See this StackOverflow question, in particular the answer by atiretoo which computes the SE in R. A more detailed description of these standard errors can be found here. This is for a binomial GLM with no constraints, which of course is not the case for our model.
Are the standard errors similar to the estimates we get from bootstrapping?
If so, this reduces the need for bootstrapping.
Is the sampling distribution actually normal on the link scale?
I suspect not, since the parameters are constrained to sum-to-less-than-one on the response scale.
Steps to investigate:
Simulate a bunch of data and manually estimate the sampling distribution.
Do this for a couple different variants - some with a lot of shared mutations (highly multicollinear) and some with only a few.
Calculate the SE from $(X^TWX)^{-1}$ for a single model, compare to manual SE.
Calculate SE from bootstrapping for a single model, compare to manual SE.
This analysis could be a vignette to demonstrate just how important it is to properly specify the variants.
See this StackOverflow question, in particular the answer by
atiretoowhich computes the SE in R. A more detailed description of these standard errors can be found here. This is for a binomial GLM with no constraints, which of course is not the case for our model.Steps to investigate:
This analysis could be a vignette to demonstrate just how important it is to properly specify the variants.