We recently conducted a conjoint study in several countries. We want to present our results for the total sample and by country. Is it best to use a single analysis and include interactions or dummy terms rather than analyze each country separately? Our understanding is that with HB this isn't possible.
Probably the real answer is "it depends." The real answer is to run different models and see which one does the best (highest fit statistics, lowest error when predicting holdout tasks, etc.) Based on some research we've seen, it is typically better to run one large HB estimation rather than many small ones. This is typically the case until your sample sizes reaches probably in the neighborhood of 700-800. The use of covariates and tweaking HB settings might change these recommendations in the future as more research is done.
Theoretically, if the countries vary a lot it might be possible to run separate estimations (provided you run a design test with your expected analysis sample size) and better model people from each country if they are (1) different from the other countries and (2) quite alike within a country. With the release of CBC/HB v5, it is now possible to include covariates, such as country, during your utility estimation. This is probably the best approach from a theoretical standpoint. You can read about how to use covariates and see if they are doing anything for the model here: Application of Covariates within Sawtooth Software’s CBC/HB Program: Theory and Practical Example (2009). Most methodologies also allow you to use covariates from inside the SSI Web system as well.
Theoretically, covariates would be the best approach if there are big differences between countries. Dummy terms wouldn't work in a design because they would be static within a respondent. Interaction terms are used to build more complex models, such as those that allow for different price sensitivities for each brand.