CVA is derived from ideas and practice regarding ratings-based conjoint analysis dating back to the early 1970s.
Researchers back then had limited ability to deal with interaction terms. The favorite trick was to take two factors (attributes) and combine them into one. For example, two 3-level attributes could become a single 9-level attribute (representing all 9 combinations). However, this increased the number of parameters to estimate. Before combining, the number of terms to estimate was (3-1) + (3-1) = 4. After creating the 9-level interaction, the number of terms is (9-1) = 8. So, this increases the number of questions each respondent needs to answer so that the individual-level OLS regression works.
Today, most Sawtooth Software conjoint researchers use CBC instead of CVA. CBC offers advantages for estimating interaction effects over CVA. Because CBC designs typically involve many more versions (blocks) of the questionnaire across respondents, the experimental designs often support the robust estimation of all potential 2-way interaction effects; not just the one or few interaction effects the researcher plans for ahead of time.
However, it could be said that since CVA software nowadays supports 10 versions of the questionnaire, it could give more opportunity to examine interaction effects via HB estimation. Sawtooth Software could go back and build more sophistication into the CVA software to do this. However, the conjoint world has largely moved away from CVA typically toward CBC, so this would significant effort on our part to add sophisticated features to a fading technique.
Sophisticated Sawtooth Software users can bolster CVA's ability to handle interaction effects by using CVA's capability to field 10 versions of the questionnaire, but then doing their own dummy-coding (for potential interaction effects) to build their own raw data file for estimating the models in our standalone HB-Reg software.