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Goodness‐Of‐Fit Tests for Ordinal Response Regression Models

Author

Listed:
  • Stuart R. Lipsitz
  • Garrett M. Fitzmaurice
  • Geert Molenberghs

Abstract

In this paper, goodness‐of‐fit test statistics for ordinal regression models are proposed, which have approximate χ2‐distributions when the model has been correctly specified. The statistics proposed can be viewed as extensions of the Hosmer‐Lemeshow statistic to ordinal categorical data and can be easily calculated by using existing statistical software for analysing ordinal response data The methods are illustrated by using data from an arthritis clinical trial comparing the drug auranofin and placebo therapy for the treatment of rheumatoid arthritis, in which the response is a self‐assessment of arthritis, classified as poor, fair and good. The covariates of interest are age, gender, treatment and base‐line response. A proportional odds model is fitted to the data, and the proposed goodness‐of‐fit statistics are applied to the fitted model. Also, the small sample properties of the proposed goodness‐of‐fit statistics are compared in a simulation study.

Suggested Citation

  • Stuart R. Lipsitz & Garrett M. Fitzmaurice & Geert Molenberghs, 1996. "Goodness‐Of‐Fit Tests for Ordinal Response Regression Models," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 45(2), pages 175-190, June.
    • Handle: RePEc:bla:jorssc:v:45:y:1996:i:2:p:175-190
    DOI: 10.2307/2986153
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    Cited by:

    1. 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.
    2. Mohamed A. Eltarkawe & Shelly L. Miller, 2018. "The Impact of Industrial Odors on the Subjective Well-Being of Communities in Colorado," IJERPH, MDPI, vol. 15(6), pages 1-24, May.
    3. Leonardo Salvatore Alaimo & Mariantonietta Fiore & Antonino Galati, 2020. "How the Covid-19 Pandemic Is Changing Online Food Shopping Human Behaviour in Italy," Sustainability, MDPI, vol. 12(22), pages 1-18, November.
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    5. Dimitris Zavras, 2021. "Studying Satisfaction with the Restriction Measures Implemented in Greece during the First COVID-19 Pandemic Wave," World, MDPI, vol. 2(3), pages 1-12, July.
    6. Yongcheng Wang & Yiik Diew Wong & Kelvin Goh, 2021. "Perceived importance of inclusive street dimensions: a public questionnaire survey from a vision(ing) perspective," Transportation, Springer, vol. 48(2), pages 699-721, April.
    7. Sirin, Selahattin Murat & Yilmaz, Berna N., 2021. "The impact of variable renewable energy technologies on electricity markets: An analysis of the Turkish balancing market," Energy Policy, Elsevier, vol. 151(C).
    8. Christine Mauracher & Isabella Procidano & Marco Valentini, 2019. "How Product Attributes and Consumer Characteristics Influence the WTP, Resulting in a Higher Price Premium for Organic Wine," Sustainability, MDPI, vol. 11(5), pages 1-15, March.
    9. Kemmawadee Preedalikit & Daniel Fernández & Ivy Liu & Louise McMillan & Marta Nai Ruscone & Roy Costilla, 2024. "Row mixture-based clustering with covariates for ordinal responses," Computational Statistics, Springer, vol. 39(5), pages 2511-2555, July.

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