This paper summarized different rotation criteria since the 1940’s and thoroughly discussed advantages and disadvantages of each criterion. Important notes are taken as following:
There are two types of rotations, orthogonal and oblique rotation. Orthogonal rotations imply uncorrelated factors and lead to simpler factor loading patterns (e.g., perfect cluster configuration); however are less plausible representation of reality. Oblique rotations allow correlation between factors and are more plausible, but will lead to more complex configuration where each variable has a complexity (cross loadings) of at most m-1.
The most popular orthogonal rotation criteria may be varimax and quartimax, while the most popular oblique rotation criterion may be direct quartimin, which solved the problems of oblique rotation (factor collapse). These rotation criteria are widely implemented in statistical packages and are often used by applicationers.
Several rotation criteria are discussed and the conclusions are summarized below:
n CF family rotation : varimax belongs to this family. A positive characteristic of the CF family is that none of its members can results in factor collapse under direct oblique rotation.
n Geomin rotation : for oblique rotation only. Not recommended for orthogonal rotation.
n Minimum entropy rotation : recommended for orthogonal rotation only, and is unsatisfactory in oblique rotation.
n Information criterion : gives good results in both orthogonal and oblique rotation.
The paper also discussed some ways of rotating to a partially specified target. Rotation to a partially specified target has similarities to confirmatory factor analysis, because values for some factor loadings must be specified in advance. During the process of rotating, the target may be changed. Previously misspecified elements of the loading matrix can be left unspecified, while any previously unspecified elements of the loadings matrix can be specified to be zero.
Problem of standardization of factor loadings is also discussed. By multiplying a positive definite diagonal matrix to the initial factor matrix, the simplicity of the pattern of a rotated solution can be improved.
Low communalities have little effect on the final varimax solution (see, e.g., Kaiser, 1958). In order to ensure that all variables have the same influence on the rotated solution, it is recommended that the standardization should yield a matrix with equal row sums of squares. It is equivalent to assigning weights to each variable. The weights are chosen to be inverse square roots of communalities.
The Kaiser standardization is frequently employed both in orthogonal and oblique rotation.
The above paragraphs can be used as reference to analytic rotation in EFA.