Guidance Needed on Comparing Models with Latent Discrete Variables When Using Marginalized Log-Likelihood

Hello everyone,

I am currently exploring the comparison of models that incorporate latent discrete variables, similar to the approach detailed in this Stan case study: DINA Model with Independent Attributes.

My primary query revolves around the utilization of target += statements within Stan for representing the marginalized log-likelihood. I aim to understand whether these values can be directly employed for computing model comparison indices such as WAIC, LOO, or DIC. I’m especially interested in whether this process is straightforward or requires additional steps.

I would greatly appreciate any insights, experiences, or advice from those who have navigated similar endeavors. Furthermore, if there are any pertinent references or resources that delve into this topic, I would be keen to explore them.

Thank you for your time and assistance!