R-squared for Bayesian Regression Models

Andrew Gelman, Ben Goodrich, Jonah Gabry and Aki Vehtari

The American Statistician, 2019, vol. 73, issue 3, 307-309

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.

Date: 2019
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DOI: 10.1080/00031305.2018.1549100

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