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Title: Coordinate representation of three-factorial compositional data Authors:  Kamila Facevicova - Palacky University Olomouc (Czech Republic) [presenting]
Karel Hron - Palacky University (Czech Republic)
Peter Filzmoser - Vienna University of Technology (Austria)
Abstract: Compositional data are commonly defined as positive vectors carrying relative information. Their relative nature prevents from applying standard statistical methods directly to raw compositions; instead, it is preferred to express compositional data in real logratio coordinates prior to their further processing. When a composition is formed according to more than just one factor, which results in so called compositional tables or cubes, the usual coordinate systems, designed primarily for vector compositional data, do not reflect the data structure sufficiently. The aim is to present an alternative coordinate representation of three-factorial compositional data - compositional cubes, which besides its favorable interpretation allows also to decompose the original data structure onto different sources of interactions between factors and to analyze these sources separately. The proposed methodology will be applied to real-world data and the possible use of spatial clustering and robust statistical methods will be discussed.