WAIC is an extension of the Akaike Information Criterion (AIC) that is
more fully Bayesian than the Deviance Information Criterion (DIC).

Like DIC, WAIC estimates the effective number of parameters to adjust
for overfitting. Two adjustments have been proposed. pWAIC1 is similar
to pD in the original DIC. In contrast, pWAIC2 is calculated with
variance more similarly to pV, which Gelman proposed for DIC. Gelman
et al. (2014, p.174) recommends pWAIC2 because its results are closer
in practice to the results of leave-one-out cross-validation
(LOO-CV). pWAIC is considered an approximation to the number of
unconstrained and uninformed parameters, where a parameter counts as 1
when estimated without contraint or any prior information, 0 if fully
constrained or all information comes from the prior distribution, or
an intermediate number if both the data and prior are informative,
which is usually the case.

Gelman et al. (2014, p. 174) scale the WAIC of Watanabe (2010) by a
factor of 2 so that it is comparable to AIC and DIC. WAIC is then
reported as \(-2(lppd - pWAIC)\). Gelman et al. (2014) prefer WAIC
to AIC or DIC when feasible, which is less often than AIC or DIC.
The `LaplacesDemon`

function requires the model
specification function to return the model-level deviance, which is
\(-2(LL)\), where \(LL\) is the sum of the record-level
log-likelihood. Therefore, if the user desires to calculate WAIC, then
the record-level log-likelihood must be monitored.