This function is deprecated. Please use the new
compare(..., x = list())
A vector or matrix with class
'compare.loo' that has its own
print method. If exactly two objects are provided in
x, then the difference in expected predictive accuracy and the
standard error of the difference are returned. If more than two objects are
provided then a matrix of summary information is returned (see Details).
When comparing two fitted models, we can estimate the difference in their
expected predictive accuracy by the difference in
elpd_waic (or multiplied by -2, if desired, to be on the
When that difference,
elpd_diff, is positive then the expected
predictive accuracy for the second model is higher. A negative
elpd_diff favors the first model.
compare() with more than two models, the values in the
se_diff columns of the returned matrix are
computed by making pairwise comparisons between each model and the model
with the best ELPD (i.e., the model in the first row).
elpd_diff column is equal to the difference in
elpd_loo, do not expect the
se_diff column to be equal to the
the difference in
To compute the standard error of the difference in ELPD we 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 (journal version, preprint arXiv:1507.04544).
Vehtari, A., Simpson, D., Gelman, A., Yao, Y., and Gabry, J. (2019). Pareto smoothed importance sampling. preprint arXiv:1507.02646