# The industrialization and Political Democracy Example from Bollen (1989), page
# 332
model <- "
# Latent variable definitions
ind60 =~ x1 + x2 + x3
dem60 =~ y1 + a*y2 + b*y3 + c*y4
dem65 =~ y5 + a*y6 + b*y7 + c*y8
# (Latent) regressions
dem60 ~ ind60
dem65 ~ ind60 + dem60
# Residual correlations
y1 ~~ y5
y2 ~~ y4 + y6
y3 ~~ y7
y4 ~~ y8
y6 ~~ y8
"
utils::data("PoliticalDemocracy", package = "lavaan")
fit <- asem(model, PoliticalDemocracy, test = "none")
#> ℹ Using MVN log-likelihood.
#> ℹ Finding posterior mode.
#> ✔ Finding posterior mode. [249ms]
#>
#> ℹ Computing the Hessian.
#> ✔ Computing the Hessian. [687ms]
#>
#> ℹ Performing VB correction.
#> ✔ Performing VB correction. [622ms]
#>
#> ℹ Using skew normal approximation.
#> ⠙ Fitting skew normal to 0/28 marginals.
#> ⠹ Fitting skew normal to 20/28 marginals.
#> ✔ Fitting skew normal to 28/28 marginals. [3.8s]
#>
#> ℹ Sampling posterior covariances.
#> ✔ Sampling posterior covariances. [389ms]
#>
summary(fit)
#> INLAvaan 0.2.0.9004 ended normally after 70 iterations
#>
#> Estimator BAYES
#> Optimization method NLMINB
#> Number of model parameters 28
#>
#> Number of observations 75
#>
#> Model Test (User Model):
#>
#> Marginal log-likelihood -1644.774
#>
#> Parameter Estimates:
#>
#> Marginalisation method SKEWNORM
#> VB correction TRUE
#>
#> Latent Variables:
#> Estimate SD 2.5% 97.5% KLD Prior
#> ind60 =~
#> x1 1.000
#> x2 2.210 0.146 1.942 2.513 0.065 normal(0,10)
#> x3 1.842 0.156 1.537 2.150 0.028 normal(0,10)
#> dem60 =~
#> y1 1.000
#> y2 (a) 1.206 0.149 0.929 1.514 0.006 normal(0,10)
#> y3 (b) 1.188 0.125 0.950 1.441 0.004 normal(0,10)
#> y4 (c) 1.267 0.126 1.023 1.518 0.028 normal(0,10)
#> dem65 =~
#> y5 1.000
#> y6 (a) 1.206 0.149 0.929 1.514 0.006 normal(0,10)
#> y7 (b) 1.188 0.125 0.950 1.441 0.004 normal(0,10)
#> y8 (c) 1.267 0.126 1.023 1.518 0.028 normal(0,10)
#>
#> Regressions:
#> Estimate SD 2.5% 97.5% KLD Prior
#> dem60 ~
#> ind60 1.474 0.396 0.699 2.250 0.000 normal(0,10)
#> dem65 ~
#> ind60 0.597 0.241 0.121 1.065 0.001 normal(0,10)
#> dem60 0.863 0.075 0.719 1.014 0.008 normal(0,10)
#>
#> Covariances:
#> Estimate SD 2.5% 97.5% KLD Prior
#> .y1 ~~
#> .y5 0.281 0.392 -0.004 1.532 0.003 beta(1,1)
#> .y2 ~~
#> .y4 0.274 0.703 0.136 2.899 0.003 beta(1,1)
#> .y6 0.343 0.746 0.817 3.746 0.000 beta(1,1)
#> .y3 ~~
#> .y7 0.184 0.663 -0.356 2.246 0.001 beta(1,1)
#> .y4 ~~
#> .y8 0.107 0.487 -0.504 1.411 0.007 beta(1,1)
#> .y6 ~~
#> .y8 0.312 0.582 0.255 2.540 0.012 beta(1,1)
#>
#> Variances:
#> Estimate SD 2.5% 97.5% KLD Prior
#> .x1 0.087 0.020 0.053 0.133 0.025 gamma(1,.5)[sd]
#> .x2 0.132 0.074 0.031 0.312 0.066 gamma(1,.5)[sd]
#> .x3 0.498 0.097 0.339 0.718 0.034 gamma(1,.5)[sd]
#> .y1 2.011 0.492 1.216 3.132 0.031 gamma(1,.5)[sd]
#> .y2 7.928 1.469 5.517 11.254 0.025 gamma(1,.5)[sd]
#> .y3 5.221 1.035 3.523 7.562 0.033 gamma(1,.5)[sd]
#> .y4 3.362 0.803 2.068 5.197 0.006 gamma(1,.5)[sd]
#> .y5 2.485 0.527 1.625 3.682 0.038 gamma(1,.5)[sd]
#> .y6 5.160 0.972 3.563 7.360 0.028 gamma(1,.5)[sd]
#> .y7 3.729 0.784 2.443 5.500 0.037 gamma(1,.5)[sd]
#> .y8 3.384 0.754 2.158 5.095 0.008 gamma(1,.5)[sd]
#> ind60 0.453 0.090 0.307 0.660 0.008 gamma(1,.5)[sd]
#> .dem60 3.932 0.923 2.465 6.059 0.000 gamma(1,.5)[sd]
#> .dem65 0.280 0.205 0.034 0.796 0.092 gamma(1,.5)[sd]
