a coherent system of functions with respect to a subcomposition and ana- lyze the space of parts. This leads to understanding why measures like covariance and correlation depend on the subcomposition considered, while measures like the distance between parts are independent of the same. It allows the defnition of a novel index of proportionality between parts.