I have a 14 items scales that consist of 4 sub-scales (1st- 3  items, 2nd-4 items, 3rd-3items and 4th- 4 items). Second sub-scale has 4 items with the first item asking Yes/No question. If the respondent  answer "NO" then they are to skip the other 3 questions and proceed to  next item that measures the 3rd sub-scale. Due to this skipping for  those who said No, there are many missing data for that 2nd sub-scale  (only about 13% of the total sample responded to 2nd sub-scale items  with Yes to that Yes/No question and have valid responses. (Note each  sub-scale has scoring mechanism that those who said "No" and misses the  next 3 items will automatically receive 100 on a scale from 0 to 100 for sub-scale score.)

So, I only have about 15% of the entire sample who responded to that yes/no items in results only those provided me response on the latter 3 items.

So, what would be the right way to conduct CFA/SEM with these kind of instrument? I am just not  clear with how to proceed as i've never dealt with this Yes/No questions forcing respondents skip some questions.

Any advice will be greatly appreciated