This study examines linking relationships among latent test scores and how these latent linking relationships relate to observed-score linkings. Equations are used to describe the effects of correlation between underlying latent dimensions and the similarity or dissimilarity of test composition on linking functions among latent test scores. These…

The use of Candecomp to fit scalar products in the context of INDSCAL is based on the assumption that the symmetry of the data matrices involved causes the component matrices to be equal when Candecomp converges. Ten Berge and Kiers gave examples where this assumption is violated for Gramian data matrices. These examples are believed to be local…

Let X be a statistical variable representing student ratings of University teaching. It is natural to assume for X an ordinal scale consisting of k categories (in ascending order of satisfaction). At first glance, student ratings can be summarized by a location index (such as the mode or the median of X) associated with a convenient measure of…

An integrated method for rotating and rescaling a set of configurations to optimal agreement in subspaces of varying dimensionalities is developed. The approach relates existing orthogonal rotation techniques as special cases within a general framework, based on a partition of variation that provides measures of agreement. (Author/TJH)

The geometric properties and Euclidean nature of dissimilarity coefficients defined on finite sets are discussed. Several particular transformations are presented that preserve Euclideanarity. The study of a one-parameter family adds to current knowledge of the metric and Euclidean structure of coefficients based on binary data. (SLD)

A model for preferential and triadic choice is derived in terms of weighted sums of central F distribution functions. It is a probabilistic generalization of Coombs' (1964) unfolding model from which special cases can be derived easily. This model for binary choice can be easily related to preference ratio judgments. (SLD)

A method of optimal scaling for multivariate ordinal data--OSMOD--is described, within a generalized principal component analysis. It yields a: multidimensional configuration of items, unidimensional scale of category weights for each item, and multidimensional configuration of subjects. OSMOD involves solving an eigenvalue problem and executing a…

A globally optimal solution is presented for a class of functions composed of a linear regression function and a penalty function for the sums of squared regression weights. A completing-the-squares approach is used, rather than calculus, because it yields global minimality easily in two of three cases examined. (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)

The distance approach to nonlinear multivariate analysis proposed by J. J. Meulman (1986) is reviewed. Several generalizations are discussed by combining features from the conventional multivariate analysis approach, which seeks weighted sums of variables, with the alternative approach, which seeks to fit distances. (SLD)

An algorithm based on the majorization theory of J. de Leeuw and W. J. Heiser is presented for fitting the slide-vector model. It views the model as a constrained version of the unfolding model. A three-way variant is proposed, and two examples from market structure analysis are presented. (SLD)

This paper proposes a generalization of Thurstonian probabilistic choice models for analyzing both multiple preference responses and their relationships. The approach is illustrated by modeling data from two multivariate preference experiments. Preliminary data analyses show that the extension can yield an adequate representation of multivariate…

The current state of multidimensional scaling using the city-block metric is reviewed, with attention to (1) substantive and theoretical issues; (2) recent algorithmic developments and their implications for analysis; (3) isometries with other metrics; (4) links to graph-theoretic models; and (5) prospects for future development. (SLD)

A reparameterization of the general Euclidean model for the external analysis of preference data and a simple least squares method for fitting the model to metric single stimulus data are discussed. The reformulated model is less general than is the earlier formulation by J. D. Carroll (1972). (SLD)

A weighted Euclidean distance model is proposed that incorporates a latent class approach (CLASCAL). The contribution to the distance function between two stimuli is per dimension weighted identically by all subjects in the same latent class. A model selection strategy is proposed and illustrated. (SLD)