Maximum likelihood estimation in models from item response theory: II. Item parameters

Abstract

Item response theory (IRT) offers a conceptual framework for explaining the responses on psychological tests through mathematical models that include parameters for the respondents as well as for the items that make up the test. This article, which is the second in a series of three that review the principles underlying parameter estimation in IRT models, focuses on the procedures used to estimate the item parameters. In particular, we review three variants of maximum likelihood estimation: joint maximum likelihood, conditional maximum likelihood, and marginal maximum likelihood. For each variant, we highlight its main characteristics, together with its advantages and limitations. Finally, we illustrate these procedures with an example of an analysis of the responses to a multiple-choice test.