On Refined Principal Component Method for Factor Analysis

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.

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