I am using a GLM to model a percentage outcome variable. Because the outcome is a percentage, I need to supply the model with weights. There is an argument that the weighting variable also has value as a fixed effect. Is it valid to include the variable as weights and as a fixed effect?
As an example, let's say I have data on the uptake of a blood-pressure test at some health clinics. There is evidence to suggest that bigger clinics are inherently 'better', say because they are more resilient to staff absences. Therefore I would want to know how 'big' the clinic is but I would also want to use this to mark the relative importance of each clinic's observations.
Could this 'interact' in the sense that smaller clinics, who perform less well, will be weighted less than bigger clinics who perform better because of their size?