What is the difference between principal component analysis and factor analysis?

What are difference between varimax, quartimax and equamax rotation in factor analysis?

• In factor analysis,varimax, quartimax and equamax rotation are the commonly used methods in orthogonal rotation.

• Answer:

  varimax rotation A method for rotating axes of a plot such that the eigenvectors remain orthogonal as they are rotated. These rotations are used in principal component analysis so that the axes are rotated to a position in which the sum of the variances of the loadings is the maximum possible == All rotations in Minitab's Factor Analysis are orthogonal rotations, which result in uncorrelated factor scores and orthogonal factor loadings. These rotations move the entire factor structure in a rigid frame around the origin. The communalities are unchanged from the unrotated to the rotated solution. The goal of rotation is to obtain a simpler factor loading pattern that is easier to interpret than the original factor pattern. Specifically, the quartimax rotation (gamma = 0) maximizes the variance of the squared factor loadings in each variable, i.e., simplifies the rows of the factor loading matrix. In each variable the large loadings are increased and the small ones are decreased so that each variable will only load on a few factors. In contrast, the varimax rotation (gamma = 1) maximizes the squared factor loadings in each factor, i.e., simplifies the columns of the factor loading matrix. In each factor the large loadings are increased and the small ones are decreased so that each factor only has a few variables with large loadings by Minitab == Criteria suitable only for orthogonal rotations varimax and vgpf apply the orthogonal varimax rotation. varimax maximizes the variance of the squared loadings within factors (columns of A). It is equivalent to cf(1/p) and to oblimin(1). varimax, the most popular rotation, is implemented with a dedicated fast algorithm and ignores all optimize_options. Specify vgpf to switch to the general GPF algorithm used for the other criteria. quartimax uses the quartimax criterion. quartimax maximizes the variance of the squared loadings within the variables (rows of A). For orthogonal rotations, quartimax is equivalent to cf(0) and to oblimax. equamax specifies the orthogonal equamax rotation. equamax maximizes a weighted sum of the varimax and quartimax criteria, reflecting a concern for simple structure within variables (rows of A) as well as within factors (columns of A). equamax is equivalent to oblimin(p/2) and cf(f/(2p)). by Stata