Inverse logistic regression vs. repeated-measures vs. latent class?

Question

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:

1. 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.
2. 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...)
3. 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.

Answer 1

My first thought would be to regress education (using a proportional odds model or whatever is appropriate for your education variable) on person-level variables and a few simple transportation choice aggregates. The main variable that comes to mind is the proportion of train vs. bus rides (%train), but if you only have two event level variables -- distance and duration -- then another option would be %train-near, %train-far, %train-short, %train-long.

If something simple like the above won't work because you have too many event level variables or you're not willing to categorize them, then your first thought of using a logistic regression with random effects for person-level variables (I presume) is the right idea. However, I would modify your suggestion by using a structural equation model (SEM) to regress education on transportation choice, which is in turn regressed on event and person level variables (except for education) and the random effects. Education can additionally be regressed directly on the event and person level variables. All regressions are estimated simultaneously. This can be done in Mplus, but currently is not possible in R, as far as I know, because none of the SEM packages (lavaan, sem, e.g.) allow for mixed effects like those offered by the lme4 package. It can probably be done in SAS with a lot of coding. No idea about other software.

Is your second thought of regressing education on combinations of your predictors feasible given the number of combinations and amount of data? How many event and person level variables do you have?

Latent class regression wouldn't make sense for your data because individual response patterns aren't comparable (e.g. person 1 might have chosen 00 for near-short, near-short and person 2 might have chosen 0000 for far-long, far-long, far-long, far long -- you could recode response vectors with a lot of missing values, but there are better approaches).