Fit Structural Equation Models

Fit a Structural Equation Model (SEM).

Usage

bsem(..., cp = "srs",
     dp = NULL, n.chains = 3, burnin, sample,
     adapt, mcmcfile = FALSE, mcmcextra = list(), inits = "simple",
     convergence = "manual", target = "stan", save.lvs = FALSE,
     wiggle = NULL, wiggle.sd = 0.1, prisamp = FALSE, jags.ic = FALSE,
     seed = NULL, bcontrol = list())

Arguments

...: Default lavaan arguments. See lavaan.
cp: Handling of prior distributions on covariance parameters: possible values are "srs" (default) or "fa". Option "fa" is only available for target="jags".
dp: Default prior distributions on different types of parameters, typically the result of a call to dpriors(). See the dpriors() help file for more information.
n.chains: Number of desired MCMC chains.
burnin: Number of burnin/warmup iterations (not including the adaptive iterations, for target="jags"). Defaults to 4000 or target="jags" and 500 for Stan targets.
sample: The total number of samples to take after burnin. Defaults to 10000 for target="jags" and 1000 for Stan targets.
adapt: For target="jags", the number of adaptive iterations to use at the start of sampling. Defaults to 1000.
mcmcfile: If TRUE, the JAGS/Stan model will be written to file (in the lavExport directory). Can also supply a character string, which serves as the name of the directory to which files will be written.
mcmcextra: A list with potential names syntax (unavailable for target="stan"), monitor, data, and llnsamp. The syntax object is a text string containing extra code to insert in the JAGS/Stan model syntax. The data object is a list of extra data to send to the JAGS/Stan model. If moment_match_k_threshold is specified within data the looic of the model will be calculated using moment matching. The monitor object is a character vector containing extra JAGS/Stan parameters to monitor. The llnsamp object is only relevant to models with ordinal variables, and specifies the number of samples that should be drawn to approximate the model log-likelihood (larger numbers imply higher accuracy and longer time). This log-likelihood is specifically used to compute information criteria.
inits: If it is a character string, the options are currently "simple" (default), "Mplus", "prior", or "jags". In the first two cases, parameter values are set as though they will be estimated via ML (see lavaan). The starting parameter value for each chain is then perturbed from the original values through the addition of random uniform noise. If "prior" is used, the starting parameter values are obtained based on the prior distributions (while also trying to ensure that the starting values will not crash the model estimation). If "jags", no starting values are specified and JAGS will choose values on its own (and this will probably crash Stan targets). You can also supply a list of starting values for each chain, where the list format can be obtained from, e.g., blavInspect(fit, "inits"). Finally, you can specify starting values in a similar way to lavaan, using the lavaan start argument (see the lavaan documentation for all the options there). In this case, you should also set inits="simple", and be aware that the same starting values will be used for each chain.
convergence: Useful only for target="jags". If "auto", parameters are sampled until convergence is achieved (via autorun.jags()). In this case, the arguments burnin and sample are passed to autorun.jags() as startburnin and startsample, respectively. Otherwise, parameters are sampled as specified by the user (or by the run.jags defaults).
target: Desired MCMC sampling, with "stan" (pre-compiled marginal approach) as default. Also available is "vb", which calls the rstan function vb(). Other options include "jags", "stancond", and "stanclassic", which sample latent variables and provide some greater functionality (because syntax is written "on the fly"). But they are slower and less efficient.
save.lvs: Should sampled latent variables (factor scores) be saved? Logical; defaults to FALSE
wiggle: Labels of equality-constrained parameters that should be "approximately" equal. Can also be "intercepts", "loadings", "regressions", "means".
wiggle.sd: The prior sd (of normal distribution) to be used in approximate equality constraints. Can be one value, or (for target="stan") a numeric vector of values that is the same length as wiggle.
prisamp: Should samples be drawn from the prior, instead of the posterior (target="stan" only)? Logical; defaults to FALSE
jags.ic: Should DIC be computed the JAGS way, in addition to the BUGS way? Logical; defaults to FALSE
seed: A vector of length n.chains (for target "jags") or an integer (for target "stan") containing random seeds for the MCMC run. If NULL, seeds will be chosen randomly.
bcontrol: A list containing additional parameters passed to run.jags (or autorun.jags) or stan. See the manpage of those functions for an overview of the additional parameters that can be set.

