Generalized structured component analysis (GSCA) is a multivariate method for specifying and examining interrelationships between observed variables and components. Despite its data-analytic flexibility honed over the decade, GSCA always defines every component as a linear function of observed variables, which can be less optimal when observed…

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)

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 is presented for the best least-squares fitting correlation matrix approximating a given missing value or improper correlation matrix. The proposed algorithm is based on a solution for C. I. Mosier's oblique Procrustes rotation problem offered by J. M. F. ten Berge and K. Nevels (1977). It is shown that the minimization problem…

Homogeneity analysis, or multiple correspondence analysis, is usually applied to k separate variables. In this paper, it is applied to sets of variables by using sums within sets. The resulting technique is referred to as OVERALS. It uses the notion of optimal scaling, with transformations that can be multiple or single. The single transformations…

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)

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)