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Research Article |

On Different Extraction Methods of Factor Analysis

This study aims at examining and comparing different methods of extracting factor analysis and applying such to real life scenario. Factor analysis simplifies complex and diverse relationships existing among a set of observed variables. This is carried out by unfolding common factor connecting unrelated variables that provide insight to the underlying data structure. Since common factors have unit variance, the variance of a given variable is partitioned into common variance and unique variance which were used to generate the total variance. The model assumptions for both random and non-random factor score analyses were examined to ascertain whether or not the model contains the model parameters to be estimated. Different methods of extracting factor analysis were examined and applied for possible comparison. The centroid method maximizes the sum of loadings without giving recourse to the signs; the principal factor method accounts for the maximum feasible amount of variance in the variables being factored and the maximum likelihood method maximizes the relationship between the sample of data and the population from which the sample is drawn. It was established that the principal component method is scale invariant while the maximum likelihood method of factor analysis provides the best estimate for the reproduced correlation matrix with convergence to the best value. It is therefore asserted that different extraction methods produce different solutions.

Factors, Correlation Matrix, Eigen Value, Communality, Common Variance, Factor Scores

APA Style

Adeyeye, A. C., Olusegun, K. S., Rafiu, O. A. (2023). On Different Extraction Methods of Factor Analysis. Science Journal of Applied Mathematics and Statistics, 11(3), 48-55.

ACS Style

Adeyeye, A. C.; Olusegun, K. S.; Rafiu, O. A. On Different Extraction Methods of Factor Analysis. Sci. J. Appl. Math. Stat. 2023, 11(3), 48-55. doi: 10.11648/j.sjams.20231103.12

AMA Style

Adeyeye AC, Olusegun KS, Rafiu OA. On Different Extraction Methods of Factor Analysis. Sci J Appl Math Stat. 2023;11(3):48-55. doi: 10.11648/j.sjams.20231103.12

Copyright © 2023 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License ( which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

1. C. A. Mertler, R.V. Reinhart. Advanced and Multivariate Statistical Methods. Practical Application and Interpretation, New York: Routledge (2017).
2. C.R. Kothari, G. Gaurav, Research Methodology, Methods and Techniques, 3rd ed., New Age International Publishers, New-Delhi (2013).
3. F. Benaych-Georges, N. Raj-Rao, The Singular Values and Vectors of Low Rank Perturbations of Large Rectangular Random Matrices, Journal of Multivariate Analysis 111 (2012) 120–135.
4. F. Walker, G. Welch, Demystifying Factor Analysis: How it Works and How to Use it, U.S.A., Xlibris Co-oporation (2010).
5. I. Jolliffe, Principal Component Analysis, New York: Springer-Verlag (1986).
6. L.S. Meyers, G. Gamst, A. J. Guarino, Applied Multivariate Research: Design and Interpretation, Los Angeles: SAGE. (2017).
7. M.M. Wall, F. Wang, Generalized Common Spatial Factor Model, Biostatistics 4 (4) (2003) 569-582.
8. N. Islam, M. Z. Mamun, Factors for Not Buying Life Insurance Policiesina Developing Country, A Case of Bangledesh, Journal of Business Administration, 1& 2: (2005) 31.
9. P.J. Kpolorie, IBM SPSS Statistics Excellent Guide, U.S.A.: Amazon (2021). KDP.
10. R.A. Johnson, D.W. Wichern, Applied Multivariate Statistical Analysis, New Jersey: Pearson Prentice Hall (2019).
11. R. M. Warner, Applied Statistics: From Bi-variate through Multivariate Techniques, Los Angeles (2013).
12. S. Noora, Factor Analysis as a Tool for Survey Analysis, American Journal of Applied Mathematics and Statistics (2021).
13. T. M. Boron, Confirmatory Factor Analysis for Applied Research, New-York: Gullford Press (2015).
14. R. D. William, G. Mathew, Multivariate Analysis, Methods and Applications, John Wiley &Sons Inc. (1984).