Is there a reason why all the variance weights from a Poisson GLM are equal when a square root link is used? That is (on R):
glm(Y~X1+X2+X3+X4, family=poisson(link=sqrt), data=df)$weights
Always returns equal weights for all observations when a square root link is used; but different weights when the canonical (log) link is used. Does anyone know why?