Finiteness of the weighted likelihood estimator and applications to CAT

The purpose of this talk is to present some recent research on the weighted likelihood estimator (WLE) of ability in item response theory (IRT). This estimator is quite commonly used as an alternative to usual maximum likelihood and Bayesian estimators. However, the uestion of providing finite ability estimates was left unsolved and led to some controversy. Recently, Magis and Verhelst (in press) established that the WLE always returns finite values, independently of the IRT model, the number of items, and the item responses. This general result will be briefly outlined.

The finiteness of the WLE has straightforward impact within the field of computerized adaptive testing (CAT). One technical and crucial issue in CAT is to accurately estimate the latent ability at the early stages of the adaptive process, when only a few items are available. Currently heuristic adjustments are adviced to avoid infinite estimates with only a few item responses. In this talk it will be highlighted how the use of the WLE throughout the CAT can be a promising and performant approach to solve this issue.