# Linear growth model with a time-varying covariate
mod <- "
# Intercept and slope with fixed coefficients
i =~ 1*t1 + 1*t2 + 1*t3 + 1*t4
s =~ 0*t1 + 1*t2 + 2*t3 + 3*t4
# (Latent) regressions
i ~ x1 + x2
s ~ x1 + x2
# Time-varying covariates
t1 ~ c1
t2 ~ c2
t3 ~ c3
t4 ~ c4
"
utils::data("Demo.growth", package = "lavaan")
str(Demo.growth)
#> 'data.frame': 400 obs. of 10 variables:
#> $ t1: num 1.726 -1.984 0.32 0.777 0.449 ...
#> $ t2: num 2.142 -4.401 -1.269 3.531 -0.773 ...
#> $ t3: num 2.77 -6.02 1.56 3.14 -1.5 ...
#> $ t4: num 2.516 -7.0296 2.8685 5.3637 0.0785 ...
#> $ x1: num -1.16 -1.75 0.92 2.36 -1.09 ...
#> $ x2: num 0.174 -1.577 -0.142 0.708 -1.01 ...
#> $ c1: num -0.0277 -2.032 0.0524 0.0191 0.6524 ...
#> $ c2: num 0.555 0.125 -1.258 0.647 0.731 ...
#> $ c3: num 0.254 -1.564 -1.803 -0.432 -0.754 ...
#> $ c4: num -1.0064 1.2293 -0.3273 -1.0324 -0.0275 ...
fit <- agrowth(mod, data = Demo.growth, nsamp = 100)
#> ℹ Finding posterior mode.
#> ✔ Finding posterior mode. [175ms]
#>
#> ℹ Computing the Hessian.
#> ✔ Computing the Hessian. [89ms]
#>
#> ℹ Performing VB correction.
#> ✔ VB correction; mean |δ| = 0.051σ. [181ms]
#>
#> ⠙ Fitting 0/17 skew-normal marginals.
#> ✔ Fitting 17/17 skew-normal marginals. [893ms]
#>
#> ℹ Adjusting copula correlations (NORTA).
#> ✔ Adjusting copula correlations (NORTA). [92ms]
#>
#> ⠙ Posterior sampling and summarising.
#> ✔ Posterior sampling and summarising. [139ms]
#>
summary(fit)
#> INLAvaan 0.2.4.9000 ended normally after 83 iterations
#>
#> Estimator BAYES
#> Optimization method NLMINB
#> Number of model parameters 17
#>
#> Number of observations 400
#>
#> Model Test (User Model):
#>
#> Marginal log-likelihood -2565.904
#> PPP (Chi-square) 0.930
#>
#> Information Criteria:
#>
#> Deviance (DIC) 4997.022
#> Effective parameters (pD) 17.311
#>
#> Parameter Estimates:
#>
#> Marginalisation method SKEWNORM
#> VB correction TRUE
#>
#> Latent Variables:
#> Estimate SD 2.5% 97.5% NMAD Prior
#> i =~
#> t1 1.000
#> t2 1.000
#> t3 1.000
#> t4 1.000
#> s =~
#> t1 0.000
#> t2 1.000
#> t3 2.000
#> t4 3.000
#>
#> Regressions:
#> Estimate SD 2.5% 97.5% NMAD Prior
#> i ~
#> x1 0.608 0.060 0.491 0.726 0.000 normal(0,10)
#> x2 0.604 0.064 0.478 0.730 0.000 normal(0,10)
#> s ~
#> x1 0.262 0.029 0.206 0.318 0.000 normal(0,10)
#> x2 0.522 0.031 0.462 0.582 0.000 normal(0,10)
#> t1 ~
#> c1 0.144 0.050 0.046 0.242 0.000 normal(0,10)
#> t2 ~
#> c2 0.289 0.046 0.199 0.379 0.000 normal(0,10)
#> t3 ~
#> c3 0.328 0.045 0.240 0.415 0.000 normal(0,10)
#> t4 ~
#> c4 0.331 0.059 0.216 0.445 0.000 normal(0,10)
#>
#> Covariances:
#> Estimate SD 2.5% 97.5% NMAD Prior
#> .i ~~
#> .s 0.153 0.042 -0.012 0.155 0.006 beta(1,1)
#>
#> Intercepts:
#> Estimate SD 2.5% 97.5% NMAD Prior
#> .t1 0.000
#> .t2 0.000
#> .t3 0.000
#> .t4 0.000
#> .i 0.580 0.062 0.459 0.702 0.000 normal(0,10)
#> .s 0.958 0.030 0.900 1.015 0.000 normal(0,10)
#>
#> Variances:
#> Estimate SD 2.5% 97.5% NMAD Prior
#> .t1 0.590 0.080 0.441 0.756 0.003 gamma(1,.5)[sd]
#> .t2 0.605 0.055 0.504 0.721 0.001 gamma(1,.5)[sd]
#> .t3 0.488 0.056 0.386 0.603 0.001 gamma(1,.5)[sd]
#> .t4 0.544 0.097 0.362 0.741 0.012 gamma(1,.5)[sd]
#> .i 1.099 0.114 0.889 1.335 0.000 gamma(1,.5)[sd]
#> .s 0.229 0.027 0.180 0.284 0.001 gamma(1,.5)[sd]
