library(INLAvaan)
# 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)
#> ℹ Mode finding and Hessian computation.
#> ✔ Posterior mode and Hessian. [313ms]
#>
#> ℹ Performing VB correction.
#> ✔ VB correction; mean |δ| = 0.177σ. [376ms]
#>
#> ⠙ Fitting 0/28 skew-normal marginals.
#> ⠹ Fitting 19/28 skew-normal marginals.
#> ✔ Fit 28/28 skew-normal marginals. [2.6s]
#>
#> ℹ Adjusting copula correlations (NORTA).
#> ✔ Adjust copula correlations (NORTA). [326ms]
#>
#> ⠙ Posterior sampling and summarising.
#> ✔ Summarise 1000 posterior draws. [1.2s]
#>
#> ℹ Fit measures: PPP, DIC, LOO, WAIC.
summary(fit)
#> INLAvaan 0.2.5.9004 ended normally after 82 iterations
#>
#> Estimator BAYES
#> Optimization method NLMINB
#> Number of model parameters 28
#>
#> Number of observations 75
#>
#> Model Test (User Model):
#>
#> Marginal log-likelihood -1652.945
#> PPP (Chi-square) 0.532
#>
#> Information Criteria:
#>
#> Deviance (DIC) 3170.276
#> Effective parameters (pD) 27.409
#>
#> Parameter Estimates:
#>
#> Marginalisation method SKEWNORM
#> VB correction TRUE
#>
#> Latent Variables:
#> Estimate SD 2.5% 97.5% NMAD Prior
#> ind60 =~
#> x1 1.000
#> x2 2.220 0.148 1.950 2.533 0.007 normal(0,10)
#> x3 1.840 0.156 1.548 2.160 0.004 normal(0,10)
#> dem60 =~
#> y1 1.000
#> y2 (a) 1.211 0.146 0.943 1.515 0.004 normal(0,10)
#> y3 (b) 1.189 0.122 0.964 1.445 0.005 normal(0,10)
#> y4 (c) 1.277 0.129 1.044 1.551 0.007 normal(0,10)
#> dem65 =~
#> y5 1.000
#> y6 (a) 1.211 0.146 0.943 1.515 0.004 normal(0,10)
#> y7 (b) 1.189 0.122 0.964 1.445 0.005 normal(0,10)
#> y8 (c) 1.277 0.129 1.044 1.551 0.007 normal(0,10)
#>
#> Regressions:
#> Estimate SD 2.5% 97.5% NMAD Prior
#> dem60 ~
#> ind60 1.468 0.394 0.712 2.258 0.002 normal(0,10)
#> dem65 ~
#> ind60 0.587 0.243 0.116 1.071 0.000 normal(0,10)
#> dem60 0.868 0.078 0.721 1.025 0.004 normal(0,10)
#>
#> Covariances:
#> Estimate SD 2.5% 97.5% NMAD Prior
#> .y1 ~~
#> .y5 0.642 0.394 -0.081 1.465 0.003 beta(1,1)
#> .y2 ~~
#> .y4 1.459 0.707 0.191 2.965 0.007 beta(1,1)
#> .y6 2.215 0.739 0.877 3.780 0.012 beta(1,1)
#> .y3 ~~
#> .y7 0.803 0.643 -0.368 2.156 0.006 beta(1,1)
#> .y4 ~~
#> .y8 0.403 0.489 -0.508 1.412 0.004 beta(1,1)
#> .y6 ~~
#> .y8 1.347 0.605 0.293 2.663 0.005 beta(1,1)
#>
#> Variances:
#> Estimate SD 2.5% 97.5% NMAD Prior
#> .x1 0.090 0.022 0.053 0.138 0.006 gamma(1,.5)[sd]
#> .x2 0.132 0.067 0.031 0.283 0.031 gamma(1,.5)[sd]
#> .x3 0.509 0.101 0.342 0.735 0.003 gamma(1,.5)[sd]
#> .y1 2.046 0.505 1.189 3.161 0.010 gamma(1,.5)[sd]
#> .y2 8.012 1.452 5.571 11.242 0.000 gamma(1,.5)[sd]
#> .y3 5.335 1.065 3.579 7.736 0.001 gamma(1,.5)[sd]
#> .y4 3.434 0.798 2.066 5.183 0.008 gamma(1,.5)[sd]
#> .y5 2.523 0.541 1.623 3.732 0.005 gamma(1,.5)[sd]
#> .y6 5.259 0.970 3.625 7.411 0.002 gamma(1,.5)[sd]
#> .y7 3.827 0.811 2.476 5.640 0.006 gamma(1,.5)[sd]
#> .y8 3.487 0.758 2.193 5.156 0.006 gamma(1,.5)[sd]
#> ind60 0.461 0.090 0.311 0.664 0.003 gamma(1,.5)[sd]
#> .dem60 3.995 0.919 2.471 6.055 0.002 gamma(1,.5)[sd]
#> .dem65 0.275 0.197 0.027 0.750 0.044 gamma(1,.5)[sd]
