Computes the WAIC of a fitted INLAvaan model from unit log-likelihoods
evaluated over posterior draws. Single-level models are scored per
subject; two-level models are scored per cluster by default, matching the
units used by loo(). For a two-level model type = "loso" instead
scores the conditional (leave-one-unit-out) WAIC; see Details.
Usage
waic(x, ...)
# S3 method for class 'INLAvaan'
waic(
x,
type = c("auto", "loso", "loco"),
units = NULL,
nsamp = NULL,
cores = NULL,
verbose = FALSE,
...
)
# S3 method for class 'inlavaan_internal'
waic(
x,
type = c("auto", "loso", "loco"),
units = NULL,
nsamp = NULL,
cores = NULL,
verbose = FALSE,
...
)Arguments
- x
A fitted INLAvaan object (or its
inlavaan_internallist).- ...
Not used.
- type
Unit type:
"auto"(default) resolves to per-subject for single-level models and per-cluster (marginal WAIC) for two-level models."loso"on a two-level model scores the conditional (leave-one-unit-out) WAIC instead (with a warning; see Details);"loco"cannot be forced on a model without clusters.- units
Optional integer vector of unit indices to score; defaults to all units.
- nsamp
Number of posterior draws. Defaults to the
nsampused when fitting the model.- cores
Number of cores for evaluating draws. The default
NULLruns serially; parallelism must be requested explicitly.- verbose
Logical; print progress (default
FALSE).
Value
An object of class inlavaan_waic: a list with per_unit
(pointwise lpd, p_waic, elpd_waic, with the same unit/group
identification as loo()), estimates (matrix with rows
elpd_waic, p_waic, waic and columns Estimate, SE), type,
n_units, n_groups, and nsamp.
Details
For each posterior draw \(\theta_s\) (drawn with the same copula
sampler used for the fit's posterior summaries) and unit \(u\), the
log-likelihood \(\log p(y_u \mid \theta_s)\) is evaluated; then
\(\mathrm{lpd}_u = \log \tfrac{1}{S}\sum_s p(y_u \mid \theta_s)\),
\(p_{\mathrm{waic},u} = \mathrm{var}_s \log p(y_u \mid \theta_s)\), and
\(\mathrm{elpd}_{\mathrm{waic}} = \sum_u (\mathrm{lpd}_u -
p_{\mathrm{waic},u})\) with \(\mathrm{WAIC} = -2\,
\mathrm{elpd}_{\mathrm{waic}}\). Unlike loo(), this is a sampling-based
estimate: results vary with the random draws, and units with
\(p_{\mathrm{waic},u} > 0.4\) trigger a reliability warning (also
annotated when printing). The same model restrictions as loo() apply,
and so does the flavour rule: fits with fixed.x = TRUE are scored
conditionally on the exogenous covariates, fits with fixed.x = FALSE
jointly (see loo()).
Marginal vs conditional WAIC (two-level models). The default
per-cluster scoring is the marginal WAIC, which corresponds to
leave-one-cluster-out cross-validation – prediction for a new cluster.
Setting type = "loso" scores the conditional WAIC, corresponding to
leave-one-unit-out – prediction for a new observation within an
observed cluster (each row contributes the conditional density of its
observed entries given the rest of its cluster). The two answer different
questions and are easily conflated (Merkle, Furr & Rabe-Hesketh, 2019);
the per-cluster marginal is the usual model-comparison target, so it is
the default, and type = "loso" warns. This matches loo(type = "loso")
– the two compute the same estimand by sampling and by Taylor expansion.
Under the default test = "standard", inlavaan() computes the WAIC at
fit time by reusing the posterior draws the fit already produced (when
the model is supported and nsamp >= 100), and
stores it with the fit: waic(fit) then returns the stored result when
called with default arguments, and fitmeasures() reports waic,
p_waic, se_waic as part of "all" for free. If the loo package is
attached it masks this generic, but dispatch on INLAvaan objects
continues to work.
Examples
# \donttest{
HS.model <- "
visual =~ x1 + x2 + x3
textual =~ x4 + x5 + x6
speed =~ x7 + x8 + x9
"
utils::data("HolzingerSwineford1939", package = "lavaan")
fit <- acfa(HS.model, HolzingerSwineford1939, meanstructure = TRUE)
#> ℹ Finding posterior mode.
#> ✔ Finding posterior mode. [108ms]
#>
#> ℹ Computing the Hessian.
#> ✔ Computing the Hessian. [52ms]
#>
#> ℹ Performing VB correction.
#> ✔ VB correction; mean |δ| = 0.146σ. [107ms]
#>
#> ⠙ Fitting 0/30 skew-normal marginals.
#> ✔ Fitting 30/30 skew-normal marginals. [768ms]
#>
#> ℹ Adjusting copula correlations (NORTA).
#> ✔ Adjusting copula correlations (NORTA). [121ms]
#>
#> ⠙ Posterior sampling and summarising.
#> ⠹ Posterior sampling and summarising.
#> ✔ Posterior sampling and summarising. [542ms]
#>
#> ℹ Computing Taylor LOO.
#> ✔ Computing Taylor LOO. [485ms]
#>
#> ℹ Computing WAIC from the posterior draws.
#> ✔ Computing WAIC from the posterior draws. [238ms]
#>
waic(fit)
#> WAIC (INLAvaan)
#> Computed from 1000 posterior draws and 301 subjects
#>
#> Estimate SE
#> elpd_waic -3769.3 42.9
#> p_waic 32.1 2.1
#> waic 7538.5 85.7
#>
#> 8 units with p_waic > 0.4: the WAIC may be unreliable; prefer loo().
# }