The issue of the number of factors to be retained in a factor analysis has been an undefined. Be that as it may, this paper tries to x-ray the number of factors (k) to be retained in a factor analysis for different sample sizes using the method of Principal Factor estimation when the number of variables are ten (10). Stimulated data were used for sample sizes of 30, 50 and 70 and the Akaike Information Criterion (AIC), the Schwarz Information Criterion (SIC) and the Hannan Quinne Information Criterion (HQIC) values were obtained when the number of factors(k) are two, three, and five (2,3 and 5). It was discorvered that the AIC, SIC, and HQIC values are smallest when k = 5, and highest when k = 2 for the sample sizes of 30 and 70. But, for a sample of 50, the values of these information criteria is smallest for k = 3, highest for k=5. Hence, conclusion is drawn that for the sample sizes of 30 and 70, the optimal number of factors to retain is 5 and 3 for the sample size of 70. This implies that, the number of factors to retain is a function of the sample size of the data.
| Published in | American Journal of Theoretical and Applied Statistics (Volume 2, Issue 6) |
| DOI | 10.11648/j.ajtas.20130206.13 |
| Page(s) | 166-175 |
| 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), 2024. Published by Science Publishing Group |
Factor Analysis, Factor Rotation, Principal Factors Estimation Method, Hannan Quinne Information Criteria, Akaike, Schwarz
| [1] | Akaike, H. (1973). Information Theory and Extension of the Maximum Likelihood Principle; Second International Symposium on Information Theory (B.N. Petrov and F. Csaki, Eds.). Budapest Hungary: Akademia Kiado, 267-281 |
| [2] | Bai, J., and Serena, N.(2002). Determing the Number of Factors in Appoximate Factor Models. Econometrica 70,1,192-221 |
| [3] | Harman, H.H. (1976). Modern Factor Analysis (3rd Ed.). Chicago: The University of Chicago Press. |
| [4] | Johnson, R.A., and Wichern, D.W. (2007). Applied Multivariate Statistical Analysis (6th Ed.). Prentics Hall, Englewood Cliffs, New Jersey. |
| [5] | Lawley, D.N., and Maxwell, A.E. (1963). Factor Analysis as a Statistical Method. London: Butterworth. |
| [6] | Onyeagu, S.I. (2003). A First Course in Multivariate Statistical Analysis (1st Ed.). Mega Concept Publishers. |
| [7] | Spearman, C. (1904). ‘General Intelligence’ Objectively Determined and Measured, American Journal of Psychology,15, 201-293. |
| [8] | Thurstone, L.L., (1947). Multiple Factor Analysis. Chicago: University of Chicago Press. |
APA Style
Nwosu Dozie. F., Onyeagu Sidney. I., Osuji George A. (2013). Method of Principal Factors Estimation of Optimal Number of Factors: An Information Criteria Approach. American Journal of Theoretical and Applied Statistics, 2(6), 166-175. https://doi.org/10.11648/j.ajtas.20130206.13
ACS Style
Nwosu Dozie. F.; Onyeagu Sidney. I.; Osuji George A. Method of Principal Factors Estimation of Optimal Number of Factors: An Information Criteria Approach. Am. J. Theor. Appl. Stat. 2013, 2(6), 166-175. doi: 10.11648/j.ajtas.20130206.13
AMA Style
Nwosu Dozie. F., Onyeagu Sidney. I., Osuji George A. Method of Principal Factors Estimation of Optimal Number of Factors: An Information Criteria Approach. Am J Theor Appl Stat. 2013;2(6):166-175. doi: 10.11648/j.ajtas.20130206.13
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Download@article{10.11648/j.ajtas.20130206.13,
author = {Nwosu Dozie. F. and Onyeagu Sidney. I. and Osuji George A.},
title = {Method of Principal Factors Estimation of Optimal Number of Factors: An Information Criteria Approach},
journal = {American Journal of Theoretical and Applied Statistics},
volume = {2},
number = {6},
pages = {166-175},
doi = {10.11648/j.ajtas.20130206.13},
url = {https://doi.org/10.11648/j.ajtas.20130206.13},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.20130206.13},
abstract = {The issue of the number of factors to be retained in a factor analysis has been an undefined. Be that as it may, this paper tries to x-ray the number of factors (k) to be retained in a factor analysis for different sample sizes using the method of Principal Factor estimation when the number of variables are ten (10). Stimulated data were used for sample sizes of 30, 50 and 70 and the Akaike Information Criterion (AIC), the Schwarz Information Criterion (SIC) and the Hannan Quinne Information Criterion (HQIC) values were obtained when the number of factors(k) are two, three, and five (2,3 and 5). It was discorvered that the AIC, SIC, and HQIC values are smallest when k = 5, and highest when k = 2 for the sample sizes of 30 and 70. But, for a sample of 50, the values of these information criteria is smallest for k = 3, highest for k=5. Hence, conclusion is drawn that for the sample sizes of 30 and 70, the optimal number of factors to retain is 5 and 3 for the sample size of 70. This implies that, the number of factors to retain is a function of the sample size of the data.},
year = {2013}
}
TY - JOUR T1 - Method of Principal Factors Estimation of Optimal Number of Factors: An Information Criteria Approach AU - Nwosu Dozie. F. AU - Onyeagu Sidney. I. AU - Osuji George A. Y1 - 2013/10/30 PY - 2013 N1 - https://doi.org/10.11648/j.ajtas.20130206.13 DO - 10.11648/j.ajtas.20130206.13 T2 - American Journal of Theoretical and Applied Statistics JF - American Journal of Theoretical and Applied Statistics JO - American Journal of Theoretical and Applied Statistics SP - 166 EP - 175 PB - Science Publishing Group SN - 2326-9006 UR - https://doi.org/10.11648/j.ajtas.20130206.13 AB - The issue of the number of factors to be retained in a factor analysis has been an undefined. Be that as it may, this paper tries to x-ray the number of factors (k) to be retained in a factor analysis for different sample sizes using the method of Principal Factor estimation when the number of variables are ten (10). Stimulated data were used for sample sizes of 30, 50 and 70 and the Akaike Information Criterion (AIC), the Schwarz Information Criterion (SIC) and the Hannan Quinne Information Criterion (HQIC) values were obtained when the number of factors(k) are two, three, and five (2,3 and 5). It was discorvered that the AIC, SIC, and HQIC values are smallest when k = 5, and highest when k = 2 for the sample sizes of 30 and 70. But, for a sample of 50, the values of these information criteria is smallest for k = 3, highest for k=5. Hence, conclusion is drawn that for the sample sizes of 30 and 70, the optimal number of factors to retain is 5 and 3 for the sample size of 70. This implies that, the number of factors to retain is a function of the sample size of the data. VL - 2 IS - 6 ER -
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