Relationship between Principal Component Analysis and Factor Analysis

In every field of scientific research and application, where the masses of data is available in multivariate form, the use of multivariate statistical analysis techniques can be implemented to achieve proper statistical inferences. The statistical modeling of data is the essential part of the multivariate analysis. The model might be the linear combinations of the original data, which can be created though the relationship between Principal Component Analysis (PCA) and Factor Analysis (FA). Such process of converting the entire data into the set of few clusters or linear models is called dimension reduction. Before applying FA, the Kaiser-Meyer-Olkin (KMO) measure of sampling adequacy test for FA is used (12). Initial factor loadings and the variamx rotated factor loadings are computed via PCA approach. The estimated factor models generated by ordinary least square method, are further used for statistical control charts. Finally the generation of the uncorrelated statistical models using the relationship between PCA and FA is carried out to enable the estimation of the future outcomes. Keywords: Correlation matrix, KMO test, Reducible Eigen space, dimension reduction, varimax rotation, uncorrelated statistical models, OLS estimated factor scores, statistical control charts.