A full-fledged matrix derivation of Sherin's matrix formulation of Kaiser's varimax criterion is provided. Matrix differential calculus is used in conjunction with the Hadamard (or Schur) matrix product. Two results on Hadamard products are presented. (Author/JKS)

Higher order factor analysis is an extension of factor analysis that is little used, but which offers the potential to model the hierarchical order often seen in natural (including psychological) phenomena more accurately. The process of higher order factor analysis is reviewed briefly, and various interpretive aids, including the Schmid-Leiman…

A desirable property of the equamax criterion for analytic rotation in factor analysis is presented. (Author)

An index of factorial simplicity, employing a quartimax transformational criteria, is developed. This index is both for each row separately and for a factor pattern matrix as a whole. The index varies between zero and one. The problem of calibrating the index is discussed. (Author/RC)

Under mild assumptions, when appropriate elements of a factor loading matrix are specified to be zero, all orthogonally equivalent matrices differ at most by column sign changes. A variety of results are given here for the more complex case in which the specified values are not necessarily zero. (Author/JKS)

Three properties of the binormamin criterion for analytic transformation in factor analysis are discussed. Particular reference is made to Carroll's oblimin class of criteria. (Author)

The accuracy of the varimax and promax methods of rotation of axes in reproducing known factor matrices was examined. It was found that only when all tests are univocal, or nearly so, could one be reasonably confident that an obtained factor matrix faithfully reproduces a contrived matrix. (Author/JKS)

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)

Necessary and sufficient conditions for rotating matrices to maximal agreement in the least-squares sense are discussed. A theorem which solves the case of two matrices is given a more straightforward proof. Other considerations in rotating matrices are discussed. (Author/JKS)

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)

Univocal varimax is an orthogonal factor rotation strategy aimed at improving upon the simple structure qualities of a preliminary varimax solution. This is accomplished by targetting for patterned rotation the highest element in each row of the varimax factor loading matrix. (Author)

Over the years, a number of rationales have been advanced to solve the problem of "blind" oblique factor transformation. By blind transformation is meant the transformation of orthogonal--and often interpretively ineffectual--factors to a position usually dictated by Thurstone's principles of simple structure, but not influenced by a…

Standard errors for maximum likelihood estimates of factor loadings are expressed in terms of the inverse of an augmented information matrix. This formulation arises naturally by viewing the problem as one in constrained maximum likelihood estimation. The constraints correspond to the form of rotation used. Results are given for canonical rotation…

A computational algorithm, called the orthotran solution, is developed for determining oblique factor analytic solutions utilizing orthogonal transformation matrices. Selected results from illustrative studies are provided. (Author/JKS)

A generalized congruence maximization procedure for the case of m matrices is presented. The orthogonal rotation procedure simultaneously maximizes the sums of all coefficients of congruence between corresponding factors of m factor matrices. (NSF)