Research Article | | Peer-Reviewed

### On Different Extraction Methods of Factor Analysis

Received: 1 October 2023    Accepted: 8 November 2023    Published: 21 November 2023
Abstract

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.

 Published in Science Journal of Applied Mathematics and Statistics (Volume 11, Issue 3) DOI 10.11648/j.sjams.20231103.12 Page(s) 48-55 Creative Commons This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. Copyright Copyright © The Author(s), 2023. Published by Science Publishing Group
Keywords

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

References
 [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.https://www.amazon.com/BM-SPSS-Statistics-Excellent-Guide-ebook/DP/B08JG4. [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).
• 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. https://doi.org/10.11648/j.sjams.20231103.12

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

• ```@article{10.11648/j.sjams.20231103.12,
author = {Awogbemi Clement Adeyeye and Koyejo Samuel Olusegun and Olowu Abiodun Rafiu},
title = {On Different Extraction Methods of Factor Analysis},
journal = {Science Journal of Applied Mathematics and Statistics},
volume = {11},
number = {3},
pages = {48-55},
doi = {10.11648/j.sjams.20231103.12},
url = {https://doi.org/10.11648/j.sjams.20231103.12},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.sjams.20231103.12},
abstract = {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.
},
year = {2023}
}
```
• ```TY  - JOUR
T1  - On Different Extraction Methods of Factor Analysis
AU  - Koyejo Samuel Olusegun
AU  - Olowu Abiodun Rafiu
Y1  - 2023/11/21
PY  - 2023
N1  - https://doi.org/10.11648/j.sjams.20231103.12
DO  - 10.11648/j.sjams.20231103.12
T2  - Science Journal of Applied Mathematics and Statistics
JF  - Science Journal of Applied Mathematics and Statistics
JO  - Science Journal of Applied Mathematics and Statistics
SP  - 48
EP  - 55
PB  - Science Publishing Group
SN  - 2376-9513
UR  - https://doi.org/10.11648/j.sjams.20231103.12
AB  - 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.

VL  - 11
IS  - 3
ER  - ```
Author Information
• Statistics Programme, National Mathematical Centre, Abuja, Nigeria

• Statistics Department, Federal University of Technology, Akure, Nigeria

• Mathematics Programme, National Mathematical Centre, Abuja, Nigeria

• Sections