loo (version 2.0.0)

compare: Model comparison


Compare fitted models on LOO or WAIC.


compare(..., x = list())

# S3 method for compare.loo print(x, ..., digits = 1)



At least two objects returned by loo (or waic).


A list of at least two objects returned by loo (or waic). This argument can be used as an alternative to specifying the objects in ....


For the print method only, the number of digits to use when printing.


A vector or matrix with class 'compare.loo' that has its own print method. If exactly two objects are provided in ... or x, then the difference in expected predictive accuracy and the standard error of the difference are returned (see Details). The difference will be positive if the expected predictive accuracy for the second model is higher. If more than two objects are provided then a matrix of summary information is returned.


When comparing two fitted models, we can estimate the difference in their expected predictive accuracy by the difference in elpd_loo or elpd_waic (multiplied by \(-2\), if desired, to be on the deviance scale). To compute the standard error of this difference we can use a paired estimate to take advantage of the fact that the same set of \(N\) data points was used to fit both models. These calculations should be most useful when \(N\) is large, because then non-normality of the distribution is not such an issue when estimating the uncertainty in these sums. These standard errors, for all their flaws, should give a better sense of uncertainty than what is obtained using the current standard approach of comparing differences of deviances to a Chi-squared distribution, a practice derived for Gaussian linear models or asymptotically, and which only applies to nested models in any case.


Vehtari, A., Gelman, A., and Gabry, J. (2017a). Practical Bayesian model evaluation using leave-one-out cross-validation and WAIC. Statistics and Computing. 27(5), 1413--1432. doi:10.1007/s11222-016-9696-4. (published version, arXiv preprint).

Vehtari, A., Gelman, A., and Gabry, J. (2017b). Pareto smoothed importance sampling. arXiv preprint: http://arxiv.org/abs/1507.02646/


Run this code
loo1 <- loo(log_lik1)
loo2 <- loo(log_lik2)
print(compare(loo1, loo2), digits = 3)
print(compare(x = list(loo1, loo2)))

waic1 <- waic(log_lik1)
waic2 <- waic(log_lik2)
compare(waic1, waic2)
# }
# }

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