# 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 Mode finding and Hessian computation.
#> ✔ Posterior mode and Hessian. [159ms]
#>
#> ℹ Performing VB correction.
#> ✔ VB correction; mean |δ| = 0.081σ. [149ms]
#>
#> ⠙ Fitting 0/21 skew-normal marginals.
#> ✔ Fit 21/21 skew-normal marginals. [971ms]
#>
#> ℹ Adjusting copula correlations (NORTA).
#> ✔ Adjust copula correlations (NORTA). [158ms]
#>
#> ⠙ Posterior sampling and summarising.
#> ✔ Summarise 100 posterior draws. [335ms]
#>
#> ℹ Fit measures: PPP, DIC, LOO, WAIC.
summary(fit)
#> INLAvaan 0.2.5.9004 ended normally after 66 iterations
#>
#> Estimator BAYES
#> Optimization method NLMINB
#> Number of model parameters 21
#>
#> Number of observations 301
#>
#> Model Test (User Model):
#>
#> Marginal log-likelihood -3848.435
#> PPP (Chi-square) 0.000
#>
#> Information Criteria:
#>
#> Deviance (DIC) 7552.079
#> Effective parameters (pD) 20.466
#>
#> Parameter Estimates:
#>
#> Marginalisation method SKEWNORM
#> VB correction TRUE
#>
#> Latent Variables:
#> Estimate SD 2.5% 97.5% NMAD Prior
#> visual =~
#> x1 0.907 0.082 0.748 1.068 0.009 normal(0,10)
#> x2 0.502 0.081 0.344 0.662 0.000 normal(0,10)
#> x3 0.663 0.078 0.512 0.817 0.002 normal(0,10)
#> textual =~
#> x4 1.001 0.058 0.891 1.117 0.003 normal(0,10)
#> x5 1.114 0.064 0.993 1.243 0.003 normal(0,10)
#> x6 0.926 0.055 0.823 1.037 0.003 normal(0,10)
#> speed =~
#> x7 0.616 0.074 0.466 0.758 0.003 normal(0,10)
#> x8 0.732 0.073 0.586 0.872 0.014 normal(0,10)
#> x9 0.681 0.075 0.537 0.833 0.016 normal(0,10)
#>
#> Covariances:
#> Estimate SD 2.5% 97.5% NMAD Prior
#> visual ~~
#> textual 0.449 0.064 0.318 0.567 0.001 beta(1,1)
#> speed 0.465 0.084 0.298 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 0.565 0.117 0.341 0.797 0.011 gamma(1,.5)[sd]
#> .x2 1.150 0.107 0.956 1.374 0.001 gamma(1,.5)[sd]
#> .x3 0.856 0.097 0.672 1.054 0.003 gamma(1,.5)[sd]
#> .x4 0.379 0.049 0.287 0.480 0.003 gamma(1,.5)[sd]
#> .x5 0.455 0.059 0.344 0.577 0.003 gamma(1,.5)[sd]
#> .x6 0.364 0.045 0.281 0.456 0.002 gamma(1,.5)[sd]
#> .x7 0.823 0.090 0.662 1.015 0.004 gamma(1,.5)[sd]
#> .x8 0.506 0.087 0.346 0.689 0.023 gamma(1,.5)[sd]
#> .x9 0.569 0.090 0.392 0.742 0.007 gamma(1,.5)[sd]
#> visual 1.000
#> textual 1.000
#> speed 1.000
