Title: Shrinkage Estimation of the Three-Parameter Logistic Model

Authors: Michela Battauz, Ruggero Bellio

Affiliation: University of Udine

Abstract:
The three-parameter logistic model is an item response theory model used with
dichotomous items. It is well known that the parameters of the model are
weekly identifiable and that the maximization of the likelihood, which is
performed using numerical algorithms, is prone to convergence issues. In this
talk, we propose the use of a penalized likelihood for the estimation of the
item parameters. Two main approaches are explored. The first approach is based
on the inclusion of a ridge-type penalty on the guessing parameters in the
likelihood function. Model-based shrinkage estimation constitutes the second
approach explored, which is pursued employing the bias reduction methodology.
The performance of the methods is investigated through simulation studies and
a real data example.