Compare Bayesian Models Fitted with INLAvaan

Usage

compare(x, y, ...)

# S4 method for class 'INLAvaan'
compare(x, y, ...)

Arguments

x, y, ...: An object of class INLAvaan or inlavaan_internal.

Value

A data frame of class compare.inlavaan_internal containing model fit statistics.

Details

The function computes the log Bayes Factor (logBF) relative to the best fitting model (the one with the highest Marginal Log-Likelihood).

The output table sorts models by descending Marginal Log-Likelihood.

Marg.Loglik: The approximated marginal log-likelihood.
DIC: Deviance Information Criterion (if available).
pD: Effective number of parameters (if available).
logBF: The natural logarithm of the Bayes Factor relative to the best model.

References

https://lavaan.ugent.be/tutorial/groups.html

Examples

# \donttest{
# Model comparison on multigroup analysis (measurement invariance)
HS.model <- "
  visual  =~ x1 + x2 + x3
  textual =~ x4 + x5 + x6
  speed   =~ x7 + x8 + x9
"
utils::data("HolzingerSwineford1939", package = "lavaan")

# Configural invariance
fit1 <- acfa(HS.model, data = HolzingerSwineford1939, group = "school")
#> ℹ Finding posterior mode.
#> ✔ Finding posterior mode. [236ms]
#> 
#> ℹ Computing the Hessian.
#> ✔ Computing the Hessian. [703ms]
#> 
#> ℹ Performing VB correction.
#> ✔ VB correction; mean |δ| = 0.024σ. [320ms]
#> 
#> ⠙ Fitting skew normal to 0/60 marginals.
#> ⠹ Fitting skew normal to 6/60 marginals.
#> ⠸ Fitting skew normal to 31/60 marginals.
#> ⠼ Fitting skew normal to 57/60 marginals.
#> ✔ Fitting skew normal to 60/60 marginals. [7s]
#> 
#> ℹ Sampling covariances and defined parameters.
#> ✔ Sampling covariances and defined parameters. [201ms]
#> 
#> ⠙ Computing ppp and DIC.
#> ✔ Computing ppp and DIC. [785ms]
#> 

# Weak invariance
fit2 <- acfa(
  HS.model,
  data = HolzingerSwineford1939,
  group = "school",
  group.equal = "loadings"
)
#> ℹ Finding posterior mode.
#> ✔ Finding posterior mode. [206ms]
#> 
#> ℹ Computing the Hessian.
#> ✔ Computing the Hessian. [653ms]
#> 
#> ℹ Performing VB correction.
#> ✔ VB correction; mean |δ| = 0.014σ. [352ms]
#> 
#> ⠙ Fitting skew normal to 0/54 marginals.
#> ⠹ Fitting skew normal to 3/54 marginals.
#> ⠸ Fitting skew normal to 31/54 marginals.
#> ✔ Fitting skew normal to 54/54 marginals. [6s]
#> 
#> ℹ Sampling covariances and defined parameters.
#> ✔ Sampling covariances and defined parameters. [192ms]
#> 
#> ⠙ Computing ppp and DIC.
#> ⠹ Computing ppp and DIC.
#> ✔ Computing ppp and DIC. [745ms]
#> 

# Strong invariance
fit3 <- acfa(
  HS.model,
  data = HolzingerSwineford1939,
  group = "school",
  group.equal = c("intercepts", "loadings")
)
#> ℹ Finding posterior mode.
#> ✔ Finding posterior mode. [186ms]
#> 
#> ℹ Computing the Hessian.
#> ✔ Computing the Hessian. [575ms]
#> 
#> ℹ Performing VB correction.
#> ✔ VB correction; mean |δ| = 0.015σ. [255ms]
#> 
#> ⠙ Fitting skew normal to 0/48 marginals.
#> ⠹ Fitting skew normal to 15/48 marginals.
#> ⠸ Fitting skew normal to 47/48 marginals.
#> ✔ Fitting skew normal to 48/48 marginals. [4.6s]
#> 
#> ℹ Sampling covariances and defined parameters.
#> ✔ Sampling covariances and defined parameters. [196ms]
#> 
#> ⠙ Computing ppp and DIC.
#> ✔ Computing ppp and DIC. [740ms]
#> 

# Compare models
compare(fit1, fit2, fit3)
#> Bayesian Model Comparison (INLAvaan)
#> Models ordered by marginal log-likelihood
#> 
#>  Model No.params Marg.Loglik      DIC       pD   logBF
#>   fit3        48   -3914.197 7661.318 123.9249   0.000
#>   fit2        54   -3934.800 7594.939 110.7050 -20.603
#>   fit1        60   -3958.118 7721.328 178.0657 -43.921
# }