# waic

##### Widely applicable information criterion (WAIC)

The `waic`

methods can be used to compute WAIC from the pointwise
log-likelihood. However, we recommend LOO-CV using PSIS (as implemented by
the `loo`

function) because PSIS provides useful diagnostics and
effective sample size and Monte Carlo estimates.

##### Usage

`waic(x, ...)`# S3 method for array
waic(x, ...)

# S3 method for matrix
waic(x, ...)

# S3 method for function
waic(x, ..., data = NULL, draws = NULL)

##### Arguments

- x
A log-likelihood array, matrix, or function. See the

**Methods (by class)**section below for a detailed description of how to specify the inputs for each method.- draws, data, ...
For the function method only. See the

**Methods (by class)**section below for details on these arguments.

##### Value

A named list (of class `c("waic", "loo")`

) with components:

`estimates`

A matrix with two columns (

`"Estimate"`

,`"SE"`

) and three rows (`"elpd_waic"`

,`"p_waic"`

,`"waic"`

). This contains point estimates and standard errors of the expected log pointwise predictive density (`elpd_waic`

), the effective number of parameters (`p_waic`

) and the LOO information criterion`waic`

(which is just`-2 * elpd_waic`

, i.e., converted to deviance scale).`pointwise`

A matrix with three columns (and number of rows equal to the number of observations) containing the pointwise contributions of each of the above measures (

`elpd_waic`

,`p_waic`

,`waic`

).

##### Methods (by class)

`array`

: An \(I\) by \(C\) by \(N\) array, where \(I\) is the number of MCMC iterations per chain, \(C\) is the number of chains, and \(N\) is the number of data points.`matrix`

: An \(S\) by \(N\) matrix, where \(S\) is the size of the posterior sample (with all chains merged) and \(N\) is the number of data points.`function`

: A function`f`

that takes arguments`data_i`

and`draws`

and returns a vector containing the log-likelihood for a single observation`i`

evaluated at each posterior draw. The function should be written such that, for each observation`i`

in`1:N`

, evaluating`f(data_i = data[i,, drop=FALSE], draws = draws)`

results in a vector of length`S`

(size of posterior sample). The log-likelihood function can also have additional arguments but`data_i`

and`draws`

are required.If using the function method then the arguments

`data`

and`draws`

must also be specified in the call to`loo`

:`data`

: A data frame or matrix containing the data (e.g. observed outcome and predictors) needed to compute the pointwise log-likelihood. For each observation`i`

, the`i`

th row of`data`

will be passed to the`data_i`

argument of the log-likelihood function.`draws`

: An object containing the posterior draws for any parameters needed to compute the pointwise log-likelihood. Unlike`data`

, which is indexed by observation, for each observation the entire object`draws`

will be passed to the`draws`

argument of the log-likelihood function.The

`...`

can be used to pass additional arguments to your log-likelihood function. These arguments are used like the`draws`

argument in that they are recycled for each observation.

##### See Also

##### Examples

```
# NOT RUN {
### Array and matrix methods
LLarr <- example_loglik_array()
dim(LLarr)
LLmat <- example_loglik_matrix()
dim(LLmat)
waic_arr <- waic(LLarr)
waic_mat <- waic(LLmat)
identical(waic_arr, waic_mat)
# }
# NOT RUN {
log_lik1 <- extract_log_lik(stanfit1)
log_lik2 <- extract_log_lik(stanfit2)
(waic1 <- waic(log_lik1))
(waic2 <- waic(log_lik2))
print(compare(waic1, waic2), digits = 2)
# }
# NOT RUN {
# }
```

*Documentation reproduced from package loo, version 2.0.0, License: GPL (>= 3)*