Fit an Approximate Bayesian Structural Equation Model
Usage
asem(
model,
data,
dp = priors_for(),
marginal_method = c("skewnorm", "asymgaus", "marggaus", "sampling"),
nsamp = 500,
test = "standard",
marginal_correction = c("shortcut", "hessian", "none"),
sn_fit_logthresh = -6,
sn_fit_temp = NA,
control = list(),
verbose = TRUE,
debug = FALSE,
add_priors = TRUE,
optim_method = c("nlminb", "ucminf", "optim"),
numerical_grad = FALSE,
...
)Arguments
- model
A description of the user-specified model. Typically, the model is described using the lavaan model syntax. See
model.syntaxfor more information. Alternatively, a parameter table (eg. the output of thelavParTable()function) is also accepted.- data
An optional data frame containing the observed variables used in the model. If some variables are declared as ordered factors, lavaan will treat them as ordinal variables.
- dp
Default prior distributions on different types of parameters, typically the result of a call to
dpriors(). See thedpriors()help file for more information.- marginal_method
The method for approximating the marginal posterior distributions. Options include
"skewnorm"(skew normal),"asymgaus"(two-piece asymmetric Gaussian),"marggaus"(marginalising the Laplace approximation), and"sampling"(sampling from the joint Laplace approximation).- nsamp
The number of samples to draw for all sampling-based approaches (including posterior sampling for model fit indices).
- test
Character indicating whether to compute posterior fit indices. Defaults to "standard". Change to "none" to skip these computations.
- marginal_correction
Which type of correction to use when fitting the skew normal or two-piece Gaussian marginals.
"hessian"computes the full Hessian-based correction (slow),"shortcut"(default) computes only diagonals, and"none"(orFALSE) applies no correction.- sn_fit_logthresh
The log-threshold for fitting the skew normal. Points with log-posterior drop below this threshold (relative to the maximum) will be excluded from the fit. Defaults to
-6.- sn_fit_temp
Temperature parameter for fitting the skew normal. If
NA, the temperature will be included in the optimisation during the skew normal fit.- control
A list of control parameters for the optimiser.
- verbose
Logical indicating whether to print progress messages.
- debug
Logical indicating whether to return debug information.
- add_priors
Logical indicating whether to include prior densities in the posterior computation.
- optim_method
The optimisation method to use for finding the posterior mode. Options include
"nlminb"(default),"ucminf", and"optim"(BFGS).- numerical_grad
Logical indicating whether to use numerical gradients for the optimisation.
- ...
Additional arguments to be passed to the lavaan::lavaan model fitting function.
Value
An S4 object of class INLAvaan which is a subclass of the
lavaan::lavaan class.
Details
The asem() function is a wrapper for the more general inlavaan()
function, using the following default arguments:
int.ov.free = TRUEint.lv.free = FALSEauto.fix.first = TRUE(unlessstd.lv = TRUE)auto.fix.single = TRUEauto.var = TRUEauto.cov.lv.x = TRUEauto.efa = TRUEauto.th = TRUEauto.delta = TRUEauto.cov.y = TRUE
For further information regarding these arguments, please refer to the
lavaan::lavOptions() documentation.
Examples
# 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 Finding posterior mode.
#> ✔ Finding posterior mode. [94ms]
#>
#> ℹ Computing the Hessian.
#> ✔ Computing the Hessian. [286ms]
#>
#> ℹ Performing VB correction.
#> ✔ VB correction; mean |δ| = 0.043σ. [233ms]
#>
#> ⠙ Fitting skew normal to 0/28 marginals.
#> ⠹ Fitting skew normal to 16/28 marginals.
#> ✔ Fitting skew normal to 28/28 marginals. [1.5s]
#>
#> ℹ Sampling covariances and defined parameters.
#> ✔ Sampling covariances and defined parameters. [204ms]
#>
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
#>
#> 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 0.377 -0.007 1.464 0.003 beta(1,1)
#> .y2 ~~
#> .y4 0.271 0.751 0.259 3.197 0.006 beta(1,1)
#> .y6 0.344 0.772 0.833 3.866 0.010 beta(1,1)
#> .y3 ~~
#> .y7 0.179 0.647 -0.439 2.098 0.005 beta(1,1)
#> .y4 ~~
#> .y8 0.104 0.470 -0.490 1.358 0.003 beta(1,1)
#> .y6 ~~
#> .y8 0.316 0.586 0.325 2.623 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]
#>