I have 100 geographical regions in a country. For each region the total number of houses and the number of vacant houses have been collected yearly over 20 years. I have also some other economic indicators at the country level (GDP, interest rate etc.). Now, given the forecasts for these indicators for next year, I want to forecast next year vacancy rate.
I have first used an auto-regressive mixed-effect model in
R (package lme4) where the vacancy rate (computed as the ratio of vacant houses over the total number of houses) in a region depends on the last year's vacancy rate, the mean vacancy rate of neighboring regions, GDP and interest rate.
The problem with this model is that the vacancy rate can go outside the range [0,1], which obviously does not make sense. I need to restrict the range of the vacancy rate: a simple fix is restricting ex post.
Does anybody have experience with such models? I think that I can use some mixed multinomial logit model probably.
I would appreciate if you could provide guidance along with some