deviance: Deviance for INLAvaan Models

In INLAvaan: Approximate Bayesian Latent Variable Analysis

Deviance for INLAvaan Models

Description

Extract the (Bayesian) deviance of a fitted INLAvaan model. Unlike lavaan, which has no deviance() method, this follows the BUGS/JAGS/Stan convention: "deviance" is -2 times the log-likelihood, summarised over the posterior.

Usage

## S3 method for class 'INLAvaan'
deviance(object, type = c("mean", "plugin"), ...)

Arguments

object	An object of class INLAvaan.
type	Character. "mean" (default) returns the posterior mean deviance \bar{D} = E[-2\log p(y \mid \theta)], averaged over posterior draws. "plugin" returns the deviance evaluated at the posterior mean point estimate, \hat{D} = -2\log p(y \mid \hat\theta) (matching -2 * logLik(object, type = "plugin")). Both require the model to have been fitted with a test that includes "dic" (the default "standard" does).
...	Currently unused.

Details

\bar{D} and \hat{D} are the two ingredients of the Deviance Information Criterion, DIC = \bar{D} + p_D where p_D = \bar{D} - \hat{D} is the effective number of parameters. Use compare() to compare models by DIC (or Bayes factors, or LOO/WAIC) rather than comparing raw deviances directly.

This p_D is estimated from the posterior draws. loo() reaches the same quantity in closed form as pd_trace, the trace \mathrm{tr}(\Sigma \mathcal{I}); the two routes estimate one target but do not agree exactly in a finite sample. Neither is p_loo, which estimates something else entirely (see loo()).

Value

A length-one numeric of class inlavaan_deviance, with the effective number of parameters (pD) and DIC attached as attributes.

See Also

logLik(), compare()

Examples

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)

deviance(fit)
attr(deviance(fit), "DIC")

INLAvaan documentation built on Oct. 2, 2026, 1:07 a.m.