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.

Keywords:

• Adaptive lasso
• collapse
• fused lasso
• item response theory
• lasso
• multidimensional
• polytomous responses

Article information

Conflict of interest disclosures: The author signed a form for disclosure of potential conflicts of interest. The author did not report any financial or other conflicts of interest in relation to the work described.

Ethical principles: The author affirms having followed professional ethical guidelines in preparing this work. These guidelines include obtaining informed consent from human participants, maintaining ethical treatment and respect for the rights of human or animal participants, and ensuring the privacy of participants and their data, such as ensuring that individual participants cannot be identified in reported results or from publicly available original or archival data.

Funding: This work was partially supported by Grant PRIN 2015 prot. 2015EASZFS_003 from the Italian Government, partially supported by Grant PRID 2017 from the University of Udine.

Role of the funders/sponsors: None of the funders or sponsors of this research had any role in the design and conduct of the study; collection, management, analysis, and interpretation of data; preparation, review, or approval of the manuscript; or decision to submit the manuscript for publication.

Acknowledgments: The author would like to thank the anonymous reviewers and the editor for their comments on prior versions of this manuscript. The ideas and opinions expressed herein are those of the author alone, and endorsement by the author’s institution is not intended and should not be inferred.