statsmodels/statsmodels — pull request #1214 by josef-pkt (2013-11-30 01:58:25+00:00)
Title: Compare lr test rebased

rebased and cleaned up version of @bashtage PR #1174

I skipped some redundant commits, and edited the commits during merge conflicts (in almost every commit).

Main change besides cleanup of reverted and unnecessary commits is in default cov_type="nonrobust" especially commit 4d517f5

I'd like to merge this before #1173 and #1176 because I saw one duplicate commit too late to drop it.

Discussion on cov_type="nonrobust"

https://github.com/statsmodels/statsmodels/pull/1189#issuecomment-29487737 and follow-up

I changed "H" for homoscedasticity to "nonrobust", both because I'm not a fan of one letter names (does H mean homo- or heteroscedasticity as in HCx), and because "nonrobust" doesn't imply that we assume homoscedasticity.

To the later point:

- We can estimate a linear model with WLS that uses an estimated heteroscedasticity function (the wresid would be homoscedastic but not the resid **if** the specification is correct). However, we can still use either a robust or a nonrobust covariance matrix after estimating with WLS.
- In Poisson and most other generalized linear models we have an implied heteroscedasticity. "nonrobust" means that the heteroscedasticity of the underlying (Q)MLE model is not assumed to be correctly specified.

Same applies to auto- or cluster correlation.

Plus, Wooldridge talks all the time of using robust or not robust covariance matrices or hypothesis tests.

So far I can think of only "nonrobust" that captures the idea that we are not robust to misspecification of the error covariance matrix. The opposite view would be the model has correctly specified second moments, but I don't know a good short name for that.