Regularized Estimation of the Four-Parameter Logistic Model

The four-parameter logistic model is an Item Response Theory model for dichotomous items that limit the probability of giving a positive response to an item into a restricted range, so that even people at the extremes of a latent trait do not have a probability close to zero or one. Despite the literature acknowledging the usefulness of this model in certain contexts, the difficulty of estimating the item parameters has limited its use in practice. In this paper we propose a regularized estimation approach for the estimation of the item parameters based on the inclusion of a penalty term in the log-likelihood function. Simulation studies show the good performance of the proposal, which is further illustrated through an application to a real-data set.