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Some recent Developments in Factor Analysis and the Search for proper Communalities

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Advances in Data Science and Classification

Abstract

This paper describes recent results on factor analytic theory which involve the so-called Ledermann bound, and discusses theoretical properties of Minimum Rank Factor Analysis as an alternative to Iterative Principal Factor Analysis and exploratory Maximum Likelihood Factor Analysis. In terms of the residual eigenvalues, the three methods have closely related object functions, and will often give highly similar solutions in practice. Nevertheless, there are important differences between the methods. The most notable points are that Maximum Likelihood Factor Analysis is a method of fitting a statistical model, and that Minimum Rank Factor Analysis yields communalities in the classical sense, thus showing how much of the common variance is explained with any given number of factors.

The author is obliged to Henk Kiers, Anne Boomsma and Ivo Molenaar for commenting on a previous draft of this paper.

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Author information

Authors and Affiliations

  1. Heijmans Institute, University of Groningen, Grote Kruisstraat 2/1, 9712 TS, Groningen, The Netherlands

    Jos M. F. ten Berge

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  1. Jos M. F. ten Berge
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Editors and Affiliations

  1. Dipartimento di Statisticà, Probabilità e Statistiche Applicate, Università di Roma “La Sapienza”, Piazzale Aldo Moro 5, I-00185, Roma, Italia

    Alfredo Rizzi

  2. Dipartimento di Metodi Quantitativi e Teoria Economica, Università “G. D’Annunzio” di Chieti, Viale Pindaro 42, I-65127, Pescara, Italia

    Maurizio Vichi

  3. Institut für Statistik und Wirtschaftsmathematik, Rheinisch-Westfälische Technische Hochschule (RWTH) Aachen, Wüllnerstraße 3, D-52056, Aachen, Germany

    Hans-Hermann Bock

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© 1998 Springer-Verlag Berlin · Heidelberg

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ten Berge, J.M.F. (1998). Some recent Developments in Factor Analysis and the Search for proper Communalities. In: Rizzi, A., Vichi, M., Bock, HH. (eds) Advances in Data Science and Classification. Studies in Classification, Data Analysis, and Knowledge Organization. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-72253-0_44

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  • DOI: https://doi.org/10.1007/978-3-642-72253-0_44

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-64641-9

  • Online ISBN: 978-3-642-72253-0

  • eBook Packages: Springer Book Archive

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