One test which is often used to investigate fit of the Rasch model to a dataset, is the Martin-Löf test for unidimensionality. This paper investigates whether (and when) its asymptotic chi-square distribution can be assumed to be appropriate. We also study the power of this test.

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The more skills a student acquires, the more successful this student is with the corresponding tasks. Empirical data shows that the success in a task grows as a logistic function of skills; this dependence is known as the Rasch model. In this paper, we provide two uncertainty-based justifications for this model: the first justification provides a simple fuzzy-based intuitive explanation for thi...

This paper deals with the reliability of composite measurement consisting of true-false items obeying the Rasch model. A definition of reliability in the Rasch model is proposed and the connection to the classical definition of reliability is shown. As a modification of the classical estimator Cronbach’s alpha, a new estimator logistic alpha is proposed. Finally, the properties of the new estim...

The mixture Rasch model is a popular for analyzing multivariate binary data. drawback of this that the number estimated parameters substantially increases with an increasing latent classes, which, in turn, hinders interpretability parameters. This article proposes regularized estimation imposes some sparsity structure on class-specific item difficulties. We illustrate feasibility proposed model...

In this study, we investigated how students’ claim, justification, uncertainty, and conditions of rebuttal contribute to the measurement of the overall scientific argumentation ability. We designed six sets of items, each of which consisted of claim, justification, uncertainty rating, and conditions of rebuttal items. These item sets addressed six investigations related to climate change and ex...

Rasch mixture models can be a useful tool when checking the assumption of measurement invariance for a single Rasch model. They provide advantages compared to manifest DIF tests when the DIF groups are only weakly correlated with the manifest covariates available. Unlike in single Rasch models, estimation of Rasch mixture models is sensitive to the specification of the ability distribution even...

A method is proposed for the detection of item bias with respect to observed or unobserved subgroups. The method uses quasi-loglinear models for the incomplete subgroup x test score x Item 1 × • • • x item k contingency table. If subgroup membership is unknown the models are Haberman's incomplete-latent-class models. The (conditional) Rasch model is formulated as a quasi-loglinear model. The pa...