R-squared for Bayesian Regression Models

By Andrew Gelman, Ben Goodrich, Jonah Gabry, Aki Vehtari. American Statistician, 2019

791 citations recorded by the source corpus.

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.

Subfields: Finance, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/4094b431a5adeb7448e49640db87e888d16d7a4d

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In Statistics and Probability

1. Abhijeet Mishra
2. David Meng-Chuen Chen
3. A. Popp
4. Benjamin Leon Bodirsky
5. T. Krueger

Citations in the corpus

• The world’s growing municipal solid waste: trends and impacts (2020, methodology): “Leave-one-out R2 (LOO-R2)—R2 based on refitting themodel with each observation left out once, see Gelman et al (2019)—is 0.58, indicating that GDPpc explains a substantial portion of the variance in waste generation.”