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 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)

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)

Recent results of Bloomfield and Watson and Knott are used to derive a class of union-intersection tests for sphericity from likelihood ratio tests of independence of two sets of variates. It is shown that the ordinary likelihood ratio test for sphericity has a natural union-intersection interpretation. (Author/RC)

A completing-the-squares type approach to the varimax rotation problem is presented. This approach yields a direct proof of global optimality of a solution for optimal rotation in a plane. (Author/LMO)

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…