Abstract
Item response theory modeling articles from 83 years of Psychometrika are sorted based on the taxonomy by Thissen and Steinberg (1986). Results from 377 research and review articles indicate that the usual unidimensional parametric item response theory models for dichotomous items were employed in 51 per cent of the articles. The usual unidimensional parametric item response theory models for polytomous items were employed in 21 per cent of the articles. The multidimensional item response theory models were employed in 11 per cent of the articles. Item response theory models from the selected psychometric textbooks are also reviewed and contrasted with those from Psychometrika to explore the instructional use of various item response models. A new classification based on data types is proposed and discussed.
Highlights
A large number of item response theory (IRT) models currently exist for analysis of item response data
Thissen and Steinberg (1986) classified item response models into four distinct types based on assumptions and constraints on the parameters: binary models, difference models, divided-by-total models, and left-side-added models
At least two measurement specialists independently reviewed each of the 377 articles for their use of IRT models and completed a checklist documenting topics and models
Summary
A large number of item response theory (IRT) models currently exist for analysis of item response data. “How are these models related?” In this study, we give answers to several related questions about IRT models based on review of two sets of materials, articles in Psychometrika and textbooks on psychometric theory. Interested readers are referred to the original, seminal work of Thissen and Steinberg (1986). In their taxonomy, Thissen and Steinberg (1986) classified item response models into four distinct types based on assumptions and constraints on the parameters: binary models, difference models, divided-by-total models, and left-side-added models. They classified, for example, the twoparameter normal ogive model and the Rasch model as the binary models; Samejima’s graded response model in normal ogive and logistic forms as the difference model; Bock’s nominal response model and Master’s partial credit model as the divide-by-total models; and Birnbaum’s three-parameter logistic model as the left-side-added model (see Thissen and Steinberg, 1986, and references therein)
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