Skip to main content
Log in

Factor Analysis Revisited

  • Original Article
  • Published:
Journal of Statistical Theory and Practice Aims and scope Submit manuscript

Abstract

Factor Analysis, one of the topics dealt with in the area of multivariate statistical analysis, is often a very difficult and confusing topic for the students. Difficulties come from the presence of too many parameters and no clear exact analytical solutions for estimating these parameters and deciding on the nature of the model. All the procedures call for help from computers and seek numerical solutions. Students see too many ad hoc procedures in this area, and this creates more confusion. It will be shown in the present discussion that exact analytical solutions can be obtained at least in the likelihood ratio procedure or Wilks’ \(\lambda \)-criterion if some special function techniques and matrix-variate distributions are used. Some of these ideas will be outlined in the present discussion. Factor analysis is discussed in all leading books on multivariate statistical analysis, see for example Anderson (An introduction to multivariate statistical analysis, 3rd edn, Wiley-Interscience, New Jersey, 2003).

This is a preview of subscription content, log in via an institution to check access.

Access this article

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Anderson TW (2003) An Introduction to Multivariate Statistical Analysis, 3rd edn. Wiley-Interscience, New Jersey

    MATH  Google Scholar 

  2. Mathai AM (1997) Jacobians of Matrix Transformations and Functions of Matrix Argument. World Scientific Publishing, New York

    Book  Google Scholar 

Download references

Acknowledgements

The author wishes to thank Professor Dr. Serge B. Provost for reading the first draft of this paper and making comments which enabled the author to improve the presentation of the material. The author declares no conflict of interest in this paper. The work is not supported by any grant from granting agencies.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to A. M. Mathai.

Additional information

This paper is dedicated to the 100th birth anniversary of Professor Dr. C.R. Rao.

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Mathai, A.M. Factor Analysis Revisited. J Stat Theory Pract 15, 75 (2021). https://doi.org/10.1007/s42519-020-00160-1

Download citation

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s42519-020-00160-1

Keywords

Navigation