On an EM-based closed-form solution for 2 parameter IRT models

Stefano Noventa; Roberto Faleh; Augustin Kelava

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arXiv · 2411.18351

On an EM-based closed-form solution for 2 parameter IRT models

Stefano Noventa·Roberto Faleh·Augustin Kelava

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Abstract

It is a well-known issue that in Item Response Theory models there is no closed-form for the maximum likelihood estimators of the item parameters. Parameter estimation is therefore typically achieved by means of numerical methods like gradient search. The present work has a two-fold aim: On the one hand, we revise the fundamental notions associated to the item parameter estimation in 2 parameter Item Response Theory models from the perspective of the complete-data likelihood. On the other hand, we argue that, within an Expectation-Maximization approach, a closed-form for discrimination and difficulty parameters can actually be obtained that simply corresponds to the Ordinary Least Square solution.

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Stefano Noventa, Roberto Faleh, Augustin Kelava. 2024-11-27. On an EM-based closed-form solution for 2 parameter IRT models. https://arxiv.org/abs/2411.18351

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