This function is deprecated. Please use the new loo_compare() function instead.

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

Arguments

... 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 ....

Value

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. If more than two objects are provided then a matrix of summary information is returned (see Details).

Details

When comparing two fitted models, we can estimate the difference in their expected predictive accuracy by the difference in elpd_loo or elpd_waic (or multiplied by -2, if desired, to be on the deviance scale).

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.

When using compare() with more than two models, the values in the elpd_diff and 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). Although the 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 se_elpd_loo.

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.

References

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

Examples

if (FALSE) {
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)
}