# The famous Holzinger and Swineford (1939) example
HS.model <- "
visual =~ x1 + x2 + x3
textual =~ x4 + x5 + x6
speed =~ x7 + x8 + x9
"
utils::data("HolzingerSwineford1939", package = "lavaan")
# Fit a CFA model with standardised latent variables
fit <- acfa(HS.model, data = HolzingerSwineford1939, std.lv = TRUE, nsamp = 100)
#> ℹ Finding posterior mode.
#> ✔ Finding posterior mode. [72ms]
#>
#> ℹ Computing the Hessian.
#> ✔ Computing the Hessian. [57ms]
#>
#> ℹ Performing VB correction.
#> ✔ VB correction; mean |δ| = 0.081σ. [93ms]
#>
#> ⠙ Fitting 0/21 skew-normal marginals.
#> ✔ Fitting 21/21 skew-normal marginals. [532ms]
#>
#> ℹ Adjusting copula correlations (NORTA).
#> ✔ Adjusting copula correlations (NORTA). [152ms]
#>
#> ⠙ Posterior sampling and summarising.
#> ✔ Posterior sampling and summarising. [79ms]
#>
summary(fit)
#> INLAvaan 0.2.4.9000 ended normally after 56 iterations
#>
#> Estimator BAYES
#> Optimization method NLMINB
#> Number of model parameters 21
#>
#> Number of observations 301
#>
#> Model Test (User Model):
#>
#> Marginal log-likelihood -3830.737
#> PPP (Chi-square) 0.000
#>
#> Information Criteria:
#>
#> Deviance (DIC) 7514.500
#> Effective parameters (pD) 19.434
#>
#> Parameter Estimates:
#>
#> Marginalisation method SKEWNORM
#> VB correction TRUE
#>
#> Latent Variables:
#> Estimate SD 2.5% 97.5% NMAD Prior
#> visual =~
#> x1 0.905 0.082 0.747 1.066 0.009 normal(0,10)
#> x2 0.501 0.081 0.344 0.661 0.000 normal(0,10)
#> x3 0.662 0.078 0.512 0.816 0.002 normal(0,10)
#> textual =~
#> x4 0.999 0.057 0.890 1.115 0.003 normal(0,10)
#> x5 1.112 0.063 0.992 1.240 0.003 normal(0,10)
#> x6 0.925 0.054 0.821 1.035 0.003 normal(0,10)
#> speed =~
#> x7 0.615 0.074 0.466 0.757 0.003 normal(0,10)
#> x8 0.731 0.073 0.585 0.871 0.014 normal(0,10)
#> x9 0.680 0.075 0.536 0.831 0.016 normal(0,10)
#>
#> Covariances:
#> Estimate SD 2.5% 97.5% NMAD Prior
#> visual ~~
#> textual 0.449 0.064 0.319 0.567 0.001 beta(1,1)
#> speed 0.465 0.083 0.299 0.625 0.011 beta(1,1)
#> textual ~~
#> speed 0.280 0.070 0.139 0.414 0.003 beta(1,1)
#>
#> Variances:
#> Estimate SD 2.5% 97.5% NMAD Prior
#> .x1 0.563 0.117 0.341 0.794 0.011 gamma(1,.5)[sd]
#> .x2 1.147 0.106 0.953 1.369 0.001 gamma(1,.5)[sd]
#> .x3 0.853 0.097 0.671 1.050 0.003 gamma(1,.5)[sd]
#> .x4 0.377 0.049 0.286 0.478 0.003 gamma(1,.5)[sd]
#> .x5 0.453 0.059 0.344 0.575 0.003 gamma(1,.5)[sd]
#> .x6 0.362 0.044 0.280 0.454 0.002 gamma(1,.5)[sd]
#> .x7 0.821 0.090 0.660 1.011 0.004 gamma(1,.5)[sd]
#> .x8 0.504 0.087 0.345 0.686 0.023 gamma(1,.5)[sd]
#> .x9 0.567 0.089 0.391 0.739 0.007 gamma(1,.5)[sd]
#> visual 1.000
#> textual 1.000
#> speed 1.000
