Ideal point discriminant analysis (IPDA) is proposed for the analysis of contingency tables of cross-classified data. Several data sets illustrate IPDA, which combines log-linear and dual scaling models to provide a spatial representation of row and column categories and allow statistical evaluation of various structural hypotheses about…

This special issues describes multidimensional scaling (MDS), with emphasis on proximity and preference models. An introduction and six papers review statistical developments in MDS study design and scrutinize MDS research in four areas of application (consumer, social, cognitive, and vocational psychology). (SLD)

When the highest-way association is present in a 3-way cross-classification of frequencies, standard logit and loglinear models have an many parameters as there are cells in the table; that is, the models are "saturated." Extensions of logit and loglinear models are described here that provide more parsimonious alternatives to saturated…

The role of conditionality in the INDSCAL and ALSCAL multidimensional scaling procedures is explained. The effects of conditionality on subject weights produced by these procedures is illustrated via a single set of simulated data. Results emphasize the need for caution in interpreting subject weights provided by these techniques. (Author/JKS)

A method based on homogeneity analysis (multiple correspondence analysis or multiple scaling) is proposed to reduce many categorical variables to one variable with "k" categories. The method is a generalization of the sum of squared distances cluster analysis problem to the case of mixed measurement level variables. (SLD)

Order analysis is discussed as a method for description of formal structures in multidimensional space. Its algorithm was derived using a combination of psychometric theory, formal logic theory, information theory, and graph theory concepts. The model provides for adjustment of its sensitivity to random variation. (Author/JKS)

A method for externally constraining certain distances in multidimensional scaling configurations is introduced and illustrated. The method is described in detail and several examples are presented. (Author/JKS)

Multidimensional scaling (MDS) a highly reliable measurement technique, often requires an overwhelming task of the subject in the data collection procedure. This investigation was designed to determine the loss of precision in solution associated with five degrees of systematic reduction in the data collection task. Data were simulated via Monte…

This study formulates a property of a quantification method, the principle of equivalent partitioning. When used with Guttman's principle of internal consistency, the combination allows the analysis of correlational data in terms of the variate(s) chosen by the investigator. Applications to multiple-choice, rank-order, and paired comparison data…

A model for the analysis of paired comparison data is presented which is metric, mathematically tractable, and has an exact algebraic solution. (Authors/MB)

Statistical methods are presented to facilitate a more complete analysis of results obtained when a scaling model is applied to data from two or more groups. Various kinds of scaling models are considered here in the multiple-group context. (Author/LMO)

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)

The Cartesian theory of dimensionality (defined in terms of geometric distances between points in the test space) and Leibnitzian theory (defined in terms of order-generative connected, transitive, and asymmetric relations) are contrasted in terms of the difference between a factor analysis and an order analysis of the same data. (Author/CTM)

Two sets of five items each from the Law School Admission Test were analyzed by two methods of factor analysis, and by the Krus-Bart ordering theoretic method of multidimensional scaling. The results indicated a conceptual gap between latent trait theoretic procedures and order theoretic procedures. (Author/CTM)

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)