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Factor Analysis Revisited

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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).

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

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

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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.

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Correspondence to A. M. Mathai.

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

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Mathai, A.M. Factor Analysis Revisited. J Stat Theory Pract 15, 75 (2021).

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