I'm currently working on a series of Poisson time series models trying to estimate the effect of a change in how the counts were obtained (switching from one diagnostic test to another) while controlling for other trends over time (say a general increase in the incidence of disease). I've got data for a number of different sites.
While I've been tinkering with GAMs as well, I've fit a series of pretty basic GLMs with time trends in them, then pooling the results. The code for this would look something like this in SAS:
PROC GENMOD data=work.data descending;
model counts = dependent_variable time time*time / link=log dist = poisson;
or this in R:
glm(counts ~ dependent_variable + time + time*time, family="poisson")
Then taking those estimates, and pooling them over the various sites. It's also been suggested to be that I try using a Poisson mixed model with a random slope and intercept for each site, rather than pooling. So essentially you'd have the fixed effect of dependent_variable, then a random effect for the intercept and time (or ideally time and time^2 though I understand that gets a bit hairy).
My issue is I have no idea how to fit one of these models, and it seems that mixed models are where everyone's documentation goes suddenly very opaque. Anyone have a simple explanation (or code) on how to fit what I'm looking to fit, and what to look out for?