The Dutch Identity is a useful way to reexpress the basic equations of item response theory (IRT) that relate the manifest probabilities to the item response functions (IRFs) and the latent trait distribution. The identity may be exploited in several ways. For example: (1) to show how IRT models behave for large numbers of items--they are…

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…

A Rasch model for ordered response categories is derived and it is shown that it retains the key features of both the Thurstone and Likert approaches to studying attitude. Key features of the latter approaches are reviewed. Characteristics in common with the Thurstone approach are: statements are scaled with respect to their affective values;…

This article examines the affect of misfit on methods to minimize the inaccuracy of the Item Response Theory (IRT). Three of the most commonly used IRT models were fit in this simulation. (RB)

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…

Residual patterns should be studied in order to understand when and why data deviate from a model. This paper illustrates some techniques for exploring residual patterns resulting from the difference between observed and expected scores as predicted by a Rasch model for polychotomous data. The score residual divided by its standard deviation is…

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.…

This article presents a non-mathematical introduction to latent trait test models and some of their features. Latent trait models are compared to classical test models. Two promising applications of latent trait models and available computer programs are discussed. (Author/JKS)

This article explains the Rasch model for sample-free item analysis and test-free person measurement. It shows how to estimate model parameters from data and how to evaluate the statistical fit of these estimates to the data. Attention is paid to practical considerations. (Author/JKS)

This paper summarizes three studies that illustrate how application of the three-parameter logistic test model helped solve three relatively intractable testing problems. The three problems are: designing a multi-purpose test, evaluating an multi-level test, and equating a test on the basis of pretest statistics. (Author/JKS)

An elaboration of a psychometric model for rated data, which belongs to the class of Rasch models, is shown to provide a model with two parameters, one characterizing location and one characterizing dispersion. Characteristics of the dispersion parameter are discussed. (Author/JKS)

A probablistic approach to classification and diagnosis of erroneous rules of operations that result from misconceptions ("bugs") in a procedural domain of arithmetic is introcuced. Variability of response errors is explicitly treated through item response theory. As a concrete example, a signed-number subtraction dataset is analyzed.…

A model is presented for item responses when different examinees use different strategies to arrive at their answers and when only those answers, not choice or strategy or subtask results, can be observed. Using substantive theory to differentiate the likelihoods of response vectors under a fixed set of solution strategies, responses are modeled…

An accepted criterion for gauging the fairness of examinees' scores, derived from judge-awarded ratings, has been the size of the correlation between the judges and the inter-rater reliability. Various means of achieving inter-rater reliability were reviewed, and a model to measure inter-rater reliability is forwarded. Both theoretical and…