2
$\begingroup$

After multiple imputation (imputed dataset = 20), I would like to conduct Bayesian Model Estimation with Adaptive Metropolis Hastings Sampling (amh) -- using the MCMC method.

How can I pool the results together to obtain the following:

  • Parameter Summary (Marginal MAP estimation)
  • parameter MAP SD Q2.5 Q97.5 Rhat SERatio effSize accrate

  • MAP: Univariate marginal MAP estimation
  • mMAP: Multivariate MAP estimation (penalized likelihood estimate)
  • Mean: Mean of posterior distributions

I am wondering if I could extract and combine the estimates of the parameter (e.g., MAP) from each MCMC iteration from each imputed dataset -- giving me 10,000 iterations X 20 dataset = 200,000 estimates. I will then calculate the final/pooled estimates.

$\endgroup$

1 Answer 1

1
$\begingroup$

Combine the samples from all the individual fits to the imputed data and then use the pooled posterior samples as you would a single fit (e.g. to compute expectations, quantiles, ...).

As the number of imputed datasets grows, this would approach something close to the posterior of a model that does the imputation and fitting in a single big model. This is e.g. what the brms package does with its brm_multiple: https://paul-buerkner.github.io/brms/articles/brms_missings.html#imputation-before-model-fitting-1

$\endgroup$
1
  • $\begingroup$ Hi Martin, thank you very much! This is from the LAM::AMH package. Are you able to tell us what do the Rhat SERatio effSize and accrate mean? $\endgroup$
    – conner
    Jun 22, 2023 at 14:03

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.