Models of modern test theory imply statistical independence among responses, generally referred to as "local independence." One violation of local independence occurs when the response to one item governs the response to a subsequent item. Expanding on a formulation of this kind of violation as a process in the dichotomous Rasch model,…

Assessments in response formats with ordered categories are ubiquitous in the social and health sciences. Although the assumption that the ordering of the categories is working as intended is central to any interpretation that arises from such assessments, testing that this assumption is valid is not standard in psychometrics. This is surprising…

This commentary examines the role of the unit from the perspective of the definition of measurement in physics as the ratio of two magnitudes, one of which is defined as the unit; it is an important and timely contribution to measurement in the social sciences. There are many different points that could be commented upon, but the author will…

Rasch models are characterised by sufficient statistics for all parameters. In the Rasch unidimensional model for two ordered categories, the parameterisation of the person and item is symmetrical and it is readily established that the total scores of a person and item are sufficient statistics for their respective parameters. In contrast, in the…

Reflects on the development of the unidimensional Rasch model for ordered categories and the resistance to some of its initially counterintuitive implications, especially that the thresholds that partition the continuum to form the ordered categories can show an empirical problem with the data. (SLD)

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;…

Uses a framework previously developed to relate outcomes based education and B. Bloom's "Taxonomy of Educational Objectives" to consider ways in which modern test theory can be used to connect aspects of assessment to the curriculum framework and to consider insights this connection might provide. (SLD)

Two classes of graded response models, one based on the work of L. L. Thurstone and the other on the work of G. Rasch, are juxtaposed and shown to satisfy important but mutually incompatible criteria and to reflect different response processes. Implications of the choice between these models are discussed. (Author/SLD)

The hyperbolic cosine unfolding model for direct responses (HCMDR) of persons to individual stimuli is elaborated in three ways. The specialization of the second parameter is shown to be a property of the data, and not arbitrary. The HCMDR is used to construct an elegant model for pairwise preferences. (SLD)

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 unidimensional model for responses to statements that have an unfolding structure was constructed from the cumulative Rasch model for ordered response categories. A joint maximum likelihood estimation procedure was investigated. Analyses of data from a small simulation and a real data set show that the model is readily applicable. (SLD)

In circumstances where judges are required to make ratings of performance, it is usually required to have two or more raters who are trained to agree on independent ratings of the same performance. It is suggested that such a requirement may produce the paradox of attenuation associated with item analysis, in which too high a correlation between…