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On Refi ned Principal Component Method for Factor Analysis

AUTHOR(S):

D. F. Nwosu; S. I. Onyeagu; J.I. Mbegbu; V. U. Ekhosuehi

JOURNAL: Journal of the Nigerian Statistical Association Vol. 28, 2016
YEAR: 2016

ABSTRACT

This paper is centred on the development of a method, known as the refined Principal Component Method (rPCM), for the construction of the underlying relationships between variables. The proposed method settles the perturbing issue in the literature on the initial assumption of exact dependence of variables on the factors in the classical Principal Component Method (PCM). The development of the rPCM is hinged on matrix splitting. Theoretical aspects of eigenvalues and eigenvectors as it relates to symmetric and commutative matrices are carefully applied. Findings reveal that the rPCM generates results as that of the PCM and gives better factor loadings and communalities in terms of the error matrix and the admissible error than that of the PCM.

BIBLIOGRAPHY

Boik, R. J. (2013). Model-based principal components of correlation matrices. Journal of Multivariate Analysis, 116: 310 - 331.

Choi, J. H. (2010). Penalized Maximum Likelihood Factor Analysis. PhD Thesis,University of Minnesota.

Climent, J.-J. and Perea, C. (1998). Some comparison theorems for weak nonnegative splittings of bounded operators. Linear Algebra and its Applications, 275/276: 77-106.

Elsner, L. (1989). Comparisons of weak regular splitting and multisplitting methods.Numerische Mathematik 56(2-3): 283 - 289.

Jedrzejec, H. A. and Woznicki, Z. I. (2001). On properties of some matrix splitting.Electronic Journal of Linear Algebra 8: 47-52.

Parmet, Y., Schechtman, E. and Sherman, M. (2010).Factor analysis revisited - How many factors are there? Communications in Statistics - Simulation and Computation,39: 1893 { 1908.

Qi, X., Luo, R. and Zhao, H. (2013). Sparse principal component analysis by choice of norm. Journal of Multivariate Analysis, 114: 127 - 160.

Rencher, A. C. (2002). Methods of Multivariate Analysis (2nd Ed.). John Wiley & Sons Inc., New York.

Shen, H. and Huang, J. Z. (2008). Sparse principal component analysis via regularized low rank matrix approximation. Journal of Multivariate Analysis, 99: 1015 - 1034.

Song, Y. Z. (1991). Comparisons of nonnegative splittings of matrices. Linear Algebra and its Applications, 154/156: 433-455.

Torokhti, A. and Friedland, S. (2009). Towards theory of generic principal component analysis. Journal of Multivariate Analysis, 100: 661 - 669.

Woznicki, Z. (2001). Matrix splitting principles. International Journal of Mathematics and Mathematical Sciences, 28(5): 251 - 284.

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Journal of the Nigerian Statistical Association Vol. 28, 2016
2016

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