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Widely Applicable Information Criterion (WAIC)

Source: R/loo.R
waic.brmsfit.Rd

Compute the widely applicable information criterion (WAIC) based on the posterior likelihood using the loo package. For more details see waic.

Usage

# S3 method for class 'brmsfit'
waic(
  x,
  ...,
  compare = TRUE,
  resp = NULL,
  pointwise = FALSE,
  model_names = NULL
)

Arguments

x

A brmsfit object.

...

More brmsfit objects or further arguments passed to the underlying post-processing functions. In particular, see prepare_predictions for further supported arguments.

compare

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

resp

Optional names of response variables. If specified, predictions are performed only for the specified response variables.

pointwise

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.

model_names

If NULL (the default) will use model names derived from deparsing the call. Otherwise will use the passed values as model names.

Value

If just one object is provided, an object of class loo. If multiple objects are provided, an object of class loolist.

Details

See loo_compare for details on model comparisons. For brmsfit objects, WAIC is an alias of waic. Use method add_criterion to store information criteria in the fitted model object for later usage.

References

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.

Examples

# \dontrun{
# model with population-level effects only
fit1 <- brm(rating ~ treat + period + carry,
            data = inhaler)
#> Compiling Stan program...
#> Start sampling
#> 
#> SAMPLING FOR MODEL 'anon_model' NOW (CHAIN 1).
#> Chain 1: 
#> Chain 1: Gradient evaluation took 1.1e-05 seconds
#> Chain 1: 1000 transitions using 10 leapfrog steps per transition would take 0.11 seconds.
#> Chain 1: Adjust your expectations accordingly!
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#> Chain 1:  Elapsed Time: 0.032 seconds (Warm-up)
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#> Chain 1:                0.062 seconds (Total)
#> Chain 1: 
#> 
#> SAMPLING FOR MODEL 'anon_model' NOW (CHAIN 2).
#> Chain 2: 
#> Chain 2: Gradient evaluation took 6e-06 seconds
#> Chain 2: 1000 transitions using 10 leapfrog steps per transition would take 0.06 seconds.
#> Chain 2: Adjust your expectations accordingly!
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#> Chain 2:                0.068 seconds (Total)
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#> 
#> SAMPLING FOR MODEL 'anon_model' NOW (CHAIN 3).
#> Chain 3: 
#> Chain 3: Gradient evaluation took 5e-06 seconds
#> Chain 3: 1000 transitions using 10 leapfrog steps per transition would take 0.05 seconds.
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#> 
#> SAMPLING FOR MODEL 'anon_model' NOW (CHAIN 4).
#> Chain 4: 
#> Chain 4: Gradient evaluation took 5e-06 seconds
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#> Chain 4:  Elapsed Time: 0.032 seconds (Warm-up)
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#> Chain 4:                0.063 seconds (Total)
#> Chain 4: 
(waic1 <- waic(fit1))
#> Warning: 
#> 2 (0.3%) p_waic estimates greater than 0.4. We recommend trying loo instead.
#> 
#> Computed from 4000 by 572 log-likelihood matrix.
#> 
#>           Estimate   SE
#> elpd_waic   -529.6 25.9
#> p_waic         6.3  1.0
#> waic        1059.1 51.7
#> 
#> 2 (0.3%) p_waic estimates greater than 0.4. We recommend trying loo instead. 

# model with an additional varying intercept for subjects
fit2 <- brm(rating ~ treat + period + carry + (1|subject),
            data = inhaler)
#> Compiling Stan program...
#> Start sampling
#> 
#> SAMPLING FOR MODEL 'anon_model' NOW (CHAIN 1).
#> Chain 1: 
#> Chain 1: Gradient evaluation took 5.8e-05 seconds
#> Chain 1: 1000 transitions using 10 leapfrog steps per transition would take 0.58 seconds.
#> Chain 1: Adjust your expectations accordingly!
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#> Chain 1:                2.509 seconds (Total)
#> Chain 1: 
#> 
#> SAMPLING FOR MODEL 'anon_model' NOW (CHAIN 2).
#> Chain 2: 
#> Chain 2: Gradient evaluation took 6e-05 seconds
#> Chain 2: 1000 transitions using 10 leapfrog steps per transition would take 0.6 seconds.
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#> 
#> SAMPLING FOR MODEL 'anon_model' NOW (CHAIN 3).
#> Chain 3: 
#> Chain 3: Gradient evaluation took 4.5e-05 seconds
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#> 
#> SAMPLING FOR MODEL 'anon_model' NOW (CHAIN 4).
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#> Chain 4: Gradient evaluation took 4.5e-05 seconds
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(waic2 <- waic(fit2))
#> Warning: 
#> 26 (4.5%) p_waic estimates greater than 0.4. We recommend trying loo instead.
#> 
#> Computed from 4000 by 572 log-likelihood matrix.
#> 
#>           Estimate   SE
#> elpd_waic   -519.5 26.1
#> p_waic        83.6  7.4
#> waic        1039.1 52.2
#> 
#> 26 (4.5%) p_waic estimates greater than 0.4. We recommend trying loo instead. 

# compare both models
loo_compare(waic1, waic2)
#>  model elpd_diff se_diff p_worse diag_diff diag_elpd
#>   fit2       0.0     0.0      NA                    
#>   fit1     -10.0     4.4    0.99                    
# }