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…

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 nonmetric algorithm, pairwise partitioning, is developed to identify feature-based similarity structures. Presents theorems about the validity of the features identified by the algorithm, and reports results of Monte Carlo simulations that estimate the probabilities of identifying valid features for different feature structures and amounts of…

A probabilistic choice model, based on L. L. Thurstone's Law of Comparative Judgment Case V, is developed for paired comparisons data about psychological stimuli. The model assumes that each stimulus is measured on a small number of physical variables. An algorithm for estimating parameters is illustrated with real data. (SLD)

A model is presented for item responses when different subjects use different strategies, but only responses--not choice of strategy--can be observed. Substantive theory is used to differentiate the likelihoods of response vectors under a fixed set of strategies, and response probabilities are modeled via item parameters for each strategy. (TJH)

An extension is proposed for the network algorithm introduced by C.R. Mehta and N.R. Patel to construct exact tail probabilities for testing the general hypothesis that item responses are distributed according to the Rasch model. A simulation study indicates the efficiency of the algorithm. (SLD)