Be careful about interaction effects discovered in pooled analysis (counts or aggregate logit) for CBC datasets as the increase in fit due to interactions for pooled models will usually not transfer over to HB models.
So, if you are planning on HB estimation for CBC, you should know that we have found that interactions that are statistically significant under aggregate analysis usually tend to go away in HB modeling. (That indicates that the interactions in pooled analysis were mainly due to unrecognized heterogeneity...but HB explains that heterogeneity.) To include them in HB modeling would not only make the HB run longer, but often can lead to overfitting.
A few years ago, we did an investigation with I think around 22 different CBC datasets and found that interaction effects only made a decent improvement in holdout validation for about 4 of the datasets. For this investigation, we used jack-knife sampling to systematically hold out 1 or 2 choice tasks for each respondent, while estimating the HB model with the remaining tasks. Over and over again...
Lately in our trainings, we've advised our users who intend to use HB for their final models to be very cautious about including interaction terms in their HB models. Interactions that seem very significant in aggregate logit or counts usually just don't add much value to HB estimation.
To check your CBC dataset for the value of interactions in HB, we've built the "CBC/HB Model Explorer" which is an add-on to our CBC/HB standalone system. If you are licensed to use our CBC/HB system, then you can install our CBC/HB Model Explorer tool. It does the jack-knife sampling and calls CBC/HB software repeatedly in batch mode. It takes usually about 5 to 10 hours to run to investigate interaction terms for a CBC data set. So, it takes some time commitment
If you are interested, the CBC/HB Model Explorer may be downloaded from the following webpage (scan this page to find it): https://www.sawtoothsoftware.com/support/downloads/tools-scripts