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)

Both the attenuation paradox of traditional test theory and the assumption of local independence in person-item response theory have caused problems in interpretation. This paper demonstrates that the two are related concepts, and, through this demonstration, both are clarified. It is demonstrated that the breakdown of local independence leads to…

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…

The relatively hard problem of transforming a given set of curves to curves with the same shape can sometimes be reduced to the easier problem of rendering curves parallel. In this paper a group is associated with the given curves, and it is shown that the reduction from the hard problem to the easy problem is valid whenever the group is…

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)

This proposal attempts to follow in Allan Birnbaum's tradition by using Bayesian ideas to show that his mental test model possesses even broader applicability than previously realized. Birnbaum's two significant contributions to the theories of statistics and educational testing are: (1) the proof that the sufficiency and conditionality principles…

The purpose of this paper is to present a generalization of the concept of item difficulty to test items that measure more than one dimension. Three common definitions of item difficulty were considered: the proportion of correct responses for a group of individuals; the probability of a correct response to an item for a specific person; and the…

Two methods of constucting equal-interval scales for educational achievement are discussed: Thurstone's absolute scaling method and Item Response Theory. Alternative criteria for choosing a scale are contrasted. It is argued that clearer criteria are needed for judging the appropriateness and usefulness of alternative scaling procedures.…

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)

DICOT, a computer program for the Rasch analysis of classroom tests, is described. Results are presented in a self-explanatory form. Person ability and item difficulty estimates are expressed in a familiar metric. Person and item fit statistics provide a diagnosis of individual children and identification of problematic items. (Author/DWH)

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)

Large-scale educational assessments differ from familiar educational measurements by attempting to provide information about the levels and natures of skills in populations rather than in individuals. That the distinct purposes of assessment require different methodologies than individual measurement was recognized by the development of…