Details

The bsem function is a wrapper for the more general blavaan function, using the following default lavaan arguments: int.ov.free = TRUE, int.lv.free = FALSE, auto.fix.first = TRUE (unless std.lv = TRUE), auto.fix.single = TRUE, auto.var = TRUE, auto.cov.lv.x = TRUE, auto.th = TRUE, auto.delta = TRUE, and auto.cov.y = TRUE.

Value

An object of class lavaan, for which several methods are available, including a summary method.

References

Edgar C. Merkle, Ellen Fitzsimmons, James Uanhoro, & Ben Goodrich (2021). Efficient Bayesian Structural Equation Modeling in Stan. Journal of Statistical Software, 100(6), 1-22. URL http://www.jstatsoft.org/v100/i06/.

Edgar C. Merkle & Yves Rosseel (2018). blavaan: Bayesian Structural Equation Models via Parameter Expansion. Journal of Statistical Software, 85(4), 1-30. URL http://www.jstatsoft.org/v85/i04/.

Yves Rosseel (2012). lavaan: An R Package for Structural Equation Modeling. Journal of Statistical Software, 48(2), 1-36. URL http://www.jstatsoft.org/v48/i02/.

Examples

# The industrialization and Political Democracy Example
# Bollen (1989), page 332
data(PoliticalDemocracy, package = "lavaan")

model <- '
  # latent variable definitions
     ind60 =~ x1 + x2 + x3
     dem60 =~ y1 + a*y2 + b*y3 + c*y4
     dem65 =~ y5 + a*y6 + b*y7 + c*y8

  # regressions
    dem60 ~ ind60
    dem65 ~ ind60 + dem60

  # residual correlations
    y1 ~~ y5
    y2 ~~ y4 + y6
    y3 ~~ y7
    y4 ~~ y8
    y6 ~~ y8
'

if (FALSE) { # \dontrun{
# mildly informative priors for mv intercepts and loadings
fit <- bsem(model, data = PoliticalDemocracy,
            dp = dpriors(nu = "normal(5,10)", lambda = "normal(1,.5)"))
summary(fit)
} # }

