Decomposing compositional data: minimum chi-squared reduced-rank approximations on the simplex
نویسنده
چکیده
The logratio transformation (Aitchison, 1981, 1986) opened the way to statistically rigorous analysis of compositional data. Most statistical problems in compositional data analysis can be formulated in terms of logratios, and solved accordingly. However, some problems are more easily described and solved in terms of raw compositional variables. Raw compositions with k components are restricted to a k-1 dimensional subspace of the real space, a so-called simplex, defined by the following two constraints:
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