Performance of Principal Components Estimation Method on the Quality of Factor Analysis without and with Varimax Rotation

Abstract

The objective of this work was to evaluate the performance of the principal components estimation method on the quality of estimates of some parameters of exploratory factor analysis (EFA), without and with varimax rotation. To this end, 18 parametric correlation matrices (r) were imposed. These matrices were obtained from combinations between six different values of parametric communalities of four normally distributed random variables with three different proportions of distances between the parametric factorial loadings of the first two orthogonal factors. For each matrix r, the following parameters were defined: the first two eigenvalues (l1 and l2), the matrix of factor loadings (G), the four communalities () and the matrix of the specific factors (Y). After the 36 factor analyses, the respective estimates of these parameters were obtained, and their respective absolute deviations between the estimates obtained a posteriori and the parameters known a priori were evaluated. With the results of the Student's t test at 5% significance applied to the response surface analysis, it was concluded that the principal components estimation method for estimating orthogonal factors was not adequate and the varimax rotation improved relatively little the quality of the SFA estimates.