# A short run for rough results
fit <- bsem(model, data = PoliticalDemocracy, burnin = 100, sample = 100,
            dp = dpriors(nu = "normal(5,10)", lambda = "normal(1,.5)"),
            n.chains = 2)
#> 
#> SAMPLING FOR MODEL 'stanmarg' NOW (CHAIN 1).
#> Chain 1: 
#> Chain 1: Gradient evaluation took 0.000315 seconds
#> Chain 1: 1000 transitions using 10 leapfrog steps per transition would take 3.15 seconds.
#> Chain 1: Adjust your expectations accordingly!
#> Chain 1: 
#> Chain 1: 
#> Chain 1: WARNING: There aren't enough warmup iterations to fit the
#> Chain 1:          three stages of adaptation as currently configured.
#> Chain 1:          Reducing each adaptation stage to 15%/75%/10% of
#> Chain 1:          the given number of warmup iterations:
#> Chain 1:            init_buffer = 15
#> Chain 1:            adapt_window = 75
#> Chain 1:            term_buffer = 10
#> Chain 1: 
#> Chain 1: Iteration:   1 / 200 [  0%]  (Warmup)
#> Chain 1: Iteration:  20 / 200 [ 10%]  (Warmup)
#> Chain 1: Iteration:  40 / 200 [ 20%]  (Warmup)
#> Chain 1: Iteration:  60 / 200 [ 30%]  (Warmup)
#> Chain 1: Iteration:  80 / 200 [ 40%]  (Warmup)
#> Chain 1: Iteration: 100 / 200 [ 50%]  (Warmup)
#> Chain 1: Iteration: 101 / 200 [ 50%]  (Sampling)
#> Chain 1: Iteration: 120 / 200 [ 60%]  (Sampling)
#> Chain 1: Iteration: 140 / 200 [ 70%]  (Sampling)
#> Chain 1: Iteration: 160 / 200 [ 80%]  (Sampling)
#> Chain 1: Iteration: 180 / 200 [ 90%]  (Sampling)
#> Chain 1: Iteration: 200 / 200 [100%]  (Sampling)
#> Chain 1: 
#> Chain 1:  Elapsed Time: 0.866 seconds (Warm-up)
#> Chain 1:                0.629 seconds (Sampling)
#> Chain 1:                1.495 seconds (Total)
#> Chain 1: 
#> 
#> SAMPLING FOR MODEL 'stanmarg' NOW (CHAIN 2).
#> Chain 2: 
#> Chain 2: Gradient evaluation took 0.000278 seconds
#> Chain 2: 1000 transitions using 10 leapfrog steps per transition would take 2.78 seconds.
#> Chain 2: Adjust your expectations accordingly!
#> Chain 2: 
#> Chain 2: 
#> Chain 2: WARNING: There aren't enough warmup iterations to fit the
#> Chain 2:          three stages of adaptation as currently configured.
#> Chain 2:          Reducing each adaptation stage to 15%/75%/10% of
#> Chain 2:          the given number of warmup iterations:
#> Chain 2:            init_buffer = 15
#> Chain 2:            adapt_window = 75
#> Chain 2:            term_buffer = 10
#> Chain 2: 
#> Chain 2: Iteration:   1 / 200 [  0%]  (Warmup)
#> Chain 2: Iteration:  20 / 200 [ 10%]  (Warmup)
#> Chain 2: Iteration:  40 / 200 [ 20%]  (Warmup)
#> Chain 2: Iteration:  60 / 200 [ 30%]  (Warmup)
#> Chain 2: Iteration:  80 / 200 [ 40%]  (Warmup)
#> Chain 2: Iteration: 100 / 200 [ 50%]  (Warmup)
#> Chain 2: Iteration: 101 / 200 [ 50%]  (Sampling)
#> Chain 2: Iteration: 120 / 200 [ 60%]  (Sampling)
#> Chain 2: Iteration: 140 / 200 [ 70%]  (Sampling)
#> Chain 2: Iteration: 160 / 200 [ 80%]  (Sampling)
#> Chain 2: Iteration: 180 / 200 [ 90%]  (Sampling)
#> Chain 2: Iteration: 200 / 200 [100%]  (Sampling)
#> Chain 2: 
#> Chain 2:  Elapsed Time: 0.714 seconds (Warm-up)
#> Chain 2:                0.667 seconds (Sampling)
#> Chain 2:                1.381 seconds (Total)
#> Chain 2: 
#> Warning: The largest R-hat is 1.05, indicating chains have not mixed.
#> Running the chains for more iterations may help. See
#> https://mc-stan.org/misc/warnings.html#r-hat
#> Warning: Bulk Effective Samples Size (ESS) is too low, indicating posterior means and medians may be unreliable.
#> Running the chains for more iterations may help. See
#> https://mc-stan.org/misc/warnings.html#bulk-ess
#> Warning: Tail Effective Samples Size (ESS) is too low, indicating posterior variances and tail quantiles may be unreliable.
#> Running the chains for more iterations may help. See
#> https://mc-stan.org/misc/warnings.html#tail-ess
#> Computing post-estimation metrics (including lvs if requested)...
#> Warning: blavaan WARNING: As specified, the theta covariance matrix is neither diagonal nor unrestricted, so the actual prior might differ from the stated prior. See
#>  https://arxiv.org/abs/2301.08667
summary(fit)
#> blavaan 0.5.6.1316 ended normally after 100 iterations
#> 
#>   Estimator                                      BAYES
#>   Optimization method                             MCMC
#>   Number of model parameters                        31
