brms (version 1.10.2)

WAIC.brmsfit: Compute the WAIC


Compute the widely applicable information criterion (WAIC) based on the posterior likelihood using the loo package.


# S3 method for brmsfit
WAIC(x, ..., compare = TRUE, newdata = NULL,
  re_formula = NULL, allow_new_levels = FALSE,
  sample_new_levels = "uncertainty", new_objects = list(), subset = NULL,
  nsamples = NULL, pointwise = NULL, nug = NULL)

WAIC(x, ...)



A fitted model object typically of class brmsfit.


Optionally more fitted model objects.


A flag indicating if the information criteria of the models should be compared to each other via compare_ic.


An optional data.frame for which to evaluate predictions. If NULL (default), the orginal data of the model is used.


formula containing group-level effects to be considered in the prediction. If NULL (default), include all group-level effects; if NA, include no group-level effects.


A flag indicating if new levels of group-level effects are allowed (defaults to FALSE). Only relevant if newdata is provided.


Indicates how to sample new levels for grouping factors specified in re_formula. This argument is only relevant if newdata is provided and allow_new_levels is set to TRUE. If "uncertainty" (default), include group-level uncertainty in the predictions based on the variation of the existing levels. If "gaussian", sample new levels from the (multivariate) normal distribution implied by the group-level standard deviations and correlations. This options may be useful for conducting Bayesian power analysis. If "old_levels", directly sample new levels from the existing levels.


A named list of objects containing new data, which cannot be passed via argument newdata. Currently, only required for objects passed to cor_sar and cor_fixed.


A numeric vector specifying the posterior samples to be used. If NULL (the default), all samples are used.


Positive integer indicating how many posterior samples should be used. If NULL (the default) all samples are used. Ignored if subset is not NULL.


A flag indicating whether to compute the full log-likelihood matrix at once or separately for each observation. The latter approach is usually considerably slower but requires much less working memory. Accordingly, if one runs into memory issues, pointwise = TRUE is the way to go. By default, pointwise is automatically chosen based on the size of the model.


Small positive number for Gaussian process terms only. For numerical reasons, the covariance matrix of a Gaussian process might not be positive definite. Adding a very small number to the matrix's diagonal often solves this problem. If NULL (the default), nug is chosen internally.


If just one object is provided, an object of class ic. If multiple objects are provided, an object of class iclist.

Methods (by class)

  • brmsfit: WAIC method for brmsfit objects


When comparing models fitted to the same data, the smaller the WAIC, the better the fit. For brmsfit objects, waic is an alias of WAIC. Use method add_ic to store information criteria in the fitted model object for later usage.


Vehtari, A., Gelman, A., & Gabry J. (2016). Practical Bayesian model evaluation using leave-one-out cross-validation and WAIC. In Statistics and Computing, doi:10.1007/s11222-016-9696-4. arXiv preprint arXiv:1507.04544.

Gelman, A., Hwang, J., & Vehtari, A. (2014). Understanding predictive information criteria for Bayesian models. Statistics and Computing, 24, 997-1016.

Watanabe, S. (2010). Asymptotic equivalence of Bayes cross validation and widely applicable information criterion in singular learning theory. The Journal of Machine Learning Research, 11, 3571-3594.


Run this code
# model with population-level effects only
fit1 <- brm(rating ~ treat + period + carry,
            data = inhaler, family = "gaussian")

# model with an additional varying intercept for subjects
fit2 <- brm(rating ~ treat + period + carry + (1|subject),
            data = inhaler, family = "gaussian")
# compare both models
WAIC(fit1, fit2)                          
# }
# }

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