Maximum likelihood estimation in models from item response theory: III. Precision of the estimators

Abstract

Item response theory (IRT) provides a conceptual framework for explaining response patterns to psychological instruments. IRT models include parameters for the persons who respond to the instrument as well as for the items that constitute it. Methods from inferential statistics make it possible to estimate the values of these parameters from data observed in a sample. In this article, we explore the use of the information function to quantify the precision of the estimators obtained through the method of maximum likelihood estimation. Our aim is to present, clearly and concisely, the definition, the intuitive interpretation, and the most important properties of the information function through examples and illustrations, while also providing a succinct exposition of the statistical tools and the mathematical derivations required to achieve a deeper comprehension of the concepts discussed. Keywords: Parameter estimation; maximum likelihood; Rasch model; Fisher information; item response theory.