A unidimensional latent trait model for continuous ratings extends Andrich's rating formulation which assumes the response process at latent thresholds is based on the dichotomous Rasch model. The separability of the structural and incidental parameters is demonstrated and a procedure for estimating the parameters is outlined. (Author/GDC)

Four discussions of test construction based on item response theory (IRT) are presented. The first discussion, "Test Design as Model Building in Mathematical Programming" (T. J. J. M. Theunissen), presents test design as a decision process under certainty. A natural way of modeling this process leads to mathematical programming. General…

The rationale behind the method of estimating the operating characteristics of discrete item responses when the test information of the Old Test is not constant was presented previously. In the present study, two subtests of the Old Test, i.e. Subtests 1, and 2, each of which has a different non-constant test information function, are used in…

The assumptions of the Rasch model are discussed and the Rasch model is reformulated as a quasi-independence model. Using ordinary contingency table methods, the Rasch model can be tested generally or against less restrictive quasi-loglinear models to investigate specific violations of its assumptions. (Author/BW)

A method is proposed to equate different sets of items administered to different groups of individuals using the Rasch model. A Rasch equating model was formulated to describe one common Rasch scale in different groups with different but overlapping sets of items. The item parameters can then be estimated simultaneously, avoiding different…

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)

A test theory model based on the Thurstone judgmental model is described. By restricting various parameters of the model, 3 Rasch models, 2 pseudo-Rasch models, 3 two-parameter models, and a Weber's Law model are derived. (Author/CTM)

A general dichotomous condition is derived for the unidimensional polytomous Rasch model. The robustness of the dichotomous analysis is investigated in a simulation study. The model shows a close relation with the two-parameter Birnbaum model. (TJH)

Latent trait test models for responses to dichotomously scored items are considered from the point of view of parameter estimation using a Bayesian statistical approach and the EM estimation algorithm. An example using the Rasch model is presented. (Author/JKS)

One of the major theoretical and practical developments in testing is latent trait analysis and item response theory. This report provides a guide for practitioners in understanding, evaluating, and using these developments to meet their testing needs. (Author)

A method based on the likelihood ratio procedure is presented for use in selecting a measurement model from among the Rasch, two-parameter, and three-parameter logistic latent trait models. (Author/BW)

Two-group classification is discussed when a unidimensional latent trait "theta" is appropriate for explaining data. If data have a monotone likelihood ratio, then optimal allocation rules can be based on its magnitude when allocation must be made to one of the two groups related to the unidimensional latent trait. (SLD)

A maximin model for test design based on item response theory is proposed. Only the relative shape of target test information function is specified. It serves as a constraint subject to which a linear programing algorithm maximizes the test information. The model is illustrated, and alternative models are discussed. (TJH)

Approximately 1200 Danish school children aged 8, 11, and 14 participated in a questionnaire study under the caption, "Why I like to read." Data from Denmark formed part of an international study, in which 12 other countries used the same questionnaire to explore various functions of reading and to compare them over different countries.…

A statistical method is described and illustrated which provides confidence envelopes around item response functions. Examples of 95 percent confidence envelopes for the one-, two-, and three-parameter logistic response models are given. In addition, the authors describe N-line plots, which show the genesis of the envelope as well as the density…