Maximum Likelihood Item Response Theory Estimation

Abstract An overview and short didactic for three common estimation techniques for parameters in item response theory models are described: (a) joint maximum likelihood, (b) conditional maximum likelihood, and (c) marginal maximum likelihood. Specifically, likelihood equations fundamental to all three estimation approaches are presented first and joint as well as conditional maximum likelihood estimation are briefly described next. The main part of the entry focuses on an extended description of marginal maximum likelihood estimation and illustrates, in a step‐by‐step fashion, how it makes use of the EM algorithm and a fully Bayesian estimation framework to estimate item parameters. A brief description of how person parameters are subsequently estimated follows. Finally, a few words on alternative estimation approaches are offered.