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)

Presents two methods for including weights in distance-based nonlinear multivariate data analysis. One method assigns weights to the objects, while the other is concerned with differential weighing of groups of variables. Discusses applications of these weighting schemes and proposed an algorithm to minimize the corresponding loss function. (SLD)

The frequencies of "m" independent "p-way" contingency tables are analyzed by a model that assumes that the ordinal category data in each of "m" groups are generated from a latent continuous multivariate normal distribution. The model permits analysis of several groups of individuals simultaneously. (TJH)

Homogeneity analysis (multiple correspondence analysis), which is usually applied to "k" separate variables, was applied to sets of variables by using sums within sets. The resulting technique, OVERALS, uses optimal scaling. The corresponding OVERALS computer program minimizes a least squares loss function via an alternating least…

A probabilistic choice model, based on L. L. Thurstone's Law of Comparative Judgment Case V, is developed for paired comparisons data about psychological stimuli. The model assumes that each stimulus is measured on a small number of physical variables. An algorithm for estimating parameters is illustrated with real data. (SLD)

Canonical analysis of two convex polyhedral cones involves looking for two vectors whose square cosine is a maximum. New results about the properties of the optimal solution to this problem are presented. The convergence of an alternating least squares algorithm and properties of limits of calculated sequences are discussed. (SLD)