Include stated attribute non-attendance in CBC/HB

Dear all,

In my survey I asked respondents to rank attributes of a choice experiment according to the importance covered in their decisional process.
For each attribute, I also asked respondents to report how often they ignored it (in a likert scale where 1="Never ignored" and 4="Always ignored").
Since I wanted to avoid the complete exclusion of some attributes from the estimation, I am now looking for ways to include such stated attribute non-attendance in CBC/HB. I thought about the following options:
1) Including stated attribute ranking and/or info on degree of non-attendance as covariates in the upper-level model;
2) In the lower-level model, finding a way to "shrink" those attributes with lower ranking and/or that have been ignored more often.

Any idea about which approach might be the best and how it could be implemented in CBC/HB?

Thanks in advance.