# 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)
#> ℹ Using MVN log-likelihood.
#> ℹ Finding posterior mode.
#> ✔ Finding posterior mode. [148ms]
#>
#> ℹ Computing the Hessian.
#> ✔ Computing the Hessian. [362ms]
#>
#> ℹ Performing VB correction.
#> ✔ Performing VB correction. [312ms]
#>
#> ℹ Using skew normal approximation.
#> ⠙ Fitting skew normal to 0/21 marginals.
#> ⠹ Fitting skew normal to 6/21 marginals.
#> ✔ Fitting skew normal to 21/21 marginals. [1.7s]
#>
#> ⠙ Computing ppp and DIC.
#> ⠹ Computing ppp and DIC.
#> ✔ Computing ppp and DIC. [2s]
#>
summary(fit)
#> INLAvaan 0.2.0.9004 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 -3830.969
#> PPP (Chi-square) 0.000
#>
#> Information Criteria:
#>
#> Deviance (DIC) 7519.099
#> Effective parameters (pD) 21.675
#>
#> Parameter Estimates:
#>
#> Marginalisation method SKEWNORM
#> VB correction TRUE
#>
#> Latent Variables:
#> Estimate SD 2.5% 97.5% KLD Prior
#> visual =~
#> x1 0.907 0.083 0.746 1.071 0.003 normal(0,10)
#> x2 0.501 0.081 0.343 0.663 0.003 normal(0,10)
#> x3 0.663 0.078 0.511 0.818 0.006 normal(0,10)
#> textual =~
#> x4 0.999 0.058 0.888 1.116 0.021 normal(0,10)
#> x5 1.112 0.063 0.990 1.238 0.023 normal(0,10)
#> x6 0.926 0.054 0.820 1.032 0.019 normal(0,10)
#> speed =~
#> x7 0.617 0.077 0.463 0.766 0.012 normal(0,10)
#> x8 0.734 0.077 0.587 0.887 0.010 normal(0,10)
#> x9 0.681 0.079 0.530 0.838 0.058 normal(0,10)
#>
#> Covariances:
#> Estimate SD 2.5% 97.5% KLD Prior
#> visual ~~
#> textual 0.449 0.064 0.317 0.568 0.000 beta(1,1)
#> speed 0.474 0.085 0.298 0.630 0.024 beta(1,1)
#> textual ~~
#> speed 0.284 0.071 0.141 0.420 0.004 beta(1,1)
#>
#> Variances:
#> Estimate SD 2.5% 97.5% KLD Prior
#> .x1 0.558 0.121 0.351 0.825 0.000 gamma(1,.5)[sd]
#> .x2 1.144 0.107 0.952 1.370 0.002 gamma(1,.5)[sd]
#> .x3 0.849 0.097 0.676 1.056 0.000 gamma(1,.5)[sd]
#> .x4 0.378 0.049 0.289 0.481 0.001 gamma(1,.5)[sd]
#> .x5 0.453 0.059 0.347 0.579 0.000 gamma(1,.5)[sd]
#> .x6 0.363 0.044 0.283 0.457 0.002 gamma(1,.5)[sd]
#> .x7 0.825 0.090 0.664 1.017 0.039 gamma(1,.5)[sd]
#> .x8 0.508 0.093 0.349 0.711 0.033 gamma(1,.5)[sd]
#> .x9 0.553 0.090 0.398 0.751 0.053 gamma(1,.5)[sd]
#> visual 1.000
#> textual 1.000
#> speed 1.000
