An algorithm is described for fitting the DEDICOM model (proposed by R. A. Harshman in 1978) for the analysis of asymmetric data matrices. The method modifies a procedure proposed by Y. Takane (1985) to provide guaranteed monotonic convergence. The algorithm is based on a technique known as majorization. (SLD)

Monotonically convergent algorithms are described for maximizing sums of quotients of quadratic forms. Six (constrained) functions are investigated. The general formulation of the functions and the algorithms allow for application of the algorithms in various situations in multivariate analysis. (SLD)

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)

Two alternating least squares algorithms are presented for the simultaneous components analysis method of R. E. Millsap and W. Meredith (1988). These methods, one for small data sets and one for large data sets, can indicate whether or not a global optimum for the problem has been attained. (SLD)

A class of oblique rotation procedures is proposed to rotate a pattern matrix so that it optimally resembles a matrix that has an exact simple pattern. It is demonstrated that the method can recover relatively complex simple structures where other simple structure rotation techniques fail. (SLD)

The DEDICOM (decomposition into directional components) model provides a framework for analyzing square but asymmetric matrices of directional relationships among "n" objects or persons in terms of a small number of components. One version of DEDICOM ignores the diagonal entries of the matrices. A straightforward computational solution…

A procedure is described for minimizing a class of matrix trace functions, which is a refinement of an earlier procedure for minimizing the class of matrix trace functions using majorization. Several trial analyses demonstrate that the revised procedure is more efficient than the earlier majorization-based procedure. (SLD)

A new procedure is proposed for handling nominal variables in the analysis of variables of mixed measurement levels, and a procedure is developed for handling ordinal variables. Using these procedures, a monotonically convergent algorithm is constructed for the FACTALS method for any mixture of variables. (SLD)

The DEcomposition into DIrectional COMponents (DEDICOM) method for analysis of asymmetric data gives representations that are identified only up to a non-singular transformation. To identify solutions, it is proposed that subspace constraints be imposed on the stimulus coefficients. Procedures are discussed for several cases. (SLD)

A general approach for fitting a model to a data matrix by weighted least squares (WLS) is studied. The approach consists of iteratively performing steps of existing algorithms for ordinary least squares fitting of the same model and is based on maximizing a function that majorizes WLS loss function. (Author/SLD)

An alternating least squares algorithm is offered for fitting the DEcomposition into DIrectional COMponents (DEDICOM) model for representing asymmetric relations among a set of objects via a set of coordinates for the objects on a limited number of dimensions. An algorithm is presented for fitting the IDIOSCAL model in the least squares sense.…

A modification of the TUCKALS3 algorithm is proposed that handles three-way arrays of order I x J x K for any I. The reduced work space needed for storing data and increased execution speed make the modified algorithm very suitable for use on personal computers. (SLD)

R. A. Bailey and J. C. Gower explored approximating a symmetric matrix "B" by another, "C," in the least squares sense when the squared discrepancies for diagonal elements receive specific nonunit weights. A solution is proposed where "C" is constrained to be positive semidefinite and of a fixed rank. (SLD)