The number of response categories in ordered response models

Iannario Maria (), Monti Anna Clara () and Scalera Pietro ()
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Iannario Maria: Department of Political Sciences, University of Naples Federico II, Napoli, Italy
Monti Anna Clara: Department of Law, Economics, Management and Quantitative Methods, University of Sannio, Benevento, Italy
Scalera Pietro: Department of Political Sciences, University of Naples Federico II, Napoli, Italy

The International Journal of Biostatistics, 2022, vol. 18, issue 2, 593-611

Abstract: The choice of the number m of response categories is a crucial issue in categorization of a continuous response. The paper exploits the Proportional Odds Models’ property which allows to generate ordinal responses with a different number of categories from the same underlying variable. It investigates the asymptotic efficiency of the estimators of the regression coefficients and the accuracy of the derived inferential procedures when m varies. The analysis is based on models with closed-form information matrices so that the asymptotic efficiency can be analytically evaluated without need of simulations. The paper proves that a finer categorization augments the information content of the data and consequently shows that the asymptotic efficiency and the power of the tests on the regression coefficients increase with m. The impact of the loss of information produced by merging categories on the efficiency of the estimators is also considered, highlighting its risks especially when performed in its extreme form of dichotomization. Furthermore, the appropriate value of m for various sample sizes is explored, pointing out that a large number of categories can offset the limited amount of information of a small sample by a better quality of the data. Finally, two case studies on the quality of life of chemotherapy patients and on the perception of pain, based on discretized continuous scales, illustrate the main findings of the paper.

Keywords: collapsibility property; efficiency; hypothesis testing; merging categories; proportional odds models; sample size (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1515/ijb-2021-0013

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