This paper introduces the generalized logit-linear item response model (GLLIRM), which represents the item-solving process as a series of dichotomous operations or steps. The GLLIRM assumes that the probability function of the item response is a logistic function of a linear composite of basic parameters which describe the operations, and the…

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)

The phenomenon of 2 x 2 x 2 arrays having nonmaximal rank with positive probability, pointed out by J. Kruskal (1989), is generalized to 2 x "n" x "n" arrays. It is concluded that a pair of asymmetric square matrices can be diagonalized simultaneously with positive probability. (SLD)

It is shown that common factors are not subject to indeterminancy to the extent that has been claimed (Guttman, 1955), because the measure of indeterminancy that has been adopted is ill-founded. (Author/RC)

ORDMET is applicable to structures obtained from additive conjoint measurement designs, unfolding theory, general Fechnerian scaling, types of multidimensional scaling, and ordinal multiple regression. A description is obtained of the space containing all possible numerical representations which can satisfy the structure, size, and shape of which…

Discusses Guttman's index of indeterminacy in light of alternative solutions which are equally likely to be correct and alternative solutions for the factor which are not equally likely to be chosen. Offers index which measures a different aspect of the same indeterminacy problem. (ROF)

Generalizing Boolean matrix decomposition to a larger class of matrix decomposition models is demonstrated, and probability matrix decomposition (PMD) models are introduced as a probabilistic version of the larger class. An algorithm is presented for the computation of maximum likelihood and maximum a posteriori estimates of the parameters of PMD…

A complete enumeration method and a Monte Carlo method are presented to calculate the probability distribution of arbitrary statistics of adjacency matrices when these matrices have the uniform distribution conditional on given row and column sums, and possibly on a given set of structural zeros. (SLD)

Considers a class of estimation procedures for the factor model. The procedures are shown to yield estimates possessing the same asymptotic sampling properties as those from estimation by maximum likelihood or generalized last squares, both special members of the class. General expressions for the derivatives needed for Newton-Raphson…

This paper provides a method for analyzing data consisting of event sequences and covariate observations associated with Markov chains. The objective is to use the covariate data to explain differences between individuals in the transition probability matrices characterizing their sequential data. (TJH)