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 Finding posterior mode.
#> ✔ Finding posterior mode. [133ms]
#>
#> ℹ Computing the Hessian.
#> ✔ Computing the Hessian. [260ms]
#>
#> ℹ Performing VB correction.
#> ✔ VB correction; mean |δ| = 0.043σ. [230ms]
#>
#> ⠙ Fitting skew normal to 0/28 marginals.
#> ⠹ Fitting skew normal to 27/28 marginals.
#> ✔ Fitting skew normal to 28/28 marginals. [1.4s]
#>
#> ℹ Sampling covariances and defined parameters.
#> ✔ Sampling covariances and defined parameters. [180ms]
#>
#> ⠙ Computing ppp and DIC.
#> ✔ Computing ppp and DIC. [565ms]
#>
summary(fit)
#> INLAvaan 0.2.3.9004 ended normally after 74 iterations
#>
#> Estimator BAYES
#> Optimization method NLMINB
#> Number of model parameters 28
#>
#> Number of observations 75
#>
#> Model Test (User Model):
#>
#> Marginal log-likelihood -1644.610
#> PPP (Chi-square) 0.128
#>
#> Information Criteria:
#>
#> Deviance (DIC) 3224.749
#> Effective parameters (pD) 63.202
#>
#> Parameter Estimates:
#>
#> Marginalisation method SKEWNORM
#> VB correction TRUE
#>
#> Latent Variables:
#> Estimate SD 2.5% 97.5% NMAD Prior
#> ind60 =~
#> x1 1.000
#> x2 2.217 0.146 1.948 2.522 0.005 normal(0,10)
#> x3 1.849 0.157 1.554 2.170 0.006 normal(0,10)
#> dem60 =~
#> y1 1.000
#> y2 (a) 1.209 0.145 0.939 1.509 0.008 normal(0,10)
#> y3 (b) 1.195 0.124 0.968 1.454 0.010 normal(0,10)
#> y4 (c) 1.288 0.130 1.050 1.563 0.008 normal(0,10)
#> dem65 =~
#> y5 1.000
#> y6 (a) 1.209 0.145 0.939 1.509 0.008 normal(0,10)
#> y7 (b) 1.195 0.124 0.968 1.454 0.010 normal(0,10)
#> y8 (c) 1.288 0.130 1.050 1.563 0.008 normal(0,10)
#>
#> Regressions:
#> Estimate SD 2.5% 97.5% NMAD Prior
#> dem60 ~
#> ind60 1.479 0.393 0.723 2.266 0.002 normal(0,10)
#> dem65 ~
#> ind60 0.594 0.242 0.126 1.075 0.000 normal(0,10)
#> dem60 0.869 0.076 0.723 1.024 0.003 normal(0,10)
#>
#> Covariances:
#> Estimate SD 2.5% 97.5% NMAD Prior
#> .y1 ~~
#> .y5 0.275 0.374 0.007 1.471 0.003 beta(1,1)
#> .y2 ~~
#> .y4 0.271 0.676 0.280 2.934 0.006 beta(1,1)
#> .y6 0.344 0.749 0.826 3.769 0.010 beta(1,1)
#> .y3 ~~
#> .y7 0.179 0.596 -0.317 2.027 0.005 beta(1,1)
#> .y4 ~~
#> .y8 0.104 0.480 1.305 -0.576 0.003 beta(1,1)
#> .y6 ~~
#> .y8 0.316 0.641 0.154 2.667 0.005 beta(1,1)
#>
#> Variances:
#> Estimate SD 2.5% 97.5% NMAD Prior
#> .x1 0.088 0.021 0.195 0.053 0.008 gamma(1,.5)[sd]
#> .x2 0.123 0.065 1.515 0.018 0.038 gamma(1,.5)[sd]
#> .x3 0.500 0.098 0.338 0.719 0.003 gamma(1,.5)[sd]
#> .y1 1.999 0.485 3.077 1.183 0.010 gamma(1,.5)[sd]
#> .y2 7.876 1.417 5.493 11.028 0.000 gamma(1,.5)[sd]
#> .y3 5.254 1.039 3.537 7.593 0.001 gamma(1,.5)[sd]
#> .y4 3.344 0.768 7.238 2.032 0.006 gamma(1,.5)[sd]
#> .y5 2.478 0.522 3.645 1.609 0.005 gamma(1,.5)[sd]
#> .y6 5.169 0.944 3.578 7.263 0.002 gamma(1,.5)[sd]
#> .y7 3.761 0.782 5.510 2.457 0.005 gamma(1,.5)[sd]
#> .y8 3.410 0.732 5.024 2.166 0.005 gamma(1,.5)[sd]
#> ind60 0.451 0.088 0.305 0.650 0.003 gamma(1,.5)[sd]
#> .dem60 3.887 0.894 5.891 2.404 0.002 gamma(1,.5)[sd]
#> .dem65 0.272 0.199 9.490 0.014 0.050 gamma(1,.5)[sd]
