Title: A regularized estimation approach for the three-parameter logistic model
Authors: Michela Battauz - University of Udine (Italy) [presenting]
Ruggero Bellio - University of Udine (Italy)
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. 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 penalty term on the guessing parameters in the likelihood function. In particular, as penalty we consider the normal density or a ridge-type penalty. The tuning parameters are selected through cross validation. 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. All the methods lead to shrinkage of the guessing parameter estimates, showing the usual bias-variance tradeoff of regularized methods. The bias-reduction method presents a smaller amount of shrinkage.