There is a unity underlying the diversity of models for the analysis of multivariate data. Essentially, they constitute a family of models, most generally nonlinear, for structural/functional relations between variables drawn from a behavior domain. (Author)

A simplification of Lord and Wingersky's method for computing the asymptotic variance-covariance matrix of maximum likelihood estimates for item and person parameters under some restrictions on the estimates is presented. Computation of the error variance-covariance matrix for the item parameters in the Rasch model is described. (NSF)

Goodness of fit tests for the Rasch model are typically large-sample, global measures. This paper offers suggestions for small-sample exploratory techniques for examining the fit of item data to the Rasch model. (Author/JKS)

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)

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…

Latent trait and latent class analyses of Likert-type data are compared. Key similarities and differences between these methods are described and illustrated by applying a latent trait model and a latent class model to the analysis of a set of "life satisfaction" data. (Author/NSF)

Two linearly constrained models based on the Rasch model are discussed. Necessary and sufficient conditions for the existence of unique conditional maximum likelihood estimators are derived. Methods for hypothesis testing within this framework are proposed. (Author/JKS)

A natural parameterization and formalization of the problem of measuring change in dichotomous data is developed. Mathematically-exact definitions of specific objectivity are presented, and the basic structures of the linear logistic test model and the linear logistic model with relaxed assumptions are clarified. (SLD)

A model for longitudinal latent structure analysis was proposed that combined the values of a latent variable at two time points in a two-dimensional latent density. The correlation coefficient between the two values of the latent variable can then be estimated. (NSF)

Tau-equivalence means that two tests produce equal true scores for individuals but that the distribution of errors for the tests could be different. This paper examines the effect of performing equipercentile equating techniques on tau-equivalent tests. (JKS)

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)

Conjunctive item response models are introduced such that: (1) sufficient statistics for latent traits are not necessarily additive in item scores; (2) items are not necessarily locally independent; and (3) existing compensatory (additive) item response models including the binomial, Rasch, logistic, and general locally independent model are…

A stochastic version of a knowledge space is developed in which knowledge states are considered as possible epochs in a subject's learning history. It specifies how a subject is channeled through and progresses along a "gradation." The model's application to artificial data is described, based on maximum likelihood methods. (TJH)

Given a loss function, an asymptotic method for optimal test design for a specified target population of examinees is presented. Also, of more practical use, given an existing unidimensional test and target population, a way is presented to find the loss function for which the test is optimal. (NSF)

Asymptotic formulas are derived for the bias in the maximum likelihood estimators of the item parameters in the logistic item response model when examinee abilities are known. Numerical results are given for a typical verbal test for college admission. (Author)