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Three-way principal balance analysis: algorithm and interpretation

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Abstract

Compositional Data Analysis can be useful for unveiling relative variability patterns among variables describing the parts of a phenomenon. Compositions are often represented as orthonormal balances associated with a sequential binary partition (SBP). Principal balances analysis (PBA) is a tool used to find a meaningful SBP by subsequently maximizing explained variability. The exact estimation of PBA is prohibitive for large datasets; therefore, algorithms providing an acceptable approximation are used instead. For compositional data of third-order, such exploratory search must account for third-mode variability. To this end, this work introduces a three-way adaptation of PBA in which estimation is carried out by Tucker3. A study on the composition of academic recruitment fields by Italian macro-region and gender/role is carried out to illustrate the merits of this procedure.

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Authors and Affiliations

  1. Department of Social Sciences, University of Naples - Federico II, Vico Monte della Pietà, 1, 80138, Naples, Italy

    Violetta Simonacci

  2. Department of Human and Social Sciences, University of Naples - L’Orientale, Largo San Giovanni Maggiore, 30, 80134, Naples, Italy

    Michele Gallo

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  1. Violetta Simonacci
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  2. Michele Gallo
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Correspondence to Michele Gallo.

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Simonacci, V., Gallo, M. Three-way principal balance analysis: algorithm and interpretation. Ann Oper Res 342, 1429–1443 (2024). https://doi.org/10.1007/s10479-022-04782-5

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