Fit an Approximate Bayesian Structural Equation Model
Usage
asem(
model,
data,
dp = priors_for(),
test = "standard",
vb_correction = TRUE,
marginal_method = c("skewnorm", "asymgaus", "marggaus", "sampling"),
marginal_correction = c("shortcut", "shortcut_fd", "hessian", "none"),
nsamp = 1000,
samp_copula = TRUE,
sn_fit_ngrid = 21,
sn_fit_logthresh = -6,
sn_fit_temp = 1,
sn_fit_sample = TRUE,
control = list(),
verbose = TRUE,
debug = FALSE,
add_priors = TRUE,
optim_method = c("nlminb", "ucminf", "optim"),
numerical_grad = FALSE,
cores = NULL,
...
)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.- test
Character indicating whether to compute posterior fit indices. Defaults to "standard". Change to "none" to skip these computations.
- vb_correction
Logical indicating whether to apply a variational Bayes correction for the posterior mean vector of estimates. Defaults to
TRUE.- 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).- marginal_correction
Which type of correction to use when fitting the skew-normal or two-piece Gaussian marginals.
"hessian"computes the full"shortcut"(default) computes only diagonals via central differences (full z-trace plus Schur complement correction),"shortcut_fd"is the same formula using forward differences (roughly half the cost, less accurate),"hessian"computes the full Hessian-based correction (slow), and"none"(orFALSE) applies no correction.- nsamp
The number of samples to draw for all sampling-based approaches (including posterior sampling for model fit indices).
- samp_copula
Logical. When
TRUE(default), posterior samples are drawn using the copula method with the fitted marginals (e.g. skew-normal or asymmetric Gaussian), with NORTA correlation adjustment. WhenFALSE, samples are drawn from the Gaussian (Laplace) approximation. Only re- sn_fit_ngrid
Number of grid points to lay out per dimension when fitting the skew-normal marginals. A finer grid gives a better fit at the cost of more joint-log-posterior evaluations. Defaults to
21.- 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. Defaults to
1(weights are the density values themselves). IfNA, the temperature is included as an additional optimisation parameter.- sn_fit_sample
Logical. When
TRUE(default), a parametric skew-normal is fitted to the posterior samples for covariance and defined parameters. WhenFALSE, these are summarised using kernel density estimation instead.- 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. Defaults to
FALSEto use analytical gradients.- cores
Integer or
NULL. Number of cores for parallel marginal fitting. WhenNULL(default), serial execution is used unless the number of free parameters exceeds 120, in which case parallelisation is enabled automatically using all available physical cores. Set to1Lto force serial execution. Ifcores > 1, marginal fits are distributed across cores usingparallel::mclapply()(fork-based; no parallelism on Windows).- ...
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. [93ms]
#>
#> ℹ Computing the Hessian.
#> ✔ Computing the Hessian. [81ms]
#>
#> ℹ Performing VB correction.
#> ✔ VB correction; mean |δ| = 0.158σ. [181ms]
#>
#> ⠙ Fitting 0/28 skew-normal marginals.
#> ✔ Fitting 28/28 skew-normal marginals. [1.2s]
#>
#> ℹ Adjusting copula correlations (NORTA).
#> ✔ Adjusting copula correlations (NORTA). [228ms]
#>
#> ⠙ Posterior sampling and summarising.
#> ✔ Posterior sampling and summarising. [360ms]
#>
summary(fit)
#> INLAvaan 0.2.4.9000 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 -1644.519
#>
#> 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 0.147 1.952 2.530 0.007 normal(0,10)
#> x3 1.840 0.155 1.550 2.157 0.004 normal(0,10)
#> dem60 =~
#> y1 1.000
#> y2 (a) 1.211 0.145 0.944 1.512 0.004 normal(0,10)
#> y3 (b) 1.189 0.122 0.965 1.443 0.005 normal(0,10)
#> y4 (c) 1.276 0.128 1.045 1.548 0.007 normal(0,10)
#> dem65 =~
#> y5 1.000
#> y6 (a) 1.211 0.145 0.944 1.512 0.004 normal(0,10)
#> y7 (b) 1.189 0.122 0.965 1.443 0.005 normal(0,10)
#> y8 (c) 1.276 0.128 1.045 1.548 0.007 normal(0,10)
#>
#> Regressions:
#> Estimate SD 2.5% 97.5% NMAD Prior
#> dem60 ~
#> ind60 1.469 0.391 0.717 2.253 0.002 normal(0,10)
#> dem65 ~
#> ind60 0.587 0.242 0.120 1.068 0.000 normal(0,10)
#> dem60 0.868 0.077 0.722 1.024 0.004 normal(0,10)
#>
#> Covariances:
#> Estimate SD 2.5% 97.5% NMAD Prior
#> .y1 ~~
#> .y5 0.276 0.376 -0.034 1.444 0.003 beta(1,1)
#> .y2 ~~
#> .y4 0.272 0.692 0.145 2.862 0.007 beta(1,1)
#> .y6 0.343 0.727 0.880 3.734 0.012 beta(1,1)
#> .y3 ~~
#> .y7 0.179 0.628 -0.321 2.145 0.006 beta(1,1)
#> .y4 ~~
#> .y8 0.106 0.458 -0.465 1.335 0.004 beta(1,1)
#> .y6 ~~
#> .y8 0.313 0.582 0.293 2.580 0.005 beta(1,1)
#>
#> Variances:
#> Estimate SD 2.5% 97.5% NMAD Prior
#> .x1 0.089 0.021 0.053 0.135 0.006 gamma(1,.5)[sd]
#> .x2 0.130 0.066 0.030 0.278 0.031 gamma(1,.5)[sd]
#> .x3 0.501 0.099 0.338 0.723 0.003 gamma(1,.5)[sd]
#> .y1 2.016 0.495 1.177 3.108 0.010 gamma(1,.5)[sd]
#> .y2 7.902 1.422 5.509 11.065 0.000 gamma(1,.5)[sd]
#> .y3 5.260 1.043 3.539 7.609 0.001 gamma(1,.5)[sd]
#> .y4 3.387 0.782 2.045 5.099 0.007 gamma(1,.5)[sd]
#> .y5 2.487 0.529 1.605 3.670 0.005 gamma(1,.5)[sd]
#> .y6 5.187 0.950 3.584 7.293 0.002 gamma(1,.5)[sd]
#> .y7 3.773 0.794 2.449 5.548 0.006 gamma(1,.5)[sd]
#> .y8 3.440 0.743 2.170 5.073 0.006 gamma(1,.5)[sd]
#> ind60 0.454 0.089 0.308 0.653 0.003 gamma(1,.5)[sd]
#> .dem60 3.941 0.900 2.447 5.959 0.002 gamma(1,.5)[sd]
#> .dem65 0.270 0.193 0.026 0.735 0.044 gamma(1,.5)[sd]
#>