Three-way principal balance analysis: algorithm and interpretation

Violetta Simonacci () and Michele Gallo ()
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Violetta Simonacci: University of Naples - Federico II
Michele Gallo: University of Naples - L’Orientale

Annals of Operations Research, 2024, vol. 342, issue 3, No 4, 1429-1443

Abstract: 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.

Keywords: Academic staff; Compositions; Logcontrast; SBP; Third-order tensors; Tucker3 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10479-022-04782-5

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