Rudy Banerjee writes:
I am trying to use the Besag, York & Mollie 1991 (BYM) model to study the sociology of crime and space/time plays a vital role. Since many of the variables and parameters are discrete in nature is it possible to develop a BYM that uses an Integer Auto-regressive (INAR) process instead of just an AR process?
I’ve seen INAR(1) modeling, even a spatial INAR or SINAR paper but they seem to be different that the way BYM is specified in the Bayes framework.
Does it even make sense to have a BYM that is INAR? I can think of discrete jumps in independent variables that affect the dependent variable in discrete jumps. (Also, do these models violate convexity requirements often required for statistical computing?)
1. To see how to fit this sort of model in a flexible way, see this Stan case study, Spatial Models in Stan: Intrinsic Auto-Regressive Models for Areal Data, from Mitzi Morris.
2. Rather than trying to get cute with your discrete modeling, I’d suggest a simple two-level approach, where you use an underlying continuous model (use whatever space-time process you want, BYM or whatever) and then you can have a discrete data model (for example, negative binomial, that is, overdispersed Poisson) on top of that.