Multidimensional achievement tests are recently gaining more importance in educational and psychological measurements. For example, multidimensional diagnostic tests can help students to determine which particular domain of knowledge they need to improve for better performance. To estimate the characteristics of candidate items (calibration) for…

In this paper, we develop a mixed stochastic approximation expectation-maximization (MSAEM) algorithm coupled with a Gibbs sampler to compute the marginalized maximum a posteriori estimate (MMAPE) of a confirmatory multidimensional four-parameter normal ogive (M4PNO) model. The proposed MSAEM algorithm not only has the computational advantages of…

Defines a random effects diagonal metric multidimensional scaling model, gives its computational algorithms, describes researchers' experiences with these algorithms, and provides an illustration of the use of the model and algorithms. (Author/SLD)

A method for the least squares regression of one squared variable on a second squared variable when the relationship between the original variables is linear is given. The problem arises in multidimensional scaling algorithms. (Author/JKS)

The concept of sequential estimation is introduced in multidimensional scaling. The sequential estimation method developed in this paper refers to continually updating estimates of a configuration as new observations are added. Using artificial data, the performance of this sequential method is illustrated. (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)

An Extended Two-Way Euclidean Multidimensional Scaling (MDS) model that assumes both common and specific dimensions is described and contrasted with the "standard" (Two-Way) MDS model. Illustrations with both artificial and real data on the judged similarity of nations are provided. (TJH)

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)

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)

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 review of existing techniques for the analysis of three-way data revealed that none were appropriate to the wide variety of data usually encountered in psychological research, and few were capable of both isolating common information and systematically describing individual differences. Such a model is developed and evaluated. (Author/JKS)

A new method to estimate the parameters of Tucker's three mode principal component model is discussed, and the convergence properties of the alternating least squares algorithm to solve the estimation problem are considered. An example is presented. (Author/JKS)

A new computing algorithm, MAPCLUS (Mathematical Programming Clustering), for fitting the Shephard-Arabie ADCLUS (Additive Clustering) model is presented. Details and benefits of the algorithm are discussed. (Author/JKS)

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)