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Generalizing R2 for deming regressions

Author

Listed:
  • Michael Bossé
  • Eric Marland
  • Gregory Rhoads
  • Jose Almer Sanqui
  • Zack BeMent

Abstract

The simple linear regression model and the associated goodness-of-fit measure, the coefficient of determination, R2, are only appropriate when all measurement errors are associated with the measurement of the data in the dependent variable. When measurement errors are assumed in both variables, a Deming regression can be used; however, there is no associated R2-type measure for this specific type of regression. In this paper, we propose a measure, Rg2 which utilizes the minimum percentage improvement of the Deming regression over either the horizontal or the vertical line through the centroid of the data. We investigate some properties of this measure and its relation to R2. We also consider other candidate methodologies for a generalized R2 measure for a Deming regression model and investigate strengths and weaknesses of each as a way of beginning the conversation about which measure is the best and for which applications it is most suited.

Suggested Citation

  • Michael Bossé & Eric Marland & Gregory Rhoads & Jose Almer Sanqui & Zack BeMent, 2023. "Generalizing R2 for deming regressions," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 52(21), pages 7731-7743, November.
    • Handle: RePEc:taf:lstaxx:v:52:y:2023:i:21:p:7731-7743
    DOI: 10.1080/03610926.2022.2059678
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