Goodness-of-Fit and Generalized Estimating Equation Methods for Ordinal Responses Based on the Stereotype Model

Daniel Fernández, Louise McMillan, Richard Arnold, Martin Spiess and Ivy Liu
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Daniel Fernández: Serra Húnter Fellow, Department of Statistics and Operations Research (DEIO), Universitat Politècnica de Catalunya · BarcelonaTech (UPC), 08028 Barcelona, Spain
Louise McMillan: School of Mathematics and Statistics, Victoria University of Wellington, Cotton Building 356, Gate 7, Kelburn Parade, Wellington 6012, New Zealand
Richard Arnold: School of Mathematics and Statistics, Victoria University of Wellington, Cotton Building 356, Gate 7, Kelburn Parade, Wellington 6012, New Zealand
Martin Spiess: Psychological Methods and Statistics, Hamburg University, 20146 Hamburg, Germany
Ivy Liu: School of Mathematics and Statistics, Victoria University of Wellington, Cotton Building 356, Gate 7, Kelburn Parade, Wellington 6012, New Zealand

Stats, 2022, vol. 5, issue 2, 1-14

Abstract: Background : Data with ordinal categories occur in many diverse areas, but methodologies for modeling ordinal data lag severely behind equivalent methodologies for continuous data. There are advantages to using a model specifically developed for ordinal data, such as making fewer assumptions and having greater power for inference. Methods : The ordered stereotype model (OSM) is an ordinal regression model that is more flexible than the popular proportional odds ordinal model. The primary benefit of the OSM is that it uses numeric encoding of the ordinal response categories without assuming the categories are equally-spaced. Results : This article summarizes two recent advances in the OSM: (1) three novel tests to assess goodness-of-fit; (2) a new Generalized Estimating Equations approach to estimate the model for longitudinal studies. These methods use the new spacing of the ordinal categories indicated by the estimated score parameters of the OSM. Conclusions : The recent advances presented can be applied to several fields. We illustrate their use with the well-known arthritis clinical trial dataset. These advances fill a gap in methodologies available for ordinal responses and may be useful for practitioners in many applied fields.

Keywords: goodness-of-fit; longitudinal data; ordinal data; stereotype model (search for similar items in EconPapers)
JEL-codes: C1 C10 C11 C14 C15 C16 (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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