I thought Stan developers/users might be interested in a recent paper co-authored with a couple of my students. We used MRP to adjust survey results for a vehicle choice model. The new angle we explored in this work was adjusting for both the human and vehicle populations. We have detailed county-level vehicle registrations (very pricey, so trying to use them as much as possible).
We asked survey respondents about their current vehicle ownership and their expected vehicle ownership (in a choice experiment). The first stage model predicts current vehicle ownership for all vehicles owned by each household, which is used to expand our demographic-only poststratification table. We then use this updated poststratification and adjust it to match the vehicle registration distribution. This poststratification table is then used to adjust results in our vehicle forecast model. To the best of my knowledge, it’s the first application of MRP in transportation. It struck me that vehicle forecasts are fairly similar to voting forecasts and it might be worth a try.
This is a work-in-progress. We certainly welcome feedback. We are also focused on distinguishing preferences between current car and pickup truck owners, which is uncommon in the literature. We find a minimal effect of increasing rebates for pickup trucks relative to small vehicles, as well as minimal effects from faster charge time. Again, these are early results.
Paper link
Thanks for sharing, @jfhawkin. I’m pinging @andrewgelman because he’s collecting MRP use cases and novel applications.
Sorry to say that there has been previous work combining MRP and transportation before this year. Do a Google search for [multilevel regression poststratification transportation]. Among the things you’ll find are:
Two of the authors of the first paper, Jonathan Auerbach and Rob Trangucci (@rtrangucci) worked with Andrew at Columbia (though I don’t know if Andrew was involved in this particular effort).
Cool! The multi-population thing comes up a lot in social surveys. For example, with the Fragile Families Study, we sometimes look at family-level summaries and sometimes at kid-level summaries. Transportation is an interesting example because you have a moving target, ha ha ha. Seriously, though, populations do change over time and this is something we don’t always think about in poststratification. Here’s a dramatic example: Is it really true that “the U.S. death rate in 2020 was the highest above normal since the early 1900s—even surpassing the calamity of the 1918 flu pandemic”? | Statistical Modeling, Causal Inference, and Social Science
Thanks for the feedback. @Bob_Carpenter, yep it looks like there have been applications in transportation.
Reviewing the papers mentioned above in more detail while updating our paper, I don’t think either actually uses MRP. The first references the Gelman and Little paper but uses multi-level regression without poststratification. The second doesn’t reference it. It just has the phrases “multi-level regression” and “poststratification” in it.