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Exploring the posterior of a hierarchical IRT model for item effects

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Summary

A one-way ANOVA structure is imposed on the item difficulty and the item discrimination parameter of a two-parameter hierarchical IRT model for item effects. Bayesian estimation of the model is illustrated for the Metropolis-Hastings within Gibbs and the data augmented Gibbs procedure. The posterior of the hierarchical IRT model is explored with respect to the location of parameters and the uncertainty of these parameter estimates. The posterior correlations among parameters are shown to be due to trade-off effects among parameters either on the same parameter scales or on different parameter scales.

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Authors and Affiliations

  1. Department of Psychology, University of Leuven, Tierisestraat 102, 3000, Leuven, Belgium

    Rianne Janssen & Paul De Boeck

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  1. Rianne Janssen
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  2. Paul De Boeck
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Additional information

We thank the editor and two referees for helpful comments. The first author is a Postdoctoral Fellow of the Fund for Scientific Research — Flanders (Belgium). The construction of the test used in the example was funded by the OBPWO grant 93.05 of the Ministry of the Flemish Community, Department of Education, awarded to Paul De Boeck and Frans Daems.

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Janssen, R., De Boeck, P. Exploring the posterior of a hierarchical IRT model for item effects. Computational Statistics 15, 421–442 (2000). https://doi.org/10.1007/PL00022714

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