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R-squared for Bayesian Regression Models |
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| Authors: | Andrew Gelman Ben Goodrich Jonah Gabry Aki Vehtari |
| Institution: | 1. Department of Statistics and Department of Political Science, Columbia University, New York, NY;2. gelman@stat.columbia.edu;4. Institute for Social and Economic Research and Policy, Columbia University, New York, NY;5. Department of Computer Science, Aalto University, Espoo, Finland |
| 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. |
| Keywords: | Bayesian methods R-squared Regression |