I have a survey that has questions grouped within domains. We would like to generate a composite score for each domain. Up to now, we have done a simple average of the question responses within each domain. We would like to change this to a weighted average, where the weights are estimated from a CFA model, and sum to 1 within each domain. We have a focus on simplicity here: we want to make sure that the domain scores can be calculated “by hand”, as the sum of weights x item responses.
Am I correct that question can be answered using CFA? Are there constraints that I need to place on the model in order to fit the above criteria that allow the domain scores to be calculated “by hand”?
Note: the survey questions are all categorical or binary. However, since we are taking a weighted average of the responses (which is a linear combination), it seems necessary to treat them as continuous in order to estimate the weights properly. Do you agree, and does this cause any sort of problem?