# How are robust standard errors applied in logistic regression

I have been reading up on robust standard errors and had a few questions regarding how their use in logistic regression.

I have read here that heteroscedasticity is not an issue in logistic regression as there are no residuals. But here I read there are any they are used for the calculation of the sandwich estimator, and here Woolridge outlines that robust standard errors will be useful for omitted variable bias or incorrect function form only as a one term Taylor series expansion is used. I also found this which also used the sandwich estimator, but not WLS, as it appears they do in the second link, and instead use the empirical variance.

Regarding these I had a few questions

1. I don't really know what the robust standard error is based on from this. Is it just the empirical Fisher matrix plugged into the sandwich estimator vs using the Fisher matrix on its own?

2. Is 1 incorrect that heteroscedasticity is a problem, just in logistic regression it doesn't deal with residuals

3. I don't understand Woolridges point on the Taylor series, when is the Taylor series used in MLE, I never learned that they are used together. Is it common to use a Taylor series to approximate the log likelihood, and when it is used, why can't higher order terms be used?

4. Wooldridge states that robust standard errors are robust to misspecification of functional form of the independent variables and omitted variable bias, and, as opposed to the linear case, should be used only when there is strong suspicison of either; this is further supported here, and but with the recommendation of bootstrapping, are there any theoretical difference with the boostrap vs the sandwich estimator?

I feel like I'm got some large gaps in my knowledge here, so any resources such as a textbook/lecture note/lecture video series that cover these topics together would be really appreciated.

Thanks

• A good place to start filling in your knowledge gaps is this entry in Dave Giles' blog. Sep 4 at 17:52
• Thanks for this, I had a read, it still doesn't really say what heteroscedasticity is in that. I read further and found davegiles.blogspot.com/2013/05/…, which defined it in terms of the probit where setting scale=1 may be a misspecification to be resolved with defining a function for scale. I thought this is underdispersion, not heteroscedasticity, and I'm not sure how this translates to the logit, which doesn't have a scale parameter, there is a similar comment on the post which is unanswered. Sep 5 at 12:08

• I don't like statistical tests for model assumptions in most cases because of the distortion of final inferences and the low power for low $N$. Sep 5 at 13:31