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R-squared for Bayesian Regression Models

Author

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  • Andrew Gelman
  • Ben Goodrich
  • Jonah Gabry
  • Aki Vehtari

Abstract

The usual definition of R2 (variance of the predicted values divided by the variance of the data) has a problem for Bayesian fits, as the numerator can be larger than the denominator. We propose an alternative definition similar to one that has appeared in the survival analysis literature: the variance of the predicted values divided by the variance of predicted values plus the expected variance of the errors.

Suggested Citation

  • Andrew Gelman & Ben Goodrich & Jonah Gabry & Aki Vehtari, 2019. "R-squared for Bayesian Regression Models," The American Statistician, Taylor & Francis Journals, vol. 73(3), pages 307-309, July.
    • Handle: RePEc:taf:amstat:v:73:y:2019:i:3:p:307-309
    DOI: 10.1080/00031305.2018.1549100
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