The Graded Response Model (GRM; Samejima, "Estimation of ability using a response pattern of graded scores," Psychometric Monograph No. 17, Richmond, VA: The Psychometric Society, 1969) can be derived by assuming a linear regression of a continuous variable, Z, on the trait, [theta], to underlie the ordinal item scores (Takane & de Leeuw in…

Association models constitute an attractive alternative to the usual log-linear models for modeling the dependence between classification variables. They impose special structure on the underlying association by assigning scores on the levels of each classification variable, which can be fixed or parametric. Under the general row-column (RC)…

Hierarchical classes models are models for "N"-way "N"-mode data that represent the association among the "N" modes and simultaneously yield, for each mode, a hierarchical classification of its elements. In this paper we present a stochastic extension of the hierarchical classes model for two-way two-mode binary data. In line with the original…

In psychological research, one often aims at explaining individual differences in S-R profiles, that is, individual differences in the responses (R) with which people react to specific stimuli (S). To this end, researchers often postulate an underlying sequential process, which boils down to the specification of a set of mediating variables (M)…

Proposed a taxonomy of latent structure assumptions for probability matrix decomposition (PMD) that includes the original PMD model and a three-way extension of the multiple classification latent class model. Simulation study results show the usefulness of the taxonomy. (SLD)

For the exploratory analysis of a matrix of proximities or (dis)similarities between objects, one often uses cluster analysis (CA) or multidimensional scaling (MDS). Solutions resulting from such analyses are sometimes interpreted using external information on the objects. Usually the procedures of CA, MDS and using external information are…

This paper presents a new hierarchical classes model, called Tucker2-HICLAS, for binary three-way three-mode data. As any three-way hierarchical classes model, the Tucker2-HICLAS model includes a representation of the association relation among the three modes and a hierarchical classification of the elements of each mode. A distinctive feature of…

A method for robust canonical discriminant analysis via two robust objective loss functions is discussed. Majorization is used at several stages in the minimization procedure to obtain a monotonically convergent algorithm. A simulation study and empirical data illustrate the procedure. (SLD)

A simulation study compares nonhierarchical clustering capabilities of a class of neural networks using Kohonen learning with a K-means clustering procedure. The focus is on the ability of the procedures to recover correctly the known cluster structure in the data. Advantages and disadvantages of the procedures are reviewed. (SLD)

This paper proposes a multidimensional generalization of Coombs' (1964) parallelogram model for "pick any/'n'" data, which result from each of a number of subjects having selected a number of objects (s)he likes most from a prespecified set of "n" objects. In the model, persons and objects are represented in a low dimensional space defined by a…

An adaptive testing algorithm is presented based on an alternative modeling framework, and its effectiveness is investigated in a simulation based on real data. The algorithm uses a latent class modeling framework in which assessed latent attributes are assumed to be categorical variables. (SLD)

A technique is presented to transform incomplete categorical data into complete data by imputing appropriate scores into missing cells. A solution of the optimization problem is suggested, and relevant psychometric theory is discussed. The average correlation should be at least 0.50 before the method becomes practical. (SLD)

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.…