The problem of characterizing the manifest probabilities of a latent trait model is considered. The approach taken here differs from the standard approach in that a population of examinees is being considered as opposed to a single examinee. Particular attention is given to the Rasch model. (Author/JKS)

Various models have been proposed for analyzing dichotomous test or questionnaire items which were constructed to reflect an assumed underlying structure (e.g., hierarchical). This paper shows that many such models are special cases of latent class analysis and discusses a currently available computer program to analyze them. (Author/JKS)

A rating response mechanism for ordered categories such as in Likert scaling, which is related to the traditional threshold formulation but distinctively different from it, is formulated. The mechanism is based on the Rasch model. Two parameters in addition to the usual Rasch parameters are identified and discussed. (Author/JKS)

A strategy for the pairwise assessment which may be used to evaluate the nature of both "prerequisite" and "transference" relations existing among a set of traits is presented. Both confirmatory and exploratory strategies are presented. An example of how the strategy would be used is presented in the exploratory context.…

Deciding whether sets of test data are consistent with any of a large class of item response models is considered. The assumption of local independence is weakened to a new condition, local nonnegative dependence (LND). Necessary and sufficient conditions are derived for a LND item response model. (Author/JKS)

The equivalence between non-parametric marginal logistic models (NMLMs) and a class of discrete marginal logistic models is examined. Parametric models offer some of the advantages of the NMLMs approach, but there are more restrictions on the manifest probabilities. (SLD)

This article organizes models for categorical item response data into three distinct classes. "Difference models" are appropriate for ordered responses, "divide-by-total" models for either ordered or nominal responses, and "left-side added" models for multiple-choice responses with guessing. Details of the taxonomy…

A latent class model for rating data is presented which provides an alternative to the latent trait approach of analyzing test data. It is the analog of Andrich's binomial Rasch model for Lazarsfeld's latent class analysis (LCA). Response probabilities for rating categories follow a binomial distribution and depend on class-specific item…

Formulas for computing the exact signed and unsigned areas between two item characteristic curves (ICCs) are presented. It is further shown that when the "c" parameters are unequal, the area between two ICCs is infinite. The significance of the exact area measures for item bias research is discussed. (Author)

Two discrimination coefficients, known as "disco" and "odisco," are proposed for measuring the extent of overlap in distributions as a direct function of the variance between the arithmetic means. These coefficients are related to K. Pearson's "eta" (1905) and R. A. Fisher's "F" (1950). (SLD)

For the six available sets of empirical data, the discrimination (slope) parameter of the logistic item characteristic curve was found to have a significant positive correlation over items with the difficulty (location) parameter. This unpleasant situation can be eliminated by a suitably chosen transformation of the ability scale. (Author/RC)

This paper develops and applies three nonparametric comparisons of the shapes of two item characteristic surfaces: (1) proportional latent odds; (2) uniform relative difficulty; and (3) item sensitivity. A method is presented for comparing the relative shapes of two item characteristic curves in two examinee populations who were administered an…

An approximate relationship is devised between the unidimensional model used in data analysis and a multidimensional model hypothesized to be generating the item responses. Scale shrinkage is successfully predicted for several sets of simulated data. (Author/LMO)

The Rasch model is generalized to a multicomponent model, so that observations of component events are not needed to apply the model. It is shown that the generalized model maintains the property of specific objectivity of the Rasch model. An application to a mathematics test is provided. (Author/JKS)

Social and naturally occurring choice phenomena are often of the "pick any" type in which the number of choices made by a subject as well as the set of alternatives from which they are chosen is unconstrained. A model and scaling method for these data are introduced. (Author/JKS)