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.

翻译：众所周知，在项目反应理论模型中，项目参数的最大似然估计量不存在闭式解。因此，参数估计通常需要通过梯度搜索等数值方法实现。本研究具有双重目标：一方面，我们从完备数据似然函数的角度，重新审视了双参数项目反应理论模型中与项目参数估计相关的基本概念。另一方面，我们论证了在期望最大化算法框架内，实际上可以获得区分度参数与难度参数的闭式解，该解恰好对应于普通最小二乘解。