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)

A method for multidimensional scaling that is highly resistant to the effects of outliers is described. Some Monte Carlo simulations illustrate the efficacy of the procedure, which performs well with or without outliers. (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)

Monte Carlo techniques were used to examine regression approaches to external unfolding. The present analysis examined the technique to determine if various characteristics of the points are recovered (such as ideal points). Generally, monotonic analyses resulted in good recovery. (TJH)

A stochastic multidimensional scaling procedure is presented for analysis of three-mode, three-way pick any/"J" data. The procedure fits both vector and ideal-point models and characterizes the effect of situations by a set of dimension weights. An application in the area of consumer psychology is discussed. (SLD)

Sufficient conditions are derived for the consistency and asymptotic normality of the least squares estimator of a trilinear decomposition model for multiway data analysis. The limiting covariance matrix is computed. (Author/SLD)

Using an infinite item test framework, it is argued that the usual assumption of local independence should be replaced by a weaker assumption--essential independence. The usual assumption of unidimensionality is replaced by a weaker and more appropriate statistically testable assumption of essential unidimensionality. (TJH)

A reparameterization of a latent class model is presented to classify and scale nomial and ordered categorical choice data simultaneously. The model extension represents a nonhomogeneous population as a mixture of homogeneous subpopulations. Simulated data and data from a magazine preference survey of 347 college students illustrate the model.…

This paper reviews the existing multidimensional item response theory (IRT) models and demonstrates how one of the models can be applied to estimation of abilities from a test measuring more than one dimension. The purposes of this paper were threefold. First, the fundamental concepts required when considering multidimensional models for the…

The effects of varying degrees of correlation between abilities and of various correlation configurations between item parameters on ability and item parameter estimation using the three parameter logistic model were examined. Ten two-trait configurations and one unidimensional test configuration for 30 item tests were simulated. Each…

The concept of a user-specified validity sector is discussed. The idea of the validity sector combines the work of M. D. Reckase (1986) and R. Shealy and W. Stout (1991). Reckase developed a methodology to represent an item in a multidimensional latent space as a vector. Item vectors are computed using multidimensional item response theory item…

The following seven statistical procedures are compared in terms of the ability to recover a unidimensional latent trait from Likert-type data: (1) factor analysis based on Pearson correlations (FA-PR); (2) factor analysis based on polychoric correlations (FA-PL); (3) the graded response model in item response theory (IRT-GRM); (4) internal…

A multidimensional item response theory (IRT) model for polytomously scored items, based on the graded response model and using the normal ogive, is developed; and an EM algorithm that may be used to estimate the parameters of the model is also discussed. The model is illustrated through a simulation study in which the polytomous item responses of…

A stochastic multidimensional unfolding (MDU) procedure is presented to represent individual differences in phased or sequential decision processes spatially. A Monte Carlo analysis demonstrates estimation proficiency and the appropriateness of the proposed model selection heuristic, and an application to capture awareness, consideration, and…

A procedure for interpreting multiple-discrimination indices from a multidimensional item-response theory analysis is described and demonstrated with responses of 1,635 high school students to a multiple-choice test. The procedure consists of converting discrimination parameter estimates to direction cosines and analyzing the angular distances…