Identifies a general algorithm for orthogonal rotation and shows that when an algorithm parameter alpha is sufficiently large, the algorithm converges monotonically to a stationary point of the rotation criterion from any starting value. Introduces a modification that does not require a large alpha and discusses the use of this modification as a…

An iterative majorization algorithm is proposed for orthogonal congruence rotation that is guaranteed to converge from every starting point. In addition, the algorithm is easier to program than the algorithm proposed by F. B. Brokken, which is not guaranteed to converge. The derivation of the algorithm is traced in detail. (SLD)

A generalized matrix procedure is developed for computing the proportionate contribution of a factor, either orthogonal or oblique, to the total common variance of a factor solution. (Author)

An iterative process is proposed for obtaining an orthogonal simple structure solution. At each iteration, a target matrix is constructed such that the relative contributions of the target majorize the original ones, factor by factor. The convergence of the procedure is proven, and the algorithm is illustrated. (SLD)

Gradient methods are employed in orthogonal oblique analytic rotation. Constraints are imposed on the elements of the transformation matrix by means of reparameterisations. (Author)

Applications to the Promax Rotation are discussed, and it is shown that these procedures solve Thurstone's hitherto intractable "invariant" box problem as well as other more common problems based on real data. (Author/RC)

Beginning with the results of Girschick on the asymptotic distribution of principal component loadings and those of Lawley on the distribution of unrotated maximum likelihood factor loadings, the asymptotic distributions of the corresponding analytically rotated loadings is obtained. The principal difficulty is the fact that the transformation…

Procrustes rotation involves fitting a factor pattern matrix to a specified target matrix in factor analysis. These rotations are useful for the investigator who wishes to see how well his data can be made to fit a hypothesized factor pattern matrix. The mathematical problems involved in these transformations are outlined and computer algorithms…

Under some circumstances, it is desirable to compare the factor patterns obtained from different factor analyses. To date, the best method of simultaneously achieving simple structure and maximum similarity is the technique devised by Bloxom (1968). This technique simultaneously rotates different factor patterns to maximum similarity and varimax…