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Three-way principal balance analysis: algorithm and interpretation

Author

Listed:
  • Violetta Simonacci

    (University of Naples - Federico II)

  • Michele Gallo

    (University of Naples - L’Orientale)

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.

Suggested Citation

  • Violetta Simonacci & Michele Gallo, 2024. "Three-way principal balance analysis: algorithm and interpretation," Annals of Operations Research, Springer, vol. 342(3), pages 1429-1443, November.
    • Handle: RePEc:spr:annopr:v:342:y:2024:i:3:d:10.1007_s10479-022-04782-5
    DOI: 10.1007/s10479-022-04782-5
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    References listed on IDEAS

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    1. J. Carroll & Jih-Jie Chang, 1970. "Analysis of individual differences in multidimensional scaling via an n-way generalization of “Eckart-Young” decomposition," Psychometrika, Springer;The Psychometric Society, vol. 35(3), pages 283-319, September.
    2. Violetta Simonacci & Michele Gallo, 2019. "Detecting Public Social Spending Patterns in Italy Using a Three-Way Relative Variation Approach," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 146(1), pages 205-219, November.
    3. Raymond Cattell, 1944. "“Parallel proportional profiles” and other principles for determining the choice of factors by rotation," Psychometrika, Springer;The Psychometric Society, vol. 9(4), pages 267-283, December.
    4. Maria Anna Di Palma & Michele Gallo, 2019. "External Information Model in a Compositional Perspective: Evaluation of Campania Adolescents’ Preferences in the Allocation of Leisure-Time," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 146(1), pages 117-133, November.
    5. John Aitchison & Michael Greenacre, 2002. "Biplots of compositional data," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 51(4), pages 375-392, October.
    6. Michele Gallo, 2015. "Tucker3 Model for Compositional Data," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 44(21), pages 4441-4453, November.
    7. Ledyard Tucker, 1966. "Some mathematical notes on three-mode factor analysis," Psychometrika, Springer;The Psychometric Society, vol. 31(3), pages 279-311, September.
    8. Marie-Pier Bergeron-Boucher & Violetta Simonacci & Jim Oeppen & Michele Gallo, 2018. "Coherent Modeling and Forecasting of Mortality Patterns for Subpopulations Using Multiway Analysis of Compositions: An Application to Canadian Provinces and Territories," North American Actuarial Journal, Taylor & Francis Journals, vol. 22(1), pages 92-118, January.
    9. Violetta Simonacci & Michele Gallo, 2017. "Statistical tools for student evaluation of academic educational quality," Quality & Quantity: International Journal of Methodology, Springer, vol. 51(2), pages 565-579, March.
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