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

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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
    Institute of Mathematics of UPC-BarcelonaTech (IMTech), 08028 Barcelona, Spain
    Centro de Investigación Biomédica en Red de Salud Mental, CIBERSAM, Instituto de Salud Carlos III, Monforte de Lemos 3-5, Pabellón 11, 28029 Madrid, Spain
    These authors contributed equally to this work.)

  • 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)

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.

Suggested Citation

  • Daniel Fernández & Louise McMillan & Richard Arnold & Martin Spiess & Ivy Liu, 2022. "Goodness-of-Fit and Generalized Estimating Equation Methods for Ordinal Responses Based on the Stereotype Model," Stats, MDPI, vol. 5(2), pages 1-14, June.
    • Handle: RePEc:gam:jstats:v:5:y:2022:i:2:p:30-520:d:829774
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    References listed on IDEAS

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