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

TL;DR

This paper proposes a novel EM-based method that derives closed-form solutions for the discrimination and difficulty parameters in 2-parameter IRT models, simplifying estimation compared to traditional numerical approaches.

Contribution

It introduces a closed-form EM algorithm for 2-parameter IRT models, providing an alternative to numerical methods for parameter estimation.

Findings

Closed-form solutions for item parameters via EM algorithm.

Simplification of parameter estimation process.

Potential reduction in computational complexity.

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.