Calculate the log marginal likelihood with bridge sampling (Meng & Wong,
1996). This is a wrapper around bridgesampling::bridge_sampler().
Therefore, log marginal likelihood calculation is currently only available
for models estimated with {rstan} using MCMC.
Arguments
- x
A measrdcm object estimated with
backend = "optim".- ...
Unused.
- force
If the criterion has already been added to the model object with
add_criterion(), should it be recalculated. Default isFALSE.
References
Meng, X.-L., & Wong, W. H. (1996). Simulating ratios of normalizing constants via a simple identity: A theoretical exploration. Statistical Sinica, 6(4), 831-860. https://www.jstor.org/stable/24306045
Examples
model_spec <- dcm_specify(
qmatrix = dcmdata::mdm_qmatrix,
identifier = "item"
)
model <- dcm_estimate(
dcm_spec = model_spec,
data = dcmdata::mdm_data,
identifier = "respondent",
method = "variational",
seed = 63277
)
#> Chain 1: ------------------------------------------------------------
#> Chain 1: EXPERIMENTAL ALGORITHM:
#> Chain 1: This procedure has not been thoroughly tested and may be unstable
#> Chain 1: or buggy. The interface is subject to change.
#> Chain 1: ------------------------------------------------------------
#> Chain 1:
#> Chain 1:
#> Chain 1:
#> Chain 1: Gradient evaluation took 0.000128 seconds
#> Chain 1: 1000 transitions using 10 leapfrog steps per transition would take 1.28 seconds.
#> Chain 1: Adjust your expectations accordingly!
#> Chain 1:
#> Chain 1:
#> Chain 1: Begin eta adaptation.
#> Chain 1: Iteration: 1 / 250 [ 0%] (Adaptation)
#> Chain 1: Iteration: 50 / 250 [ 20%] (Adaptation)
#> Chain 1: Iteration: 100 / 250 [ 40%] (Adaptation)
#> Chain 1: Iteration: 150 / 250 [ 60%] (Adaptation)
#> Chain 1: Iteration: 200 / 250 [ 80%] (Adaptation)
#> Chain 1: Success! Found best value [eta = 1] earlier than expected.
#> Chain 1:
#> Chain 1: Begin stochastic gradient ascent.
#> Chain 1: iter ELBO delta_ELBO_mean delta_ELBO_med notes
#> Chain 1: 100 -359.619 1.000 1.000
#> Chain 1: 200 -356.482 0.504 1.000
#> Chain 1: 300 -357.533 0.337 0.009
#> Chain 1: 400 -356.970 0.253 0.009
#> Chain 1: 500 -356.577 0.203 0.003
#> Chain 1: 600 -356.663 0.169 0.003
#> Chain 1: 700 -356.504 0.145 0.002
#> Chain 1: 800 -356.213 0.127 0.002
#> Chain 1: 900 -356.102 0.113 0.001
#> Chain 1: 1000 -357.671 0.102 0.002
#> Chain 1: 1100 -356.013 0.003 0.002
#> Chain 1: 1200 -356.499 0.002 0.001
#> Chain 1: 1300 -355.419 0.002 0.001
#> Chain 1: 1400 -355.379 0.002 0.001
#> Chain 1: 1500 -356.771 0.002 0.001
#> Chain 1: 1600 -355.933 0.002 0.002
#> Chain 1: 1700 -356.108 0.002 0.002
#> Chain 1: 1800 -356.069 0.002 0.002
#> Chain 1: 1900 -356.345 0.002 0.002
#> Chain 1: 2000 -356.950 0.002 0.002
#> Chain 1: 2100 -356.320 0.002 0.002
#> Chain 1: 2200 -356.238 0.001 0.002
#> Chain 1: 2300 -355.858 0.001 0.001
#> Chain 1: 2400 -355.771 0.001 0.001
#> Chain 1: 2500 -355.857 0.001 0.001 MEAN ELBO CONVERGED MEDIAN ELBO CONVERGED
#> Chain 1:
#> Chain 1: Drawing a sample of size 2000 from the approximate posterior...
#> Chain 1: COMPLETED.
#> Warning: Pareto k diagnostic value is 1.09. Resampling is disabled. Decreasing tol_rel_obj may help if variational algorithm has terminated prematurely. Otherwise consider using sampling instead.
log_mll(model)
#> [1] -349.5096