Does the inclusion of a model offset in Poisson or logistic regression convert predictor variables from counts to rates? Or does it only convert response variables from counts to rates?
I understand that offset variables are used in Poisson or logistic regression to account for differences in sampling intensity/exposure at each observation. The inclusion of an offset variable in Poisson or logistic regression allows you to model rates instead of counts. I understand the conversion from count to rate is done by including the units of observation as a predictor variable with a fixed coefficient/slope of 1.
A hypothetical situation:
To model the prevalence of virus_1 in a population of animals, I would build a model like below, where my response variable is the count of animals positive to virus_1 at each observation, and my offset, which converts this count to a rate/prevalence, would be log(total_number_animal_sampled). However, how would I include the prevalence of a second virus as a predictor variable in this model? If I was to include
count_virus_2_positive as a predictor variable would this count also be converted to a rate/prevalence because of the inclusion of the model offset?
Note that the below model also includes predictor variables that are not influenced by sampling intensity/exposure at each observation, for example the abundance of animals at site at each observation.
glmmTMB(count_virus_1_positive ~ offset(log(number_animals_sampled)) + count_virus_2_positive + count_virus_3_positive + site_abundance, data = data, family = binomial)