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Method of Principal Component Factors Estimation of Optimal Number of Factors: An Information Criteria Approach

Author Affiliations

  • 1Department of Mathematics and Statistics Federal Polytechnic Nekede, Owerri Imo State, NIGERIA
  • 2Department of Statistics Nnamdi Azikiwe University Awka, Anambra State NIGERIA
  • 3Department of Statistics Nnamdi Azikiwe University Awka, Anambra State NIGERIA
  • 4Department of Statistics, Imo State University, Owerri, PMB 2000, Owerri NIGERIA

Res. J. Mathematical & Statistical Sci., Volume 1, Issue (9), Pages 15-29, October,12 (2013)

Abstract

This paper try to x - ray the number of factors (k) to be retained in a factor analysis for different sample sizes using the method of Principal Component Factor estimation when the number of variables are ten (10). Stimulated data were used for ample size s 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 discov ered that the optimal number of factors to retain using the method of Principal Component Factors method of estimation is two (2) from all the sample sizes and also for all the methods considered except for the AIC in which the best is when k=3 follows by k=2 and k=5 respectively of sample thirty (30). Hence, conclusion is drawn that for the three sample sizes considered, the optimal number of factors to retain is 2.

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