I am using lavaan to analyse customer survey data. There are several questions in the survey data, which can be factored into categories (e.g. friendliness, efficiency) etc. There is an overall satisfaction score, so cfa or sem can be used nicely.
My problem lies in constructing a feature table from the responses, given the original survey design. In the survey design, most questions (80%) are answered by ALL participants. However, some questions divide the participants into two distinct groups. For examples, participants are asked a question, such as: "did you purchase experience A?"? If they answer "yes", they are given specific follow up questions such as rate experience A by value, quality etc. If they answered "no", the follow-up questions are different (e.g. "why not"). This creates two distinct groups in the survey (those who answered "yes" to expereince A, and those who did not).
One option is to split the analysis by groupings within lavaan, so I construct a model for those who purchased experience A, and a separate model those who did not. The problem with this approach, is I cannot compare the 80% features corresponding to questions which all participants answered in the one analysis. This means I lose power in the analysis through reduced sample size.
Is it an option to construct factors, whereby factor1 is constructed from experience A-yes, and factor2 from the other respondents. Is there a better way to think about constructing my feature table from which to run the cfa analysis?