Model comparison
Compare fitted models based on ELPD.
By default the print method shows only the most important information. Use
print(..., simplify=FALSE) to print a more detailed summary.
loo_compare(x, ...) ## Default S3 method: loo_compare(x, ...) ## S3 method for class 'compare.loo' print(x, ..., digits = 1, simplify = TRUE) ## S3 method for class 'compare.loo_ss' print(x, ..., digits = 1, simplify = TRUE)
x |
An object of class |
... |
Additional objects of class |
digits |
For the print method only, the number of digits to use when printing. |
simplify |
For the print method only, should only the essential columns of the summary matrix be printed? The entire matrix is always returned, but by default only the most important columns are printed. |
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 using loo_compare(), the returned matrix will have one row per
model and several columns of estimates. 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 largest ELPD
(the model in the first row). For this reason the elpd_diff column
will always have the value 0 in the first row (i.e., the difference
between the preferred model and itself) and negative values in subsequent
rows for the remaining models.
To compute the standard error of the difference in ELPD — which should not be expected to equal the difference of the standard errors — 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.
A matrix with class "compare.loo" that has its own
print method. See the Details section.
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
# very artificial example, just for demonstration! LL <- example_loglik_array() loo1 <- loo(LL, r_eff = NA) # should be worst model when compared loo2 <- loo(LL + 1, r_eff = NA) # should be second best model when compared loo3 <- loo(LL + 2, r_eff = NA) # should be best model when compared comp <- loo_compare(loo1, loo2, loo3) print(comp, digits = 2) # show more details with simplify=FALSE # (will be the same for all models in this artificial example) print(comp, simplify = FALSE, digits = 3) # can use a list of objects loo_compare(x = list(loo1, loo2, loo3)) ## Not run: # works for waic (and kfold) too loo_compare(waic(LL), waic(LL - 10)) ## End(Not run)
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