Goodness-of-fit and generalized estimating equation methods for ordinal responses based on the stereotype model

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 fieldsThis research has been supported by Marsden grant E2987-3648 administrated by the Royal Society of New Zealand, by grant 2017 SGR 622 (GRBIO) administrated by the Departament d’Economia i Coneixement de la Generalitat de Catalunya (Spain) and by the Ministerio de Ciencia e Innovación (Spain) [PID2019-104830RB-I00/ DOI (AEI): 10.13039/501100011033].Peer ReviewedPostprint (published version