An Iterative Maximum a Posteriori Estimation of Proficiency Level to Detect Multiple Local Likelihood Maxima

In this article the authors focus on the issue of the nonuniqueness of the maximum likelihood (ML) estimator of proficiency level in item response theory (with special attention to logistic models). The usual maximum a posteriori (MAP) method offers a good alternative within that framework; however, this article highlights some drawbacks of its use. The authors then propose an iteratively based MAP estimator (IMAP), which can be useful in detecting multiple local likelihood maxima. The efficiency of the IMAP estimator is studied and is compared to the ML and MAP methods by means of a simulation study.