I want to model a bird population in a country via regression analysis (Poisson regression due to count data). In order to optimize the sampling effort versus precision, I use a stratified random design: The country is splitted into 10 different habitats, and from each habitat I draw several random samples. Now two questions arise:

- Do I just have to use weights according to the area of each habitat, or is it more complicated to properly integrate the design?

- Do I additionally have to use the strata as predictors in regression, as fixed effects or random coefficients?