Abstract
The joint maximum likelihood estimation of the parameters of the Rasch model is hampered by several drawbacks, the most relevant of which are that: (1) the estimates are not available for item or person with perfect scores; (2) the item parameter estimates are severely biased, especially for short tests. To overcome both these problems, in this paper a new method is proposed, based on a fuzzy extension of the empirical probability function and the minimum Kullback–Leibler divergence estimation approach. The new method warrants the existence of finite estimates for both person and item parameters and results very effective in reducing the bias of joint maximum likelihood estimates.
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Acknowledgments
This research was partially funded in the framework of the project “Opportunity for young researchers”, reg. no. CZ.1.07/2.3.00/30.0016, supported by Operational Programme Education for Competitiveness and co-financed by the European Social Fund and the state budget of the Czech Republic.
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Bertoli-Barsotti, L., Lando, T., Punzo, A. (2014). Estimating a Rasch Model via Fuzzy Empirical Probability Functions. In: Vicari, D., Okada, A., Ragozini, G., Weihs, C. (eds) Analysis and Modeling of Complex Data in Behavioral and Social Sciences. Studies in Classification, Data Analysis, and Knowledge Organization. Springer, Cham. https://doi.org/10.1007/978-3-319-06692-9_4
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DOI: https://doi.org/10.1007/978-3-319-06692-9_4
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