Bayesian KMO Index

Emil Niclas Meyer-Hansen

2025-11-02

The Bayesian KMO (BKMO) index is introduced by the author in the research paper Revisiting ‘Little Jiffy, Mark IV’: Towards a Bayesian KMO index (see the Abstract below). This paper subscribes to the open science standard, is partly licensed under the CC BY 4.0 and partly under the GPL-3.0 (see the License below), and it is made freely available in PDF-format (see the 'Article - Newest Version'-folder) and HTML-format (currently deprecated).

The R function for computing the BKMO index developed in the paper is made freely available here (see the 'bkmo-R-function'-file). In accordance with the license for the paper, it is licensed under the GNU General Public License, version 3 (GPL-3.0).

Table of Contents

• Abstract
• FAQ
• Changelog
• License
• Citation

Abstract

The Kaiser-Meyer-Olkin (KMO) index is a measure of sampling adequacy used by researchers to assess whether a data matrix is factorable prior to a factor analysis. Since its conception, the KMO index has remained a Frequentist statistic, leaving researchers unable to employ the advantages of Bayesian inference when assessing sampling adequacy. Building on the increasing relevance of the Bayesian statistical approach, as well as advancements in Markov-Chain Monte Carlo methods, the author proposes a re-conceptualization of the KMO index within the Bayesian framework that enables researchers to incorporate prior information and make coherent probabilistic statements about the sampling adequacy of a data matrix.©

Keywords: Kaiser-Meyer-Olkin index, KMO index, Bayesian Kaiser-Meyer-Olkin index, BKMO index, Measure of Sampling Adequacy, MSA, Bayesian Measure of Sampling Adequacy, BMSA, Bootstrap KMO index, Robust BKMO index, Bayesian inference, Frequentist inference

FAQ

• The newest iteration of the research paper (in PDF-format) is made available in the 'Article - Newest Version'-folder.
• An archive of different iterations of the research paper and materials are made freely available in the 'Archive'-folder. Due to Github-limitations on file size, data and plots are provided on its OSF project page instead (see below).
• A (currently outdated) version of the research paper is also made available in HTML-format at the URL: (https://emeyer-hansen.github.io/bayesian-kmo/)
• Materials are also made available on its Open Science Framework (OSF) project page (DOI: 10.17605/OSF.IO/T3UPD).

Changelog

• 2025-11-02 14:37 CEST
  • [Version 2025-11-02-14-37] - Working Paper
    • Major revision based on feedback from editor.
    • Changed demonstration of the BKMO index from relying on simulated data to empirical data.
    • Substantially reduced length of paper and number of references.
    • Appendix reduced to software specifications, BKMO index function, and discussion of robust BKMO index.
• 2025-10-16 16:02 CEST
  • [Version 2025-10-16-16-01] - Working Paper
    • Minor corrections/revisions of notation and text.
    • Subtle and insubstantial changes to the wording of the license.
    • Overhauled the rmarkdown file to ease converting the entire document to LaTeX.
    • For quality assurance, all simulated data was reproduced and all analyses and results were replicated.
• 2025-09-20 14:45 CEST
  • [Version 2025-09-19-10-52-HTML] - Working Paper
    • HTML-version of v2025-09-19-10-52
    • Corrected 'Partial' to 'Anti-image' in Appendix.
• 2025-09-19 10:52 CEST
  • [Version 2025-09-19-10-52] - Working Paper
    • Major corrections/revisions of notation and text.
    • Added more content to discussions of a Robust (B)KMO index.
    • Removed changelog and citation sections.
    • Added suggested citation to the first page.
    • For quality assurance, all simulated data was reproduced and all analyses and results were replicated.
    • Subtle and insubstantial changes to the wording of the license.
• 2025-06-05 07:28 CEST
  • [Version 2025-06-03-09-14-HTML] - Working Paper (HTML Version).
• 2025-06-03 09:14 CEST
  • [Version 2025-06-03-09-14] - Working Paper (Minor Corrections).
• 2025-05-20 10:29 CEST
  • [Version 2025-05-20-10-29] - Working Paper (Initial Release).

License (Addendum)

Except where otherwise indicated, all contents of this document and associated files are licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0). All software, including but not necessarily limited to, source code, executable code, code snippets, code chunks, algorithms, and/or scripts, attributable to this document and/or its associated files are expressly excluded from the foregoing license, and unless otherwise indicated, are instead licensed under the GNU General Public License, version 3 (GPL-3.0). By engaging with this document and/or any associated files, which include, but are not necessarily limited to, downloading, using, viewing, and/or distributing any of them, in parts of whole, you agree to comply with the applicable license terms for the respective content types.

Citation

Building on previous conceptualizations, the Bayesian Keiser-Meyer-Olkin (BKMO) index is an original Bayesian re-conceptualization by Emil Niclas Meyer-Hansen, conceived as part of the paper. For correspondence, contact the author via email: emil098meyerhansen@gmail.com

Please, if you use, refer to, modify, and/or continue the development of the Bayesian KMO index, provide proper reference and citation to its founding author. An example of proper citation is provided below:

Meyer-Hansen, E. N. (2025): 'Revisiting 'Little Jiffy, Mark IV': Towards a Bayesian KMO index', Open Science Framework, Working paper (v2025-11-02-14-37). DOI: [10.17605/OSF.IO/T3UPD](https://doi.org/10.17605/OSF.IO/T3UPD)

For LaTeX users, a BibTeX entry is provided below:

@unpublished{,
  title = {Revisiting 'Little Jiffy, Mark IV': Towards a Bayesian KMO index},
  author = {Emil Niclas Meyer-Hansen},
  publisher = {Open Science Framework},
  year = {2025},
  doi = {10.17605/OSF.IO/T3UPD},
  pubstate = {Working Paper (v2025-11-02-14-37)}
}