As the title suggests, I'm pretty well befuddled about which approach makes the most sense for my data. Let me try to succinctly explain the problem.
I have binary choice data representing whether a specific person for a specific event took the train or bus. I have event level predictors (location of event, duration of event) as well as person-level predictors (income level, education level). There are multiple, but unbalanced, events per person.
Here's the slightly unusual part: I have a bunch of historic info with all predictor values as well as observed choice. I want to build a regression model from that I can then apply to new data (consisting of everything except education level) to infer with as much confidence as possible that person's education, based on their observed choices.
My thoughts on how to do this:
- Build a mixed-effect, multilevel logistic regression model, with transportation choice as my dependent variable, and education_level as one of the predictors. Now solve for education_level using something like inverse logistic regression.
- Do a regression on counts. Now, education is the dependent variable, and we sum up counts of each subset of predictor variables we've seen (eg, there were 5 nearby events where rich males took the bus, 3 faraway events where...)
- Some kind of latent class model?
What are the tradeoffs between these alternatives? Also, are there still other approaches worth examining (eg, CFA)?
(And please let me know if I need to provide more detail on the problem.)
Thank you for your time, Ian.