#>   Number of equality constraints                     3
#> 
#>   Number of observations                            75
#> 
#>   Statistic                                 MargLogLik         PPP
#>   Value                                             NA       0.520
#> 
#> Parameter Estimates:
#> 
#> 
#> Latent Variables:
#>                    Estimate  Post.SD pi.lower pi.upper     Rhat    Prior       
#>   ind60 =~                                                                     
#>     x1                1.000                                                    
#>     x2                2.102    0.134    1.859    2.357    0.996    normal(1,.5)
#>     x3                1.724    0.157    1.447    2.054    0.999    normal(1,.5)
#>   dem60 =~                                                                     
#>     y1                1.000                                                    
#>     y2         (a)    1.172    0.132    0.943    1.437    1.010    normal(1,.5)
#>     y3         (b)    1.172    0.117    0.946    1.406    1.007    normal(1,.5)
#>     y4         (c)    1.250    0.119    1.011    1.512    1.037    normal(1,.5)
#>   dem65 =~                                                                     
#>     y5                1.000                                                    
#>     y6         (a)    1.172    0.132    0.943    1.437    1.010                
#>     y7         (b)    1.172    0.117    0.946    1.406    1.007                
#>     y8         (c)    1.250    0.119    1.011    1.512    1.037                
#> 
#> Regressions:
#>                    Estimate  Post.SD pi.lower pi.upper     Rhat    Prior       
#>   dem60 ~                                                                      
#>     ind60             1.406    0.416    0.653    2.260    0.994    normal(0,10)
#>   dem65 ~                                                                      
#>     ind60             0.545    0.269    0.045    1.061    0.997    normal(0,10)
#>     dem60             0.874    0.081    0.739    1.042    0.993    normal(0,10)
#> 
#> Covariances:
#>                    Estimate  Post.SD pi.lower pi.upper     Rhat    Prior       
#>  .y1 ~~                                                                        
#>    .y5                0.597    0.368   -0.029    1.424    1.001       beta(1,1)
#>  .y2 ~~                                                                        
#>    .y4                1.450    0.711    0.244    3.072    1.027       beta(1,1)
#>    .y6                2.272    0.789    0.974    3.822    0.996       beta(1,1)
#>  .y3 ~~                                                                        
#>    .y7                0.856    0.698   -0.349    2.230    0.992       beta(1,1)
#>  .y4 ~~                                                                        
#>    .y8                0.426    0.488   -0.446    1.472    1.004       beta(1,1)
#>  .y6 ~~                                                                        
#>    .y8                1.374    0.723    0.074    3.018    0.992       beta(1,1)
#> 
#> Variances:
#>                    Estimate  Post.SD pi.lower pi.upper     Rhat    Prior       
#>    .x1                0.084    0.022    0.048    0.125    1.019 gamma(1,.5)[sd]
#>    .x2                0.144    0.072    0.023    0.310    1.010 gamma(1,.5)[sd]
#>    .x3                0.498    0.093    0.334    0.706    0.993 gamma(1,.5)[sd]
#>    .y1                1.992    0.515    1.240    3.288    1.011 gamma(1,.5)[sd]
#>    .y2                7.941    1.451    5.490   10.723    0.996 gamma(1,.5)[sd]
#>    .y3                5.190    1.098    3.446    7.739    1.000 gamma(1,.5)[sd]
#>    .y4                3.469    0.867    1.984    5.343    1.018 gamma(1,.5)[sd]
#>    .y5                2.419    0.573    1.578    3.662    0.993 gamma(1,.5)[sd]
#>    .y6                5.175    1.009    3.463    7.460    1.002 gamma(1,.5)[sd]
#>    .y7                3.750    0.767    2.154    5.378    1.007 gamma(1,.5)[sd]
#>    .y8                3.577    0.863    2.079    5.364    0.999 gamma(1,.5)[sd]
#>     ind60             0.490    0.100    0.326    0.702    0.996 gamma(1,.5)[sd]
#>    .dem60             3.971    0.919    2.452    5.931    1.001 gamma(1,.5)[sd]
#>    .dem65             0.255    0.228    0.008    0.827    1.013 gamma(1,.5)[sd]
#>