A new class of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" id="d1e1162" altimg="si346.svg"><mml:mi>α</mml:mi></mml:math>-transformations for the spatial analysis of Compositional Data

Georeferenced compositional data are prominent in many scientific fields and spatial statistics. This work addresses the problem of proposing models methods to analyze predict, through kriging, this type data. To purpose, a novel class α-transformations, named Isometric α-transformation (α-IT), is proposed, which encompasses traditional Log-Ratio (ILR) transformation. Similarly other α-transformations existing literature, it shown that ILR limit case α-IT as α tends 0 α=1 corresponds linear transformation Unlike ILR, proposed accepts 0s compositions when α>0. Maximum likelihood estimation parameter established. Prediction using kriging on transformed validated synthetic data, prediction scores computed either geometry induced by α-IT, or simplex. Application land cover shows relative superiority various approaches w.r.t. objective depends whether contained any zero component. When all components positive, cases (ILR transformations) optimal for none considered metrics. An intermediate geometry, corresponding with maximum estimate, better describes dataset geostatistical setting. amount not negligible, some side-effects gets amplified decreases, entailing poor performances both within metrics