my question concerns the calculation of interaction effects with CBC-HB.

I ran an HB analysis including an interaction of two attributes (A, 4 level and B, 2 level). The results of all main effects as well the most interaction terms were as expected unless for one interaction term (say A1 and B1/2). Here the results are reversed, meaning that while the utility should be positive for A1-B1 and negative for A1-B2 it is the other way round. For all other levels of A the interaction with B1 is always positive and with B2 always negative.

As A1 is the most unattractive level of the four, is it possible that the respondents did not choose a stimulus with the A1 level frequently enough to calculate an interaction effect? I counted how often the A1 level was actually chosen from a respondent and endet up with 711. Is that a sufficient base to calculate the interaction? Could this explain the reversed utilities? And if not, which other explanations could be possible?

Thanks a lot for your advise!