Log-Likelihood for INLAvaan Models

Extract a log-likelihood-flavoured summary from a fitted INLAvaan model. Two distinct quantities are available, deliberately not conflated: the Bayesian marginal log-likelihood (the default) and the classical log-likelihood evaluated at the posterior mean.

Usage

# S4 method for class 'INLAvaan'
logLik(object, type = c("marginal", "plugin"), ...)

# S4 method for class 'INLAvaan'
AIC(object, ..., k = 2)

# S4 method for class 'INLAvaan'
BIC(object, ...)

Arguments

object: An object of class INLAvaan.
type: Character. "marginal" (default) returns the Laplace-approximated marginal log-likelihood (log evidence), the same quantity compare() uses for Bayes factors. "plugin" returns the classical log-likelihood evaluated at the posterior mean point estimate, with df/nobs attributes and class "logLik" so it supports AIC/BIC at the point estimate. Requires the model to have been fitted with test != "none".
...: Currently unused.
k: Numeric penalty per parameter passed to the (disabled) AIC() method; see stats::AIC(). Defaults to 2.

Value

For type = "marginal", a length-one numeric of class inlavaan_logLik that prints with a note on its interpretation. For type = "plugin", a standard "logLik" object.

Details

The marginal log-likelihood already integrates over the (Laplace- approximated) posterior, so it is not on the same scale as a classical log-likelihood and should not be passed to AIC()/BIC() – doing so would double-penalise model complexity that the evidence has already accounted for. Use compare() to compare models via Bayes factors, DIC, or LOO/WAIC. The plug-in variant exists for users who specifically want a point-estimate-based classical comparison.

AIC()/BIC() on an INLAvaan fit are themselves disabled (mirroring anova()): both are large-sample asymptotic approximations to quantities INLAvaan already computes directly – AIC approximates predictive accuracy, which loo()/waic() already estimate more rigorously; BIC approximates \(-2\) times the log marginal likelihood, which logLik() already returns directly (up to the Laplace approximation). Point-estimate AIC/BIC remain available for reporting-convention purposes via AIC(logLik(object, type = "plugin")) / BIC(logLik(object, type = "plugin")).

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, std.lv = TRUE, nsamp = 100,
            test = "standard", verbose = FALSE)

# Marginal log-likelihood (log evidence)
logLik(fit)
#> 'log Lik.' -3848.435 (marginal)
#> # ℹ Laplace-approximated log evidence -- not comparable to classical
#> # ℹ logLik()/AIC()/BIC(). See `compare()` for Bayes-factor comparison.
#> 

# Classical log-likelihood at the posterior mean, AIC/BIC-compatible
ll <- logLik(fit, type = "plugin")
AIC(ll)
#> [1] 7553.147
# }