everything GMM, GLMGMM

[josef-pkt]

Similar to GLMMLE #1788 I think we can get generic GMM for GLM families and links

Score_obs are moment conditions, and we should be able to just plug them into IVGMM, similar to the examples for Poisson.

Essentially, all we are doing is using the estimating equations from the families, similar to GEE but without the GEE covariance modeling, but with instrumental variables under the assumption of some orthogonality conditions.

see #1742 for IVPoisson or GMMPoisson as already worked out special case.

[josef-pkt]

The IV idea might not work in many non-linear models. There is an additive error assumption in there to use standard IV, see Wooldridge "Quasi-maximum likelihood estimation and testing for nonlinear models with endogenous explanatory variables", Journal of Econometrics 2014
or something else I don't remember about endogeneity in Poisson and why it works with multiplicative errors.

another idea: reuse GMM as tool for conditional moment tests exploiting the similarity between score/LM tests and tests of overidentifying restrictions (with parameters estimated under the null)
(main implementation question: how much structure do we want to assume about the covariance matrix of estimation moments and conditional moment restrictions)
see #2041 and #1756

[josef-pkt]

related to last point: GMM sandwiches haven't been updated since I wrote the cov_type for the (Q)MLE models, specifically there is no cluster options.
see GMM.calc_weightmatrix

[josef-pkt]

see also #2096 for conditional moment tests and comment in description.
uses GMM replication of OLS as unit test.

[josef-pkt]

see also #1777 for just the estimating equation approach, IRLS with "foreign" variance function.

This could be done clean with GLMGMM, similar to GEE. (without IV and endogenous explanatory variables) And it would also be easy to extend to non-linear mean function (not just index function for mean), and more complicated data dependent variance functions.

And it should be easy to unit test by comparing to GLM.

[josef-pkt]

bump to 0.8 since it might not be a huge amount of work