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.