# 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. [77ms]
#>
#> ℹ Computing the Hessian.
#> ✔ Computing the Hessian. [141ms]
#>
#> ℹ Performing VB correction.
#> ✔ VB correction; mean |δ| = 0.008σ. [122ms]
#>
#> ⠙ Fitting skew normal to 0/21 marginals.
#> ✔ Fitting skew normal to 21/21 marginals. [646ms]
#>
#> ⠙ Computing ppp and DIC.
#> ✔ Computing ppp and DIC. [87ms]
#>
summary(fit)
#> INLAvaan 0.2.3.9004 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 -3830.975
#> PPP (Chi-square) 0.000
#>
#> Information Criteria:
#>
#> Deviance (DIC) 7586.196
#> Effective parameters (pD) 55.267
#>
#> Parameter Estimates:
#>
#> Marginalisation method SKEWNORM
#> VB correction TRUE
#>
#> Latent Variables:
#> Estimate SD 2.5% 97.5% NMAD Prior
#> visual =~
#> x1 0.906 0.083 0.744 1.071 0.011 normal(0,10)
#> x2 0.500 0.081 0.343 0.660 0.001 normal(0,10)
#> x3 0.662 0.078 0.511 0.818 0.005 normal(0,10)
#> textual =~
#> x4 0.999 0.058 0.889 1.116 0.004 normal(0,10)
#> x5 1.114 0.064 0.993 1.244 0.004 normal(0,10)
#> x6 0.927 0.055 0.823 1.038 0.004 normal(0,10)
#> speed =~
#> x7 0.615 0.074 0.758 0.466 0.004 normal(0,10)
#> x8 0.725 0.076 0.987 0.569 0.027 normal(0,10)
#> x9 0.686 0.079 0.538 0.848 0.034 normal(0,10)
#>
#> Covariances:
#> Estimate SD 2.5% 97.5% NMAD Prior
#> visual ~~
#> textual 0.449 0.064 0.319 0.568 0.001 beta(1,1)
#> speed 0.474 0.086 0.302 0.639 0.021 beta(1,1)
#> textual ~~
#> speed 0.280 0.071 0.138 0.415 0.003 beta(1,1)
#>
#> Variances:
#> Estimate SD 2.5% 97.5% NMAD Prior
#> .x1 0.544 0.119 1.395 0.306 0.021 gamma(1,.5)[sd]
#> .x2 1.144 0.106 0.952 1.366 0.001 gamma(1,.5)[sd]
#> .x3 0.846 0.097 1.253 0.665 0.002 gamma(1,.5)[sd]
#> .x4 0.376 0.049 0.477 0.286 0.002 gamma(1,.5)[sd]
#> .x5 0.451 0.059 0.574 0.342 0.002 gamma(1,.5)[sd]
#> .x6 0.361 0.044 0.453 0.279 0.002 gamma(1,.5)[sd]
#> .x7 0.823 0.091 0.661 1.016 0.004 gamma(1,.5)[sd]
#> .x8 0.495 0.092 1.046 0.318 0.050 gamma(1,.5)[sd]
#> .x9 0.542 0.093 1.146 0.344 0.016 gamma(1,.5)[sd]
#> visual 1.000
#> textual 1.000
#> speed 1.000
