pic: Predictive information criteria for Bayesian models fitted in...

In missingHE: Missing Outcome Data in Health Economic Evaluation

Predictive information criteria for Bayesian models fitted in JAGS using the function selection, pattern, hurdle or lmdm

Description

Efficient approximate leave-one-out cross validation (LOO), deviance information criterion (DIC) and widely applicable information criterion (WAIC) for Bayesian models, calculated on the observed data.

Usage

pic(x, criterion = "dic", cases = "cc", ...)

Arguments

x	A missingHE object containing the results of a Bayesian model fitted in cost-effectiveness analysis using the function selection, pattern, hurdle or lmdm.
criterion	type of information criteria to be produced. Available choices are 'dic' for the Deviance Information Criterion, 'waic' for the Widely Applicable Information Criterion, and 'looic' for the Leave-One-Out Information Criterion.
cases	group of cases for which information criteria should be computed for: either 'all' for all cases, 'cc' for complete cases, 'ac_e' and 'ac_c' for only the observed effect and cost cases, respectively.
...	Additional parameters that can be provided to manage the output of pic when 'looic' is selected. For more details see bayesplot.

Details

The Deviance Information Criterion (DIC), Leave-One-Out Information Criterion (LOOIC) and the Widely Applicable Information Criterion (WAIC) are methods for estimating out-of-sample predictive accuracy from a Bayesian model using the log-likelihood evaluated at the posterior simulations of the parameters. DIC is computationally simple to calculate but it is known to have some problems, arising in part from it not being fully Bayesian in that it is based on a point estimate. LOOIC can be computationally expensive but can be easily approximated using importance weights that are smoothed by fitting a generalised Pareto distribution to the upper tail of the distribution of the importance weights. WAIC is fully Bayesian and closely approximates Bayesian cross-validation. Unlike DIC, WAIC is invariant to parameterisation and also works for singular models. In finite cases, WAIC and LOOIC give similar estimates, but for influential observations WAIC underestimates the effect of leaving out one observation.

Value

A named list containing different predictive information criteria results and quantities according to the value of criterion. In all cases, the measures are computed on the observed data for the specific modules of the model selected in module.

d_bar

Posterior mean deviance (only if criterion is 'dic').

pD

Effective number of parameters calculated with the formula used by JAGS (only if criterion is 'dic')

.

dic

Deviance Information Criterion calculated with the formula used by JAGS (only if criterion is 'dic')

.

d_hat

Deviance evaluated at the posterior mean of the parameters and calculated with the formula used by JAGS (only if criterion is 'dic')

elpd, elpd_se

Expected log pointwise predictive density and standard error calculated on the observed data for the model nodes indicated in module (only if criterion is 'waic' or 'looic').

p, p_se

Effective number of parameters and standard error calculated on the cases indicated in cases. (only if criterion is 'waic' or 'looic').

looic, looic_se

The leave-one-out information criterion and standard error calculated on the cases indicated in cases. (only if criterion is 'looic').

waic, waic_se

The widely applicable information criterion and standard error calculated on the cases indicated in cases. (only if criterion is 'waic').

pointwise

A matrix containing the pointwise contributions of each of the above measures calculated on the cases indicated in cases. (only if criterion is 'waic' or 'looic').

diagnostics

A named list containing additional diagnostic measures (only if criterion is 'looic'). See loo for details about interpreting the list elements.

psis_object

A named list containing the matrix of (smoothed) log weights (only if criterion is 'looic' with the optional argument 'save_psis' is set to TRUE). See loo for details about interpreting the list elements.

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Author(s)

Andrea Gabrio

References

Plummer, M. JAGS: A program for analysis of Bayesian graphical models using Gibbs sampling. (2003).

Vehtari, A. Gelman, A. Gabry, J. (2016a) Practical Bayesian model evaluation using leave-one-out cross-validation and WAIC. Statistics and Computing. Advance online publication.

Vehtari, A. Gelman, A. Gabry, J. (2016b) Pareto smoothed importance sampling. ArXiv preprint.

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

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

See Also

jags, loo, waic

Examples

 
# For examples see the function \code{\link{selection}}, \code{\link{pattern}}, 
# \code{\link{hurdle}} or \code{\link{lmdm}}
# 
# 

missingHE documentation built on March 19, 2026, 5:06 p.m.