Regularized Estimation of the Nominal Response Model

Abstract

The nominal response model is an item response theory model that does not require the ordering of the response options. However, while providing a very flexible modeling approach of polytomous responses, it involves the estimation of many parameters at the risk of numerical instability and overfitting. The lasso is a technique widely used to achieve model selection and regularization. In this paper, we propose the use of a fused lasso penalty to group response categories and perform regularization of the unidimensional and multidimensional nominal response models. The good performance of the method is illustrated through real-data applications and simulation studies.