General algorithms are presented that can be used for optimizing matrix trace functions subject to certain constraints on the parameters. The parameter set that minimizes the majorizing function also decreases the matrix trace function, providing a monotonically convergent algorithm for minimizing the matrix trace function iteratively. (SLD)

A new algorithm to obtain the least squares solution in common factor analysis is presented. It is based on the up-and-down Marquadt algorithm developed by the present authors. Experiments in the use of the algorithm under various conditions are discussed. (Author/JKS)

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)

Joint correspondence analysis is a technique for constructing reduced-dimensional representations of pairwise relationships among categorical variables. An alternating least-squares algorithm for conducting joint correspondence analysis is presented that requires fewer iterations than the algorithm previously proposed by M. J. Greenacre. (SLD)

In FACTALS, an alternating least squares algorithm is used to fit the common factor analysis model to multivariate data. A. Mooijaart (1984) demonstrated that the algorithm is based on an erroneous assumption. This paper gives a proper solution for the loss function used in FACTALS. (Author/TJH)

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)

An algorithm, based on a solution for C. I. Mosier's oblique Procrustes rotation problem, is presented for the best least-squares fitting correlation matrix approximating a given missing value or improper correlation matrix. Results are of interest for missing value and tetrachoric correlation, indefinite matrix correlation, and constrained…

A method for robust canonical discriminant analysis via two robust objective loss functions is discussed. Majorization is used at several stages in the minimization procedure to obtain a monotonically convergent algorithm. A simulation study and empirical data illustrate the procedure. (SLD)

A model is proposed in which different sets of linear constraints are imposed on different dimensions in component analysis and classical multidimensional scaling frameworks. An algorithm is presented for fitting the model to the data by least squares. Examples demonstrate the method. (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)

A review of existing techniques for the analysis of three-way data revealed that none were appropriate to the wide variety of data usually encountered in psychological research, and few were capable of both isolating common information and systematically describing individual differences. Such a model is developed and evaluated. (Author/JKS)

A new method to estimate the parameters of Tucker's three mode principal component model is discussed, and the convergence properties of the alternating least squares algorithm to solve the estimation problem are considered. An example is presented. (Author/JKS)

A new computing algorithm, MAPCLUS (Mathematical Programming Clustering), for fitting the Shephard-Arabie ADCLUS (Additive Clustering) model is presented. Details and benefits of the algorithm are discussed. (Author/JKS)