The Candecomp/Parafac (CP) method decomposes a three-way array into a prespecified number R of rank-1 arrays, by minimizing the sum of squares of the residual array. The practical use of CP is sometimes complicated by the occurrence of so-called degenerate sequences of solutions, in which several rank-1 arrays become highly correlated in all three…

Although RC(M)-association models have become a generally useful tool for the analysis of cross-classified data, the graphical representation resulting from such an analysis can at times be misleading. The relationships present between row category points and column category points cannot be interpreted by inter point distances but only through…

Bounds are established for log odds ratios (log cross-product ratios) involving pairs of items for item response models. First, expressions for bounds on log odds ratios are provided for one-dimensional item response models in general. Then, explicit bounds are obtained for the Rasch model and the two-parameter logistic (2PL) model. Results are…

This paper focuses on model interpretation issues and employs a geometric approach to compare the potential value of using the Grade of Membership (GoM) model in representing population heterogeneity. We consider population heterogeneity manifolds generated by letting subject specific parameters vary over their natural range, while keeping other…

A new procedure for nonmetric multidimensional scaling is proposed and evaluated in this extensive article. The procedure generalizes to a wide variety of situations and types of data and is robust with respect to measurement error. The statistical development of the procedure and examples of its use are presented. (JKS)

The collection of repeated measures in psychological research is one of the most common data collection formats employed in survey and experimental research. The behavioral decision theory literature documents the existence of the dynamic evolution of preferences that occur over time and experience due to learning, exposure to additional…

In studies involving judgments of similarity or dissimilarity, a variety of other variables may also be measured. In such cases, there are important advantages to joint analyses of the dissimilarity and collateral variables. A variety of models are described for relating these and algorithms are described for fitting these to data. (Author/JKS)

Repeated measures designs have traditionally been analyzed by the univariate mixed model approach, in which the repeated measures effect is tested against an error term based on the subject by treatment interaction. This paper considers an extension of this analysis to designs in which the individual repeated measures are multivariate. (Author/JKS)

Contains a solution for the multidimensional scaling of pairwise choice when individuals are represented as dimensional weights. The analysis supplies an exact least squares solution and estimates of group unscalability parameters. (DG)

An individual differences additive model is discussed which represents individual differences in additivity by differential weighting or additive factors. A procedure for estimating model parameters for various data measurement characteristics is developed. The method is found to be very useful in describing certain types of developmental change…

This paper offers a new methodology for analyzing individual differences in preference judgments with regard to a set of stimuli. (Author)