Regularized Estimation of the Nominal Response Model

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.