R: Widely applicable information criterion (WAIC)

waic {loo} | R Documentation

## Widely applicable information criterion (WAIC)

### Description

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 class 'array'
    waic(x, ...)

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

    ## S3 method for class '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

- `loo` for approximate LOO-CV.

- `compare` for comparing models on LOOIC or WAIC.

### Examples

    ### 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)

    ## End(Not run)

[Package loo version 2.0.0 Index]