Is there heteroskedasticity in binomial GLMs?

We know a linear probability model (LPM) will produce heteroskedastic errors by definition because of how the variance of a bernoulli r.v. is defined. My question is whether the same is true for logit/probit. I know that logit/probit can theoretically be amended so that marginal effects are not biased by heteroskedasticity, but does the argument for why heteroskedasticity is certain in an LPM carry through to the nonlinear logit/probit world?

• It's still Bernoulli/binomial. The model for the parameter doesn't change that basic fact about the distribution – Glen_b -Reinstate Monica May 1 '18 at 22:47