Maximum likelihood estimation in models from item response theory: I. Person parameters

Abstract

Item response theory (IRT) provides a conceptual framework that uses mathematical models to explain observed responses on psychological or educational tests. These models include parameters for both the items comprised in the test (e.g., indicating their difficulty) and the persons responding the test (measuring their ability measured by the test). The application of an IRT model implies the estimation of these parameters from empirical data. Usually, estimation in IRT models is based on maximum likelihood. This article is the first in a series of three, aimed at researchers and students who are familiarizing themselves with IRT and who want to learn about the estimation procedures. This first article provides an introduction that presents the basic concepts in IRT, taking the Rasch model as a reference and explains the foundations and logic underlying maximum likelihood estimation. We illustrate the principles explained by applying them to data of a multiple-choice test.