An extended marginal homogeneity model is introduced for the analysis of square contingency tables with the same ordinal row and column classifications. The model hypothesizes that the ratio in each column of table delta will exhibit an exponential function of the column. (SLD)

Mathematical relationships between three-mode component analysis and stationary component analysis are explored. Theorems are presented giving constraints that must be satisfied for equivalency between component representations provided by the methods. In general, the two approaches give mathematically distinct representations. (SLD)

This paper proposes that patterns of proximity data that have been characterized in terms of asymmetric similarity may be alternatively characterized in terms of differential bias. An additive similarity and bias model is reviewed, and it is proposed that biases can be stimulus based as well as response based. (SLD)

An asymmetric version of J. Cohen's kappa statistic is presented as an appropriate measure for the agreement between two observers classifying items into nominal categories, when one observer represents the "standard." A numerical example with three categories is provided. (SLD)

In Guttman-type quantification of contingency tables and multiple-choice data (incidence data), the trivial solution because of marginal constraints is typically removed before quantification. Relevant formulas are presented for cases affected by the trivial solution and those that are not. (SLD)

H. H. Chang and W. F. Stout (1993) presented a derivation of the asymptotic posterior normality of the latent trait given examinee responses under nonrestrictive nonparametric assumptions for dichotomous item response (IRT) theory models. This paper presents an extension of their results to polytomous IRT models and defines a global information…

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)

Mathematical programing formulas are introduced as new approaches to solve the classification problem in discriminant analysis. The research literature is reviewed, and an illustration using a real-world classification problem is provided. Issues relevant to potential uses of these formulations are discussed. (TJH)

Generalizations of L. A. Goodman's RC(M) association model (1991 and earlier) are presented for three-way tables. These three-mode association models use L. R. Tucker's three-mode components model (1964, 1966) to represent the three-factor interaction or the combined effects of two- and three-factor interactions. (SLD)

Some recent methods are presented for analyzing categorical data from complex surveys involving clustering familiar in educational research. Methods that provide first-order corrections to standard multinomial-based chi-square tests by taking into account survey design effects are highlighted. Design-based calculation techniques guarantee that the…

Whether it is possible to develop a classification function that identifies the underlying range restriction from sample information alone was investigated in a simulation. Results indicate that such a function is possible. The procedure was found to be relatively accurate, robust, and powerful. (SLD)

This paper presents a detailed derivation of method of moments estimates used in computer programs for the four-parameter beta compound binomial strong true score model. A procedure is presented to deal with the case in which the usual method of moments estimates do not exist or result in invalid parameter estimates. The results presented…

A rational model of human categorization behavior is presented that assumes that categorization reflects the derivation of optimal estimates of the probability of unseen features of objects. A case is made that categorization behavior can be predicted from the structure of the environment. (SLD)

This paper focuses on three aspects related to the conceptualization and application of canonical correlation analysis as a dominant statistical model: (1) partial canonical correlation analysis and its application in statistical testing; (2) the relation between canonical correlation analysis and discriminant analysis; and (3) the relation…

Using several data sets, the relative performance of the beta binomial model and two more general strong true score models in estimating several indices of classification consistency is examined. It appears that the beta binomial model can provide inadequate fits to raw score distributions compared to more general models. (TJH)