I’m attempting to model varying effects of different loan characteristics on defaults in rstanarm. When my model only has varying intercepts everything runs fine, when I add any predictor to get a varying slope none of my chains start due to underflows “Log probability evaluates to log(0)”. I attempted to initialize the intercept term at its eventual mean (~ -6) but that didn’t solve the problem (and I imagine that wasn’t the problem to begin with since it was working fine in the varying intercepts case). What I find puzzling is that the initialization only breaks down when I add varying slopes. Typically I would think my initializations are off the support of their pdfs, but all of my random slopes should take values on the real line. One fear is with >2200 parameters I am getting underflow issues that can’t be solved.
If someone could enlighten me as to how I can initialize a wider range of slopes for my varying slopes (perhaps widening the uniform from which every parameter is drawn), I would appreciate not having to write my own stan code in this case. I know you can write a function or specify a list, but those options seem difficult/not fruitful when my matrix of varying parameters has over 1000 rows.
My other concern is that since there are over 1000 groups I will not be able to successfully initialize any chains just by randomly initializing.
One other thing is that some of my groups have few observations and my model may barely be identified, while I assume this makes my model less stable I wasn’t sure if it would make my model that much more difficult to initialize.
And lastly my model levels are state:3-digit ZIP:individual.