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, ...) # S3 method for default loo_compare(x, ...) # S3 method for compare.loo print(x, ..., digits = 1, simplify = TRUE) # S3 method for compare.loo_ss print(x, ..., digits = 1, simplify = TRUE)
An object of class
Additional objects of class
For the print method only, the number of digits to use when printing.
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.
A matrix with class
"compare.loo" that has its own
print method. See the Details section.
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 deviance scale).
loo_compare(), the returned matrix will have one row per model
and several columns of estimates. 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 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.
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
The FAQ page on the loo website for answers to frequently asked questions.
# 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)#> elpd_diff se_diff #> model3 0.00 0.00 #> model2 -32.00 0.00 #> model1 -64.00 0.00# show more details with simplify=FALSE # (will be the same for all models in this artificial example) print(comp, simplify = FALSE, digits = 3)#> elpd_diff se_diff elpd_loo se_elpd_loo p_loo se_p_loo looic se_looic #> model3 0.000 0.000 -19.589 4.284 3.329 1.152 39.178 8.568 #> model2 -32.000 0.000 -51.589 4.284 3.329 1.152 103.178 8.568 #> model1 -64.000 0.000 -83.589 4.284 3.329 1.152 167.178 8.568# can use a list of objects loo_compare(x = list(loo1, loo2, loo3))#> elpd_diff se_diff #> model3 0.0 0.0 #> model2 -32.0 0.0 #> model1 -64.0 0.0